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Call number: | 9783319444314:ONLINE Show nearby items on shelf |
Title: | Interferometry and Synthesis in Radio Astronomy |
Author(s): |
A. Richard Thompson |
Date: | 2017 |
Edition: | 3rd ed. 2017 |
Size: | 1 online resource (XLVI, 872 p. 252 illus., 10 illus. in color p.) |
Contents: | Preface -- Introduction and Historical Review -- Introductory Theory of Interferometry and Synthesis Imaging -- Analysis of the Interferometer Response -- Geometric Relationships and Polarimetry -- Antennas and Arrays -- Response of |
the Receiving System -- Design of the Analog Receiving System -- Digital Signal Processing -- Very-Long-Baseline Interferometry -- Calibration and Fourier Transformation of Visibility Data -- Deconvolution, Adaptive Calibration and | |
Applications -- Interferometer Techniques for Astrometry and Geodesy -- Propagation Effects -- Van Cittert-Zernike Theorem, Spatial Coherence and Scattering -- Radio Interference -- Related Techniques -- Principal Symbols -- Index | |
ISBN: | 9783319444314 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Physics , Observations, Astronomical , Astronomy , Physics , Astronomy, Observations and Techniques , Applied and Technical Physics |
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Call number: | 9781608077779:ONLINE Show nearby items on shelf |
Title: | Terahertz metrology |
Author(s): |
Mira Naftaly |
Date: | 2015 |
Publisher: | Artech House |
Size: | 1 online resource (386 p.) |
Contents: | Chapter 1 Terahertz Time-Domain Spectrometers -- Photoconductive Emitters and Detectors -- Optical Rectification -- Electro-Optic Detection -- Terahertz Air-Based Coherent Detection -- Cherenkov (Tilted Wavefront) Emitters and Detectors -- Continuou s-Wave Terahertz Time-Domain Spectrometer and Microwave Photonics -- Types of Continuous-Wave Terahertz Emitters and Detectors -- Time-Domain Spectrometer Configurations -- Transmission -- Reflection -- Attenuated Total Reflection -- Asynchronous Optical Sampling -- Substrate Lenses -- Commercial Systems -- Parameter Extraction in Time-Domain . Chapter 2 Spectrometers -- Material Properties and Wave Propagation -- Complex Refractive Index and Complex Permittivity -- Plane Wave Propagation Across an Interf ace.Fresnel Equations -- Plane Wave Propagation Through a Dielectric Slab -- Fabry-Perot Effect -- Extracting Optical Parameters from Terahertz Time-Domain Spectrometers Data -- Transmission-mode Terahertz Time-Domain Spectrometers: Approximation -- Trans mission-Mode Terahertz Time-Domain Spectrometers: Exact Solution -- Reflection-Mode Terahertz Time-Domain Spectrometers: Single Reflection -- Reflection-Mode Terahertz Time-Domain Spectrometers: Double Reflection -- Attenuated Total Reflection -- Preproce ssing and Postprocessing of Data -- Signal Averaging in the Time and Frequency Domains -- Signal Denoising -- Phase Unwrapping -- Sample Requirements -- Sample Thickness -- Lateral Dimensions of Samples -- Loss: Absorption, Scattering, Diffraction |
Chapter 3 Metrology for Time-Domain Spectrometers -- Performance Parameters: Sensitivity, Resolution, Precision, Accuracy, Dynamic Range, and Signal-to-Noise Ratio -- Dynamic Range and Signal-to-Noise Ratio of Terahertz Time-Domain Spectrometers -- System Performance Limits Due to Dynamic Range and Signal-to-Noise Ratio -- Frequency Resolution -- Measurement Bandwidth -- Sources of Random Noise -- Amplitude -- Phase -- Systematic Errors -- Alignment Errors -- Focal Plane Defocusing -- Delay Line Err ors -- Terahertz Beam Profile -- Chapter 4 Evaluation of Uncertainty in Time-Domain Spectroscopy -- Method of Uncertainty Evaluation -- Evaluation of Random and Systematic Errors -- Propagation and Combination of Measurement Uncertainty -- Measurement wit h Resolution Limit -- Sources of Uncertainty in Terahertz Time-Domain Spectroscopy -- Random and Systematic Errors in Amplitude -- Random and Systematic Errors in Sample Thickness -- Random and Systematic Errors in Sample Alignment -- Systematic Error in the Approximated Transfer Function -- Systematic Error Due to Reflections -- Systematic Error in Physical Constants -- Uncertainty in Optical Constants: A Combination of Variances | |
Chapter 5 Metrology for Fourier Transform Spectrometers -- Spectrometer Configurations -- Michelson -- Mach-Zender -- Polarized Fourier Transform Spectrometer (Martin-Pupplett Interferometer) -- Modes of Operation: Step and Integrate or Fast Scannin g -- Moving Stage -- General Fourier Transform Spectrometer Advantages -- Fourier Transform Spectrometer Metrology -- Encoders, Synchronizing, and Time-Stamping -- Instrument Line Function: A Spectral Resolution Limitation -- Apodization -- Cosine and Sin e Terms and Phase Correction Techniques -- Achievable Spectral Resolution -- Sample Measurement Parameter Recovery -- Thin Sample Approximation: Lossless Case -- Dispersive Medium -- Thick Sample Analysis (or Noncollimated Measurement) -- Absorption Coeff icients -- Sources of Noise and Uncertainties -- Time-Domain Errors -- (Software) Noise Reduction Techniques -- Chapter 6 Terahertz Spectrometer Calibration -- Why Calibrate Terahertz Spectrometers -- Frequency Calibration -- Gases -- Solids -- Resonant M esh Filters -- Etalons -- Summary of Frequency Calibration Standards -- Amplitude Linearity Calibration -- Reflection Standards | |
Chapter 7 Terahertz Imaging -- Image Resolution of a Terahertz Imaging System -- Data Analysis in the Far Field -- Imaging Thin Layers -- Spatial Resolution Tests -- Near-Field Imaging -- Chemical Imaging -- Focal Plane Array Microbolometer Cameras -- Chapter 8 Metrology for Vector Network Analyzers -- Vector Network Analyzers -- The Role of a Network Analyzer -- Scattering Parameters -- Vector Network Analyzer Systems -- Extender Heads -- Good Practice Tips -- Metallic Waveguides -- Basic Properti es -- Dispersion -- Standardized Sizes and Frequency Ranges -- Flanges/Interfaces -- Good Practice Tips -- Calibration Standards and Methods -- Calibration: General Principles -- Types of Calibration Standard -- One-Port Calibration Methods -- Two-Port Ca libration Methods -- Connection Repeatability -- System Verification -- Chapter 9 Terahertz Optics -- Terahertz Optical Materials -- Transparency at Terahertz Frequencies -- Inorganic Crystals for Terahertz Optics -- Polymers for Terahertz Optics -- Metal Reflectivities -- Gaussian Optics -- Gaussian Beams -- Parabolic Mirrors -- Dichroic Optical Elements -- Terahertz Transparent/Visible Opaque -- Terahertz Opaque/Visible Transparent -- Terahertz Reflective/Visible Transparent -- Terahertz Transparent/Vis ible Reflective -- Wire-Grid Polarizers -- Antireflection Coatings -- Photonic Crystal Fibers and Terahertz . Waveguides | |
Chapter 10 Terahertz Laser Sources -- Optically Pumped Gas Lasers -- P-Germanium Laser -- Quantum Cascade Lasers -- Pulsed Difference Frequency Generation -- High-Resolution Frequency Measurements Using Continuous-Wave Difference Frequency Generatio n -- Optical Parametric Oscillators -- Free Electron Lasers -- Chapter 11 Electronic Sources of Terahertz Radiation and Terahertz Detectors -- Electronic Sources of Terahertz Radiation: Introduction and Terminology -- Vacuum Electronic Sources -- Backward Wave Oscillators -- Extended Interaction Klystrons -- Solid-State Devices -- Gunn Diodes and IMPATT Oscillators and Amplifiers -- Transistor Amplifiers -- Frequency Multiplied Sources -- Source Characteristics Summary -- Detectors of Terahertz Radiation: Introduction and Terminology . Incoherent Detectors -- Golay Cell -- Pyroelectric Detectors -- Room-Temperature Bolometers -- Cryogenic Bolometers -- Photoconductive Detectors -- Semiconductor Diode Rectifiers -- Thermopiles -- Incoherent Detector Summar y -- Coherent Detectors: Introduction -- Schottky Diode Mixers -- Frequency Measurement | |
ISBN: | 9781608077762 |
Series: | eBooks |
Series: | Artech ebooks |
Keywords: | Terahertz spectroscopy. , Metrology. , Terahertz technology. |
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Call number: | 9781608075355:ONLINE Show nearby items on shelf |
Title: | Microstrip lines and slotlines |
Author(s): |
Ramesh Garg I. J. Bahl Maurizio Bozzi |
Date: | 2013 |
Edition: | Third edition. |
Publisher: | Artech House |
Size: | 1 online resource (589 p.) |
Contents: | Chapter 1 Microstrip Lines I - Quasi-Static Analyses, Dispersion Models, and Measurements -- Planar Transmission Structures -- Microstrip Field Configuration -- Methods of Microstrip Analysis Quasi-Static Analyses of a Microstrip -- Modified Conformal Transformation Method -- Finite Difference Method -- Integral Equation Meth od -- Variational Method in the Fourier Transform Domain -- Segmentation and Boundary Element Method -- Microstrip Dispersion Models -- Coupled TEM Mode and TM Mode Model -- An Empirical Relation -- Dielectric-Loaded Ridged Waveguide Model -- Empirical F ormulae for Broad Frequency Range -- Planar Waveguide Model -- Microstrip Transitions -- Coaxial-to-Microstrip Transition -- Waveguide-to-Microstrip Transition -- Microstrip Measurements -- Substrate Dielectric Constant -- Characteristic Impendance -- Pha se Velocity or Effective Dielectric Constant -- Attenuation Constant -- Fabrication -- Printed Circuit Technologies -- Hybrid Microwave Integrated Circuits -- Monolithic Integrated Circuit Technologies |
Chapter 2 Microstrip Lines II -- Fullwave Analyses, Design Considerations, and Applications -- Methods of Fullwave Analysis -- Analysis of an Open Microstrip -- Integral Equation Method in the Space Domain -- Galerkin.s Method in the Spectral Domain -- Analysis of an Enclosed Microstrip -- Integral Equation Methods -- Finite Difference Method -- Design Considerations -- Microstrip Losses -- Power Handling Capability -- Effect of Tolerances -- Effect of Dielectric Anisotropy -- Frequency Range of Ope ration -- Lumped Element Model of Microstrip Interconnect -- Other Types of Microstrip Lines -- Suspended and Inverted Microstrip Lines -- Multilayered Dielectric Microstrip -- Thin Film Microstrip -- Valley Microstrip Lines -- Buried Microstrip Line -- S uperconducting Microstrip Circuits -- Microstrip Applications -- Lumped Elements -- Passive Components -- Active Components -- Packages and Assemblies | |
Chapter 3 Microstrip Discontinuities I -- Quasi-Static Analysis and Characterization -- Discontinui ty Capacitance Evaluation -- Matrix Inversion Method -- Variational Method -- Galerkins Method in the Fourier Transform Domain -- Use of Line Sources with Charge Reversal -- Discontinuity Inductance Evaluation -- Characterization of Various Discontinuitie s -- Open Ends -- Gaps in a Microstrip -- T-Junctions -- Cross Junctions -- RF Short and Via Hole -- Compensated Microstrip Discontinuities | |
Chapter 4 Microstrip Discontinuities II: Fullwave Analysis and Measurements -- Planar Waveguide Analysis -- Discontinuity Characterization -- Compensation of Discontinuity Reactances -- Radiation and Parasitic Coupling -- Fullwave Analysis of Discon tinuities . Galerkins Method in the Spectral Domain -- Integral Equation Solution in the Space Domain -- Time Domain Methods for Microstrip Discontinuity -- Discontinuity Measurements -- Linear Resonator Method -- Ring Resonator Method -- Scattering Param eters Measurement Method | |
Chapter 5 Slotlines -- Slotline Analysis -- Approximate Analysis -- Transverse Resonance Method . Galerkins Method in the Spectral Domain -- Design Considerations -- Closed-Form Expressions -- Effect of Metal Thickness -- Effec t of Tolerances -- Losses in Slotline -- Slotline Discontinuities -- Short End Discontinuty -- Open End Discontinuity -- Variants of Slotline -- Coupled Microstrip-Slotline -- Conductor-Backed Slotline -- Conductor-Backed Slotline with Superstrate -- Slot lines with Double-Layered Dielectric -- Slotline Transitions -- Coaxial-to-Slotline Transition -- Microstrip-to-Slotline Cross-Junction Transition -- Slotline Applications -- Circuits Using T-Junctions -- Circuits Using Wideband 180° Phase Shift -- Hybrid /de Ronde.s Branchline Couplers | |
Chapter 6 Defected Ground Structure (DGS) -- Basic Structure of DGS -- Unit Cell and Periodic DGS -- Advantages and Disadvantages of DGS -- DGS Characteristics -- Stop-Band Properties -- Slow-Wave Propagation -- Realization of Transmission Lines wit h High Characteristic Impedance -- Modeling of DGS -- Full-Wave Modeling -- Equivalent Circuit Models -- Applications of DGS -- DGS-Based Filters -- Other DGS-Based Passive Components -- DGS-Based Active Circuits -- DGS-Based Antennas | |
Chapter 7 Coplan ar Lines: Coplanar Waveguide and Coplanar Strips -- Quasi-Static Conformal Mapping Analysis of CPW -- Quasi-Static Conformal Mapping Analysis of CPS -- Fullwave Analysis -- Design Considerations -- Design Equations -- Dispersion -- Effect of Metallization Thickness -- Losses in Coplanar Lines -- Dielectric Loss -- Conductor Loss -- Radiation and Surface Wave Losses -- Effect of Tolerances -- Comparison with Microstrip Line and Slotline -- Transitions -- Coax-to-CPW Transitions -- Microstrip-to-CPS Transit ions -- Microstrip-to-CPW Transition -- CPW-to-CPS Transitions -- CPS-to-Slotline Transitions -- Slotline-to-CPW Transitions -- Discontinuities in Coplanar Lines -- CAD Models for Discontinuities in Coplanar Waveguide Circuits -- CAD Models for Discontinu ities in Coplanar Strips Circuits -- Coplanar Line Circuits -- Circuits with Series and Shunt Reactances in CPW -- Circuits Using Slotline-CPW Junctions | |
Chapter 8 Coupled Microstrip Lines -- General Analysis of Coupled Lines -- Methods of Analysis -- Coupled Mode Approach -- Even- and Odd-Mode Approach -- Characteristics of Coupled Microstrip Lines -- Quasi-Static Analysis -- Fullwave Analysis -- Di spersion Models -- Measurements on Coupled Microstrip Lines -- Impedance Measurements -- Phase Constant Measurements -- Design Considerations for Coupled Microstrip Lines -- Design Equations -- Effect of Fabrication Tolerances -- Coupled Microstrip Lines with Dielectric Overlays -- Effect of Dielectric Anisotropy -- Slot-Coupled Microstrip Lines -- Coupled Multiconductor Microstrip Lines -- Discontinuities in Coupled Microstrip Lines -- Network Model -- Open-End Discontinuity | |
Chapter 9 Substrate Integrated Waveguide (SIW) -- Operation Principle -- Analysis Techniques of SIW . Equivalent Rectangular Waveguide -- Full-wave Modeling of SIW Interconnects -- Full-wave Modeling of SIW Components -- Equivalent Circuits Models o f SIW Discontinuities -- Design Considerations -- Mechanisms of Loss -- Guided.wave and Leaky-wave Regions of Operation -- Band-gap Effects in SIW Structures -- SIW Design Rules -- Substrate Integrated Folded Waveguide (SIFW) -- Half-Mode Substrate Integr ated Waveguide (HMSIW) -- Substrate Integrated Slab Waveguide (SISW) -- Substrate Integrated Ridge Waveguide (SIRW) -- Transitions Between SIW and Planar Transmission Lines -- Microstrip-to-SIW Transitions -- CPW-to-SIW Transitions -- SIW Components and A ntennas -- Passive Components -- Active Circuits -- Antennas -- System-on-Substrate (SoS) -- Fabrication Technologies and Materials -- Fabrication by PCB and LTCC Technologies -- Integration of SIW on Silicon -- Use of Novel Substrate Materials -- Solutio ns for High Frequency Operation of SIW | |
ISBN: | 9781608075355 |
Series: | eBooks |
Series: | Artech eBooks |
Keywords: | Strip transmission lines. , Microwave transmission lines. , Microwave integrated circuits. |
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Call number: | 9780750672917:ONLINE Show nearby items on shelf |
Title: | Reference data for engineers: radio, electronics, computer, and communications. |
Author(s): |
M. E. Van Valkenburg (ed.) Wendy Middleton (ed.) |
Date: | 2002 |
Edition: | 9th ed. |
Publisher: | ScienceDirect |
Size: | 1 online resource |
Contents: | Radio frequency spectrum management and time frequency standards -- International telephony recommendations -- Units, constants, and conversion factors -- Properties of materials -- Components or parts -- Fundamentals of networks -- Fourier waveform analysis -- Filters, simple bandpass design -- Filters, modern-network-theory design -- Active filter design -- Attenuators -- Measurements and analysis -- Magnetic-core transformers and reactors -- Power electronics -- rectifiers, filters, and power sup plies -- Feedback control systems -- Electron tubes -- Power grid-tube circuits -- Semiconductors and transistors -- Transistor circuits -- Integrated circuits -- Optoelectronics -- Optical communications -- Analog communications -- Digital communications -- Information theory and coding -- Computer communications networks -- Satellite and space communications -- Discrete-time signal processing -- Transmission lines -- Waveguides and resonators -- Scattering matrices -- Antennas -- Electromagnetic-wave pr opagation -- Radio noise and interference -- Broadcasting, cable television, and recording system standards -- Radar -- Radio navigation systems -- Common carrier transmission -- Switching networks and traffic concepts -- Electroacoustics -- Lasers -- Com puter organization and programming -- Logic design -- Probability and statistics -- Reliability and life testing -- Cellular telecommunications systems -- Mathematical equations -- Mathematical tables -- Miscellaneous data. |
ISBN: | 9780750672917 |
Series: | eBooks |
Series: | ScienceDirect |
Keywords: | Electronics. , Computer engineering. , Telecommunication. |
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Call number: | 1786301091:ONLINE Show nearby items on shelf |
Title: | Fourier Analysis |
Author(s): |
Ceschi |
Date: | 2017 |
Publisher: | Wiley-ISTE |
Size: | 1 online resource (267 p.) |
ISBN: | 9781786301093 |
Series: | eBooks |
Series: | Wiley Online Library |
Series: | Wiley 2016 package purchase |
Keywords: | Electrical & Electronics Engineering |
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Call number: | 0471889482:ONLINE Show nearby items on shelf |
Title: | Fourier Analysis of Time Series: An Introduction, Second Edition |
Author(s): |
Bloomfield |
Date: | 2000 |
Publisher: | Wiley-Interscience |
Size: | 1 online resource (289 p.) |
ISBN: | 9780471889489 |
Series: | eBooks |
Series: | Wiley Online Library |
Series: | Wiley 2016 package purchase |
Keywords: | Statistics |
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Call number: | 0471694630:ONLINE Show nearby items on shelf |
Title: | Applications of Fourier Analysis on Finite Non-Abelian Groups in Signal Processing and System Design |
Author(s): |
Stankovic |
Date: | 2005 |
Publisher: | Wiley-IEEE Press |
Size: | 1 online resource (265 p.) |
ISBN: | 9780471694632 |
Series: | eBooks |
Series: | Wiley Online Library |
Series: | Wiley 2016 package purchase |
Keywords: | Electrical & Electronics Engineering |
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Call number: | 0471669849:ONLINE Show nearby items on shelf |
Title: | Fourier Analysis |
Author(s): |
Stade |
Date: | 2005 |
Publisher: | Wiley-Interscience |
Size: | 1 online resource (521 p.) |
ISBN: | 9780471669845 |
Series: | eBooks |
Series: | Wiley Online Library |
Series: | Wiley 2016 package purchase |
Keywords: | Mathematics |
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Call number: | 0470744812:ONLINE Show nearby items on shelf |
Title: | Fourier Analysis on Groups |
Author(s): |
Rudin |
Date: | 1962 |
Publisher: | Wiley |
Size: | 1 online resource (286 p.) |
ISBN: | 9780470744819 |
Series: | eBooks |
Series: | Wiley Online Library |
Series: | Wiley 2016 package purchase |
Keywords: | Mathematics |
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Call number: | 0470294663:ONLINE Show nearby items on shelf |
Title: | Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing |
Author(s): |
Broughton |
Date: | 2008 |
Publisher: | Wiley-Interscience |
Size: | 1 online resource (361 p.) |
ISBN: | 9780470294666 |
Series: | eBooks |
Series: | Wiley Online Library |
Series: | Wiley 2016 package purchase |
Keywords: | Mathematics |
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Call number: | TK5102.5L298::2005 Show nearby items on shelf |
Title: | Linear Systems and Signals |
Author(s): |
B. P. (Bhagwandas Pannalal) Lathi |
Date: | 2005 |
Publisher: | Oxford University Press |
Note: | 2nd ed. |
Contents: | Signals and Systems |
Time-Domain Analysis of Continuous-Time Systems | |
Time-Domain Analysis of Discrete-Time Systems | |
Continuous-Time System Analysis using the Laplace Transform | |
Discrete-Time System Analysis using the Z-Transform | |
Continuous-Time Signal Analysis : The Fourier Series | |
Continuous-Time Signal Analysis : The Fourier Transform | |
Sampling : The Bridge from Continuous to Discrete | |
Fourier Analysis of Discrete-Time Signals | |
State-Space Analysis | |
ISBN: | 0195158334 |
Keywords: | Signal processing, Mathematics , System analysis , Linear time invariant systems , Digital filters (Mathematics) |
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Location: | MAIN |
Call number: | TK454.E46::2003 Show nearby items on shelf |
Title: | Schaum's outline of theory and problems of electric circuits |
Author(s): |
Mahmood Nahvi Joseph A. Edminister |
Date: | 2003 |
Edition: | 4th ed. |
Publisher: | New York : McGraw-Hill |
Size: | 469 p |
Contents: | Introduction -- Circuit concepts -- Circuit laws -- Analysis methods -- Amplifiers and operational circuits -- Waveforms and signals -- First order circuits -- Higher order circuits and complex frequency -- Sinusoidal steady state circuit analysis -- AC power -- Polyphase circuits -- Frequency response filters and resonance -- Two port networks -- Mutual inductance and transformers -- Circuit analysis using spice and pspice -- The laplace transform method -- fourier method of waveform analysis -- Complex number system -- Matrices an determinants |
ISBN: | 9780071393072 |
Series: | Schaum's outline series |
Keywords: | Electric circuits , Problems and exercises |
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Call number: | TA330.J44::2002 Show nearby items on shelf |
Title: | Advanced engineering mathematics |
Author(s): |
Alan Jeffrey |
Date: | 2002 |
Publisher: | Harcourt Academic Press |
Note: | Volume 2 is the solutions manual |
Contents: | Review of Prerequisites |
Vectors and Matrices | |
Vectors and Vector Spaces | |
Matrices and Systems of Linear Equations | |
Eigenvalues, Eigenvectors and Diagonalization | |
Ordinary Differential Equations | |
First Order Differential Equations | |
Second and Higher Order Linear Differential Equations and Systems | |
The Laplace Transform | |
Series Solutions of Differential Equations, Special Functions, and Sturm-Liouville Equations | |
Fourier Series | |
Fourier Integrals and the Fourier Transform | |
Vector Calculus | |
Vector Differential Calculus | |
Vector Integral Calculus | |
Complex analysis | |
Analytic Functions | |
Complex Integration | |
Laurent Series, Residues, and Contour Integration | |
The Laplace Inversion Integral | |
Particla Differential Equations | |
Numerical Mathematics | |
ISBN: | 012382592X |
Keywords: | Engineering mathematics |
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Call number: | SPRINGER-2016-9783662489932:ONLINE Show nearby items on shelf |
Title: | Mathematical Analysis II |
Author(s): |
Vladimir A Zorich |
Date: | 2016 |
Edition: | 2nd ed. 2016 |
Size: | 1 online resource (720 p.) |
Note: | 10.1007/978-3-662-48993-2 |
Contents: | 9 Continuous Mappings (General Theory) -- 10 Differential Calculus from a General Viewpoint -- 11 Multiple Integrals -- 12 Surfaces and Differential Forms in Rn -- 13 Line and Surface Integrals -- 14 Elements of Vector Analysis and Field Theory -- 1 5 Integration of Differential Forms on Manifolds -- 16 Uniform Convergence and Basic Operations of Analysis -- 17 Integrals Depending on a Parameter -- 18 Fourier Series and the Fourier Transform -- 19 Asymptotic Expansions -- Topics and Questions for Mid term Examinations -- Examination Topics -- Examination Problems (Series and Integrals Depending on a Parameter) -- Intermediate Problems (Integral Calculus of Several Variables) -- Appendices: A Series as a Tool (Introductory Lecture) -- B Change of Varia bles in Multiple Integrals -- C Multidimensional Geometry and Functions of a Very Large Number of Variables -- D Operators of Field Theory in Curvilinear Coordinates -- E Modern Formula of Newtonâ€“Leibniz -- References -- Index of Basic |
Notation -- Subject Index -- Name Index | |
ISBN: | 9783662489932 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Physics , Mathematics , Analysis , Theoretical, Mathematical and Computational Physics |
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Call number: | SPRINGER-2016-9783319397801:ONLINE Show nearby items on shelf |
Title: | Extensions of Positive Definite Functions Applications and Their Harmonic Analysis |
Author(s): |
Palle Jorgensen |
Date: | 2016 |
Size: | 1 online resource (9 p.) |
Note: | 10.1007/978-3-319-39780-1 |
ISBN: | 9783319397801 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 2160 |
Keywords: | Mathematics , Topological groups , Lie groups , Harmonic analysis , Fourier analysis , Functional analysis , Probabilities , Mathematical physics , Mathematics , Abstract Harmonic Analysis , Topological Groups, Lie Groups , Fourier Analysis , Functional Analysis , Mathematical Physics , Probability Theory and Stochastic Processes |
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Call number: | SPRINGER-2016-9783319311029:ONLINE Show nearby items on shelf |
Title: | Electrical Measurements in the Laboratory Practice |
Author(s): |
Rosario Bartiromo |
Date: | 2016 |
Size: | 1 online resource (286 p.) |
Note: | 10.1007/978-3-319-31102-9 |
Contents: | Electrical Circuits and components -- Direct current circuit analysis -- Uncertainty in electrical measurements -- Direct current measurements -- Alternating current circuit analysis -- Alternating current: special circuits -- |
Alternating current measurements -- The oscilloscope -- Circuit pulse response -- Transmission line -- App. A: Skin Effect -- App. B: Fourier Analysis | |
ISBN: | 9783319311029 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Electronic circuits , Physical measurements , Measurement , Electronics , Microelectronics , Physics , Measurement Science and Instrumentation , Electronics and Microelectronics, Instrumentation , Electronic Circuits and Devices |
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Call number: | SPRINGER-2016-9783319309675:ONLINE Show nearby items on shelf |
Title: | Writing Proofs in Analysis |
Author(s): |
Jonathan M Kane |
Date: | 2016 |
Size: | 1 online resource (4 p.) |
Note: | 10.1007/978-3-319-30967-5 |
Contents: | What Are Proofs, And Why Do We Write Them? -- The Basics of Proofs -- Limits -- Continuity -- Derivatives -- Riemann Integrals -- Infinite Series -- Sequences of Functions -- Topology of the Real Line -- Metric Spaces |
ISBN: | 9783319309675 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Fourier analysis , Functional analysis , Mathematical logic , Mathematics , Functional Analysis , Fourier Analysis , Mathematical Logic and Foundations |
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Call number: | SPRINGER-2016-9783319290461:ONLINE Show nearby items on shelf |
Title: | Measure and Integration |
Author(s): |
Hari Bercovici |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (300 p.) |
Note: | 10.1007/978-3-319-29046-1 |
Contents: | Rings of sets -- Measurability -- Integrals and Measures -- Convergence Theorems for Lebesgue Integrals -- Existence and Uniqueness of Measures -- Signed Measures, Complex Measures and Absolute Continuity -- Measure and Topology -- Product Measures -- The Lp Spaces -- Fourier Analysis -- Standard Measure Spaces. |
ISBN: | 9783319290461 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Measure theory , Functions of real variables , Mathematics , Measure and Integration , Real Functions |
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Call number: | SPRINGER-2016-9783319287393:ONLINE Show nearby items on shelf |
Title: | Nonlocal Diffusion and Applications |
Author(s): |
Claudia Bucur |
Date: | 2016 |
Size: | 1 online resource (23 p.) |
Note: | 10.1007/978-3-319-28739-3 |
Contents: | Introduction -- 1 A probabilistic motivation.-1.1 The random walk with arbitrarily long jumps -- 1.2 A payoff model.-2 An introduction to the fractional Laplacian.-2.1 Preliminary notions -- 2.2 Fractional Sobolev Inequality and Generalized Coarea F ormula -- 2.3 Maximum Principle and Harnack Inequality -- 2.4 An s-harmonic function -- 2.5 All functions are locally s-harmonic up to a small error -- 2.6 A function with constant fractional Laplacian on the ball -- 3 Extension problems -- 3.1 Water wave model -- 3.2 Crystal dislocation -- 3.3 An approach to the extension problem via the Fourier transform -- 4 Nonlocal phase transitions -- 4.1 The fractional Allen-Cahn equation -- 4.2 A nonlocal version of a conjecture by De Giorgi -- 5 Nonlocal minimal surfaces -- 5.1 Graphs and s-minimal surfaces -- 5.2 Non-existence of singular cones in dimension 2 5.3 Boundary regularity -- 6 A nonlocal nonlinear stationary SchrÃ¶dinger type equation -- 6.1 From the nonlocal Uncertainty Principle to a |
fractional weighted inequality -- Alternative proofs of some results -- A.1 Another proof of Theorem A.2 Another proof of Lemma 2.3 -- References | |
ISBN: | 9783319287393 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes of the Unione Matematica Italiana: 20 |
Keywords: | Mathematics , Functional analysis , Integral transforms , Operational calculus , Partial differential equations , Calculus of variations , Mathematics , Partial Differential Equations , Calculus of Variations and Optimal Control Optimization , Integral Transforms, Operational Calculus , Functional Analysis |
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Call number: | SPRINGER-2016-9783319278735:ONLINE Show nearby items on shelf |
Title: | New Trends in Applied Harmonic Analysis Sparse Representations, Compressed Sensing, and Multifractal Analysis |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (19 p.) |
Note: | 10.1007/978-3-319-27873-5 |
Contents: | Multifractal Analysis of Cantor-like Measures -- Multifractal Analysis and Wavelets -- An Introduction to Mandelbrot Cascades -- Lebesgue-type Inequalities for Greedy Approximation -- Results on Non-linear Approximation for Wavelet Bases in Weighte d Function Spaces -- Consequences of the Marcus/Spielman/Srivastava Solution of the Kadison-Singer Problem -- Model Sets and New Versions pf Shannon Sampling Theorem -- Stylometry and Mathematical Study of Authorship -- Thoughts on Numerical and Conceptua l Harmonic Analysis |
ISBN: | 9783319278735 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Measure theory , Computer science , Computer mathematics , Mathematics , Fourier Analysis , Abstract Harmonic Analysis , Signal, Image and Speech Processing , Measure and Integration , Mathematical Applications in Computer Science |
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Call number: | SPRINGER-2016-9783319274669:ONLINE Show nearby items on shelf |
Title: | Methods of Fourier Analysis and Approximation Theory |
Author(s): | |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (258 p.) |
Note: | 10.1007/978-3-319-27466-9 |
Contents: | 1. Introduction -- 2. Fourier analysis -- 2.1. Parseval frames -- 2.2. Hyperbolic Hardy classes and logarithmic Bloch spaces -- 2.3. Logan's and Bohman's extremal problems -- 2.4. Weighted estimates for the Hilbert transform -- 2.5. Q-Measures and uniqueness sets for Haar series -- 2.6. O-diagonal estimates for CalderÃ³n-Zygmund operators -- 3. Function spaces of radial functions -- 3.1. Potential spaces of radial functions -- 3.2. On Leray's formula -- 4. Approximation theory -- 4.1. Approximation order of Besov classes -- 4.2. Ulyanov inequalities for moduli of smoothness -- 4.3. Approximation order of Besov classes -- 5. Optimization theory and related topics -- 5.1. The Laplace-Borel transform -- 5.2. Optimization control problems -- 2 Michael Ruzhansky and Sergey Tikhonov.-5.3. Optimization control problems for parabolic equation -- 5.4. Numerical modeling of the linear filtration -- References. |
ISBN: | 9783319274669 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Numerical analysis , Mathematics , Fourier Analysis , Abstract Harmonic Analysis , Numerical Analysis |
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Call number: | SPRINGER-2016-9783319272658:ONLINE Show nearby items on shelf |
Title: | Basic Concepts in Computational Physics |
Author(s): |
Benjamin A Stickler |
Date: | 2016 |
Edition: | 2nd ed. 2016 |
Size: | 1 online resource (409 p.) |
Note: | 10.1007/978-3-319-27265-8 |
Contents: | Some Basic Remarks -- Part I Deterministic Methods -- Numerical Differentiation -- Numerical Integration -- The KEPLER Problem -- Ordinary Differential Equations â€“ Initial Value Problems -- The Double Pendulum -- Molecular Dynamics -- |
Numerics of Ordinary Differential Equations - Boundary Value Problems -- The One-Dimensional Stationary Heat Equation -- The One-Dimensional Stationary SCHRÃ–DINGER Equation -- Partial Differential Equations -- Part II Stochastic | |
Methods -- Pseudo Random Number Generators -- Random Sampling Methods -- A Brief Introduction to Monte-Carlo Methods -- The ISING Model -- Some Basics of Stochastic Processes -- The Random Walk and Diffusion Theory -- MARKOV-Chain | |
Monte Carlo and the POTTS Model -- Data Analysis -- Stochastic Optimization -- Appendix: The Two-Body Problem -- Solving Non-Linear Equations. The NEWTON Method -- Numerical Solution of Systems of Equations -- Fast Fourier Transform -- | |
Basics of Probability Theory -- Phase Transitions -- Fractional Integrals and Derivatives in 1D -- Least Squares Fit -- Deterministic Optimization | |
ISBN: | 9783319272658 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Chemistry, Physical and theoretical , Computer mathematics , Applied mathematics , Engineering mathematics , Physics , Numerical and Computational Physics , Appl.Mathematics/Computational Methods of Engineering , Computational Mathematics and Numerical Analysis , Theoretical and Computational Chemistry |
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Call number: | SPRINGER-2016-9783034809641:ONLINE Show nearby items on shelf |
Title: | Application of Holomorphic Functions in Two and Higher Dimensions |
Author(s): |
Klaus GÃ¼rlebeck |
Date: | 2016 |
Size: | 1 online resource (3 p.) |
Note: | 10.1007/978-3-0348-0964-1 |
Contents: | 1.Basic Properties of Holomorphic Functions -- 2.Conformal and Quasi-conformal Mappings -- 3.Function Theoretic Function spaces -- 4.Operator Calculus -- 5.Decompositions -- 6.Some First Order Systems of Partial Differential Equations -- 7.Boundary Value Problems of Second Order Partial Differential Equations -- 8.Some Initial-boundary Value Problems -- 9.Riemann-Hilbert Problems -- 10.Initial Boundary Value Problems on the Sphere -- 11.Fourier Transforms -- Bibliography -- Index |
ISBN: | 9783034809641 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Functional analysis , Functions of complex variables , Integral transforms , Operational calculus , Partial differential equations , Mathematics , Integral Transforms, Operational Calculus , Functions of a Complex Variable , Partial Differential Equations , Functional Analysis |
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Call number: | SPRINGER-2014-9783642540752:ONLINE Show nearby items on shelf |
Title: | Upper and Lower Bounds for Stochastic Processes [electronic resource] : Modern Methods and Classical Problems |
Author(s): |
Michel Talagrand |
Date: | 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | The book develops modern methods and in particular the generic chaining to bound stochastic processes. This methods allows in particular to get optimal bounds for Gaussian and Bernoulli processes. Applications are given tostable processes, infinitely divisible processes, matching theorems, the convergence of random Fourier series, of orthogonal series, and to functional analysis. The complete solution of a number of classical problems is given incomplete detail, and an ambitious program for future re search is laid out |
Contents: | 0. Introduction |
1. Philosophy and Overview of the Book | |
2. Gaussian Processes and the Generic Chaining | |
3. Random Fourier Series and Trigonometric Sums, I | |
4. Matching Theorems I | |
5. Bernouilli Processes | |
6. Trees and the Art of Lower Bounds | |
7. Random Fourier Series and Trigonometric Sums, II | |
8. Processes Related to Gaussian Processes | |
9. Theory and Practice of Empirical Processes | |
10. Partition Scheme for Families of Distances | |
11. Infinitely Divisible Processes | |
12. The Fundamental Conjectures | |
13. Convergence of Orthogonal Series Majorizing Measures | |
14. Matc | |
ISBN: | 9783642540752 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 0071-1136 : v60 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783642538599:ONLINE Show nearby items on shelf |
Title: | Laser Spectroscopy 1 [electronic resource] : Basic Principles |
Author(s): |
Wolfgang Demtrder |
Date: | 2014 |
Edition: | 5th Edition |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Keeping abreast of the latest techniques and applications, this new edition of the standard reference and graduate text on laser spectroscopy has been completely revised and expanded. While the general concept is unchanged, thenew edition features a broad array of new material, e.g., ultrafast lasers (atto- and femto-second lasers) and parametric oscillators, coherent matter waves, Doppler-free Fourier spectroscopy with optical frequency combs, interferencespectroscopy, quantum optics, the interferom etric detection of gravitational waves and still more applications in chemical analysis, medical diagnostics, and engineering |
Contents: | Introduction |
Absorption and Emission of Light | |
Widths and Profiles of Spectral Lines | |
Spectroscopic Instrumentation | |
Lasers as Spectroscopic Sources | |
Solutions | |
ISBN: | 9783642538599 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Spectroscopy , Microwaves , Surfaces (Physics) |
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Call number: | SPRINGER-2014-9783319078427:ONLINE Show nearby items on shelf |
Title: | Probability on Compact Lie Groups [electronic resource] |
Author(s): |
David Applebaum |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Probability theory on compact Lie groups deals with the interaction between chance and symmetry, a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applicationsin statistics and engineering (par ticularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topicspresented are: the study of measures via the non-commutative F ourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures, and the statistical problem of deconvolution. Theemphasis on compact (rather than general) Lie groups helps readers to get acquaint ed with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance ofthese groups for applications. The book is primarily aimed at researchers working in probability, stochast ic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists,statisticians and engineers who are working on related applications. A background in first year graduate level measure theoreti c probability and functional analysis is essential a background in Lie groups and representation theory iscertainly helpful but the first two chapters also offer orientation in these subjects |
Contents: | Introduction |
1.Lie Groups | |
2.Representations, Peter | |
Weyl Theory and Weights | |
3.Analysis on Compact Lie Groups | |
4.Probability Measures on Compact Lie Groups | |
5.Convolution Semigroups of Measures | |
6.Deconvolution Density Estimation | |
Appendices | |
Index | |
Bibliography | |
ISBN: | 9783319078427 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Probability Theory and Stochastic Modelling, 2199-3130 : v70 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Harmonic analysis , Fourier analysis , Functional analysis , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783319064475:ONLINE Show nearby items on shelf |
Title: | Regularity of Difference Equations on Banach Spaces [electronic resource] |
Author(s): |
Ravi P Agarwal Claudio Cuevas Carlos Lizama |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This work introduces readers to the topic of maximal regularity for difference equations. The authors systematically present the method of maximal regularity, outlining basic linear difference equations along with relevantresults. They address recent advances in the field, as well as basic semigroup and cosine operator theories in the discrete setting. The authors also identify some open problems that readers may wish to take up for further research.This book is intended for graduate students and res earchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis |
Contents: | 1.Discrete Semi groups and Cosine Operators |
2. Maximal regularity and the method of Fourier Multipliers | |
3. First Order Linear Difference Equations | |
4. First Order Semi linear Difference Equations | |
5. Second Order Linear Difference Equations | |
6. Second Order Semi linear | |
7. Applications | |
ISBN: | 9783319064475 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional equations |
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Call number: | SPRINGER-2014-9783319060743:ONLINE Show nearby items on shelf |
Title: | Functional Analysis and Applied Optimization in Banach Spaces [electronic resource] : Applications to Non-Convex Variational Models |
Author(s): |
Fabio Botelho |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physicsand engineering probl ems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation.Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dualapproach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in relatedfields |
Contents: | 1. Topological Vector Spaces |
2. The Hahn | |
Bananch Theorems and Weak Topologies | |
3. Topics on Linear Operators | |
4.Basic Results on Measure and Integration | |
5. The Lebesgue Measure in Rn | |
6. Other Topics in Measure and Integration | |
7. Distributions | |
8. The Lebesque and Sobolev Spaces | |
9. Basic Concepts on the Calculus of Variations | |
10. Basic Concepts on Convex Analysis | |
11. Constrained Variational Analysis | |
12. Duality Applied to Elasticity | |
13. Duality Applied to a Plate Model | |
14. About Ginzburg | |
Landau Type Equations: The Simpler Real Case | |
15. Full Complex Ginzb | |
ISBN: | 9783319060743 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Functional analysis , Numerical analysis |
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Call number: | SPRINGER-2014-9783319045375:ONLINE Show nearby items on shelf |
Title: | Sparse Grids and Applications - Munich 2012 [electronic resource] |
Author(s): |
Jochen Garcke Dirk Pflger |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Sparse grids have gained increasing interest in recent years for the numerical treatment of high-dimensional problems. Whereas classical numerical discretization schemes fail in more than three or four dimensions, sparse gridsmake it possible to over come the curse of dimensionality to some degree, extending the number of dimensions that can be dealt with. This volume of LNCSE collects the papers from the proceedings of the second workshop on sparsegrids and applications, demonstrating once again the importance of this numerical discretization scheme. The selected articles present recent advances on the numerical analysis of sparse grids as well as efficient data structures, andthe range of applications extends to uncertainty quantification settings a nd clustering, to name but a few examples |
Contents: | Gerrit Buse, Dirk Pfluger, and Riko Jacob: Efficient Pseudorecursive Evaluation Schemes for Non |
Adaptive Sparse Grids | |
Oliver G. Ernst and Bjorn Sprungk: Stochastic Collocation for Elliptic PDEs with Random Data The Lognormal Case | |
Michael Griebel and Helmut Harbrecht: On the Convergence of the Combination Technique | |
Michael Griebel and Jan Hamaekers: Fast Discrete Fourier Transform on Generalized Sparse Grids | |
Michael Griebel and Jens Oettershagen: Dimension | |
adaptive Sparse Grid Quadrature for Integrals with Boundary Singularities | |
Max Gunzburger, Clayton G. Webster, and Gua | |
ISBN: | 9783319045375 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Lecture Notes in Computational Science and Engineering, 1439-7358 : v97 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science Mathematics , Computer science |
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Call number: | SPRINGER-2014-9783319026428:ONLINE Show nearby items on shelf |
Title: | Multiple Wiener-It Integrals [electronic resource] : With Applications to Limit Theorems |
Author(s): |
Pter Major |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The goal of this Lecture Note is to prove a new type of limit theorems for normalized sums of strongly dependent random variables that play an important role in probability theory or in statistical physics. Here non-linearfunctionals of stationary Ga ussian fields are considered, and it is shown that the theory of WienerIt integrals provides a valuable tool in their study. More precisely, a version of these random integrals is introduced thatenables us to combine the technique of random integrals and Fourier analysis. The most important results of this theory are presented together with some non-trivial limit theorems proved with their help. This work is a new, revisedversion of a previous volume written with the goalof giving a better explanation of some of the details and the motivation behind the proofs. It does not contain essentially new results it was written to give a better insight to theold ones. In particular, a more detailed explanation of generalized fields is included to show that what is at the first sight a rather formal object is actually a useful tool for carryingout heuristic arguments |
ISBN: | 9783319026428 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Lecture Notes in Mathematics, 0075-8434 : v849 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783319025506:ONLINE Show nearby items on shelf |
Title: | Fourier Analysis [electronic resource] : Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations |
Author(s): |
Michael Ruzhansky Ville Turunen |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, andtime-frequency analysis. This coll ection of 20 refereed articles is based on selected talksgiven at the international conference Fourier Analysis and Pseudo-Differential Operators, June 2530, 2012, at Aalto University,Finland, and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012 it was also the 6th meeting in the series FourierAnalysis and Partial Differential Equations. |
Contents: | Preface |
Contributions by N. Bez, M. Sugimoto, Tang Bao Ngoc Bui, M. Reissig, F. Colombini, D. Del Santo, F. Fanelli, G. Metivier, E. Cordero, F. Nicola, L. Rodino, S. Coriasco, K. Johansson, J. Toft, V. Fischer, M. Ruzhansky, G.Garello, A. Morando, D. Grieser, E. Hunsicker, N. Habal, W. Rungrottheera, B | |
W. Schulze, C. Iwasaki, B. Kanguzhin, N. Tokmagambetov, S. Katayama, H. Kubo, M. Lassas, T. Zhou, T. Matsuyama, T. Nishitani, S. Serovajsky, K. Shakenov, S. Tikhonov, M. Zeltser, Y. Wakasugi, K. Yagdjian. | |
ISBN: | 9783319025506 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Trends in Mathematics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Global analysis , Operator theory , Differential equations, partial , Sequences (Mathematics) |
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Call number: | SPRINGER-2014-9783319022918:ONLINE Show nearby items on shelf |
Title: | Discrete Dynamical Models [electronic resource] |
Author(s): |
Ernesto Salinelli Franco Tomarelli |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This book provides an introduction to the analysis of discrete dynamical systems. The content is presented by an unitary approach that blends the perspective of mathematical modeling together with the ones of several disciplineas Mathematical Analysi s, Linear Algebra, Numerical Analysis, Systems Theory and Probability. After a preliminary discussion of several models, the main tools for the study of linear and non-linear scalar dynamical systems arepresented, paying particular attention to the stabil ity analysis. Linear difference equations are studied in detail and an elementary introduction of Z and Discrete Fourier Transform is presented. A whole chapter is devoted to thestudy of bifurcations and chaotic dynamics. One-step vector-valued dynamical systems are the subject of three chapters, where the reader can find the applications to positive systems, Markov chains, networks and search engines. Thebook is addressed mainly to students in Mathematics, Engineering, Physics, Chemistry, Biology and Eco nomics. The exposition is self-contained: some appendices present prerequisites, algorithms and suggestions for computer simulations.The analysis of several examples is enriched by the proposition of many related exercises of increasing difficulty in the last chapter the detailed solution is given for most of them |
Contents: | 1 Recursive phenomena and difference equations |
2 Linear difference equations | |
3 Discrete dynamical systems: one | |
step scalar equations | |
4 Complex behavior of nonlinear dynamical systems: bifurcations and chaos | |
5 Discrete dynamical systems: vector equations | |
6 Markov chains | |
7 Matrix | |
8 Solutions | |
ISBN: | 9783319022918 |
Series: | eBooks |
Series: | SpringerLink |
Series: | UNITEXT, 2038-5714 : v76 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Functional equations , Differentiable dynamical systems |
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Call number: | SPRINGER-2014-9783319020990:ONLINE Show nearby items on shelf |
Title: | Introduction to Partial Differential Equations [electronic resource] |
Author(s): |
Peter J Olver |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, andelsewhere. The exposition car efully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, andinclude straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material thatmotivates the student to delve further into the subject. No previous experien ce with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- andmulti-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to formthe core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximu m Principle, financial models, dispersion and solitons, Huygens' Principle, quantum mechanical systems,and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes ar e an important component of any introductory course, and the text covers the twomost basic approaches: finite differences and finite elements. Peter J. Olver is professor of mathematics at the University of Minnesota. His wide-ranging research interests a re centered on the development of symmetry-based methodsfor differential equations and their manifold applications. He is the author of over 130 papers published in major scientific research |
Contents: | What are Partial Differential Equations? |
Linear and Nonlinear Waves | |
Fourier Series | |
Separation of Variables | |
Finite Differences | |
Generalized Functions and Greens Functions | |
Complex Analysis and Conformal Mapping | |
Fourier Transforms | |
Linear and Nonlinear Evolution Equations | |
A General Framework forLinear Partial Differential Equations | |
FiniteElements and Weak Solutions | |
Dynamics of Planar Media | |
Partial Differential Equations in Space . | |
ISBN: | 9783319020990 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Undergraduate Texts in Mathematics, 0172-6056 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Differential equations, partial |
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Call number: | SPRINGER-2014-9781461488279:ONLINE Show nearby items on shelf |
Title: | A Qualitative Approach to Inverse Scattering Theory [electronic resource] |
Author(s): |
Fioralba Cakoni David Colton |
Date: | 2014 |
Publisher: | Boston, MA : Springer US : Imprint: Springer |
Size: | 1 online resource |
Note: | Inverse scattering theory is an important area of applied mathematics due to its central role in such areas as medical imaging , nondestructive testing and geophysical exploration. Until recently all existing algorithms forsolving inverse scattering problems were based on using either a weak scattering assumption or on the use of nonlinear optimization techniques. The limitations of these methods have led in recent years to an alternative approach to theinverse scattering problem which avoids the inc orrect model assumptions inherent in the use of weak scattering approximations as well as the strong a priori information needed in order to implement nonlinear optimization techniques.These new methods come under the general title of qualitative methods in inverse scattering theory and seek to determine an approximation to the shape of the scattering object as well as estimates on its material properties withoutmaking any weak scattering assumption and using essentially no a priori information on the nat ure of the scattering object. This book is designed to be an introduction to this new approach in inverse scattering theory focusing on theuse of sampling methods and transmission eigenvalues. In order to aid the reader coming from a discipline outside of mathematics we have included background material on functional analysis, Sobolev spaces, the theory of ill posedproblems and certain topics in in the theory of entire functions of a complex variable. This book is an updated and expanded version of an ear lier book by the authors published by Springer titled Qualitative Methods in InverseScattering Theory Review of Qualitative Methods in Inverse Scattering Theory All in all, the authors do exceptionally well in combining such a wide variety of mathematical material and in presenting it in a well-organized andeasy-to-follow fashion. This text certainly complements the growing body of work in inverse scattering and should well suit both new researchers to |
Contents: | 1. Functional Analysis and Sobolev Spaces |
2. Ill | |
Posed Problems | |
3. Scattering by Imperfect Conductors | |
4. Inverse Scattering Problems for Imperfect Conductors | |
5. Scattering by Orthotropic Media | |
6. Inverse Scattering Problems for Orthotropic Media | |
7. Factorization Methods | |
8. Mixed Boundary Value Problems | |
9. Inverse Spectral Problems for Transmission Eigenvalues | |
10. A Glimpse at Maxwell's Equations | |
ISBN: | 9781461488279 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Applied Mathematical Sciences, 0066-5452 : v188 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Differential equations, partial , Computer engineering |
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Call number: | SPRINGER-2014-9781461458111:ONLINE Show nearby items on shelf |
Title: | Symmetric Discontinuous Galerkin Methods for 1-D Waves [electronic resource] : Fourier Analysis, Propagation, Observability and Applications |
Author(s): |
Aurora Marica Enrique Zuazua |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | This work describes the propagation properties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. This is done by means of linear approximations on uniform meshes.First,a careful Fourier analysis is constructed, highlightingthe coexistence of two Fourier spectral branches or spectral diagrams (physical and spurious) related to the two components of the numerical solution (averages andjumps). Efficient filtering mechanisms are also develo pedby means of techniques previously proved to be appropriate for classical schemes like finite differences or P1-classical finite elements. In particular,the work presents aproof thatthe uniform observability property is recovered uniformly by considerin g initial data with null jumps and averages given by a bi-grid filtering algorithm. Finally, the bookexplains how theseresults can be extended toother more sophisticated conforming and non-conforming finite element methods, in particular to quadratic fini teelements, local discontinuous Galerkin methods and a version of the SIPG method adding penalization on the normalderivatives of the numerical solution at the grid points. This work is the first publication tocontaina rigorous analysis of the discontinuo us Galerkin methods for wave control problems. It will be of interest to a range ofresearchers specializing inwave approximations |
Contents: | 1. Preliminaries |
2. Discontinuous Galerkin approximations and main results | |
3. Bibliographical notes | |
4. Fourier analysis of the DG methods | |
5. Nonuniform observability for DG approximations of waves | |
6. Filtering mechanisms | |
7. Extensions to other numerical approximation schemes | |
8. Comments and open problems | |
A technical proof | |
References | |
ISBN: | 9781461458111 |
Series: | eBooks |
Series: | SpringerLink |
Series: | SpringerBriefs in Mathematics, 2191-8198 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Differential equations, partial , Algorithms , Numerical analysis |
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Call number: | SPRINGER-2014-9781447164340:ONLINE Show nearby items on shelf |
Title: | Mathematical Methods for Elastic Plates [electronic resource] |
Author(s): |
Christian Constanda |
Date: | 2014 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | Mathematical models of deformation of elastic plates are used by applied mathematicians and engineers in connection with a wide range of practical applications, from microchip production to the construction of skyscrapers andaircraft. This book emplo ys two important analytic techniques to solve the fundamental boundary value problems for the theory of plates with transverse shear deformation, which offers a more complete picture of the physical process ofbending than Kirchhoffs classical one. The fi rst method transfers the ellipticity of the governing system to the boundary, leading to singular integral equations on the contour of the domain. These equations, established on thebasis of the properties of suitable layer potentials, are then solved in spaces of smooth (Hlder continuous and Hlder continuously differentiable) functions. The second technique rewrites the differential system in terms ofcomplex variables and fully integrates it, expressing the solution as a combination of complex analytic potentials. The last chapter develops a generalized Fourier series method closely connected with the structure of the system,which can be used to compute approximate solutions. The numerical results generated as an illustration for the interior Dirichlet problem are accompanied by remarks regarding the efficiency and accuracy of the procedure. Thepresentation of the material is detailed and self-contained, making Mathematical Methods for Elastic Plates accessible to researchers and graduate students wit h a basic knowledge of advanced calculus |
Contents: | Singular Kernels |
Potentials and Boundary Integral Equations | |
Bending of Elastic Plates | |
The Layer Potentials | |
The Newtonian Potential | |
Existence of Regular Solutions | |
Complex Variable Treatment | |
Generalized Fourier Series | |
ISBN: | 9781447164340 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Integral equations , Materials |
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Call number: | SPRINGER-2014-9781447163954:ONLINE Show nearby items on shelf |
Title: | An Introduction to Laplace Transforms and Fourier Series [electronic resource] |
Author(s): |
Phil Dyke |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative.Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms. In this book, there is a strong emphasis onapplication with the necessary mathematical g rounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Onlyknowledge of elementary trigonometry and calculus are required as prereq uisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics ormathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and biological modelling requiring techniques for solving initial value problems |
Contents: | The Laplace Transform |
Further Properties of the Laplace Transform | |
Convolution and the Solution of Ordinary Differential Equations | |
Fourier Series | |
Partial Differential Equations | |
Fourier Transforms | |
Wavelets and Signal Processing | |
Complex Variables and Laplace Transforms | |
ISBN: | 9781447163954 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Undergraduate Mathematics Series, 1615-2085 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Functions of complex variables , Integral Transforms , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2013-9789462390096:ONLINE Show nearby items on shelf |
Title: | Applied Mathematics [electronic resource] : Data Compression, Spectral Methods, Fourier Analysis, Wavelets, and Applications |
Author(s): |
Charles K Chui Qingtang Jiang |
Date: | 2013 |
Publisher: | Paris : Atlantis Press : Imprint: Atlantis Press |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This textbook, apart from introducing the basic aspects of applied mathematics, focuses on recent topics such as information data manipulation, information coding, data approximation, data dimensionality reduction, datacompression, time-frequency and time scale bases, image manipulation, and image noise removal. The methods treated in more detail include spectral representation and frequency of the data, providing valuable information for, e.g.data compression and noise removal. Furthermore, a specia l emphasis is also put on the concept of wavelets in connection with the multi-scale structure of data-sets. The presentation of the book is elementary and easilyaccessible, requiring only some knowledge of elementary linear algebra and calculus. All impo rtant concepts are illustrated with examples, and each section contains between 10 an 25 exercises. A teaching guide, depending on the leveland discipline of instructions is included for classroom teaching and self-study |
Note: | Springer eBooks |
Contents: | Linear Spaces |
Linerar Analysis | |
Spectral Methods and Applications | |
Frequency | |
Domain Methods | |
Data Compression | |
Fourier Series | |
Fourier Time | |
Frequency Methods | |
Wavelet Transform and Filter Banks | |
Compactly Supported Wavelets | |
Wavelet Analysis | |
ISBN: | 9789462390096 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics Textbooks for Science and Engineering : v2 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer vision , Statistics , Engineering design |
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Call number: | SPRINGER-2013-9783642326660:ONLINE Show nearby items on shelf |
Title: | Multi-Layer Potentials and Boundary Problems [electronic resource] : for Higher-Order Elliptic Systems in Lipschitz Domains |
Author(s): |
Irina Mitrea Marius Mitrea |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Many phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator in a given domain. When the differential operator under discussion is ofsecond order a variety of t ools are available for dealing with such problems, including boundary integral methods, variational methods, harmonic measure techniques, and methods based on classical harmonic analysis. When thedifferential operator is of higher-order (as is the case, e .g., with anisotropic plate bending when one deals with a fourth order operator) only a few options could be successfully implemented. In the 1970s Alberto Caldern, one ofthe founders of the modern theory of Singular Integral Operators, advocated the use of layer potentials for the treatment of higher-order elliptic boundary value problems. The present monograph represents the first systematic treatmentbased on this approach. This research monograph lays, for the first time, the mathematical foundation ai med at solving boundary value problems for higher-order elliptic operators in non-smooth domains using the layer potential methodand addresses a comprehensive range of topics, dealing with elliptic boundary value problems in non-smooth domains including l ayer potentials, jump relations, non-tangential maximal function estimates, multi-traces and extensions,boundary value problems with data in WhitneyLebesque spaces, WhitneyBesov spaces, WhitneySobolev- based Lebesgue spaces, WhitneyTriebelLizorkin spaces, WhitneySobolev-based Hardy spaces, WhitneyBMO and WhitneyVMOspaces |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 Smoothness scales and Calden | |
Zygmund theory in the scalar | |
valued case | |
3 Function spaces of Whitney arrays | |
4 The double multi | |
layer potential operator | |
5 The single multi | |
layer potential operator | |
6 Functional analytic properties of multi | |
layer potentials and boundary value problems | |
ISBN: | 9783642326660 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2063 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Integral equations , Differential equations, partial , Potential theory (Mathematics) |
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Call number: | SPRINGER-2013-9783319011950:ONLINE Show nearby items on shelf |
Title: | Mathematical Physics [electronic resource] : A Modern Introduction to Its Foundations |
Author(s): |
Sadri Hassani |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics asdiverse as algebras, cla ssical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups,manifolds, Lie groups and their representations , Clifford algebras and their representations, and fiber bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision of thefirst one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first edition,namely the balance between rigor and physical application, has been maintained, as is the abun dance of historical notes and worked out examples that demonstrate the unreasonable effectiveness of mathematics in modern physics.Einstein has famously said, The most incomprehensible thing about nature is that it is comprehensible. What he had in mind w as reiterated in another one of his famous quotes concerning the question of how ... mathematics, beingafter all a product of human thought, is so admirably appropriate to the objects of reality. It is a question that comes to everyone's mind when encoun tering the highly abstract mathematics required for a deep understanding of modernphysics. It is the experience that Eugene Wigner so profoundly described as the unreasonable effectiveness of mathematics in the natural sciences. |
Note: | Springer eBooks |
Contents: | Mathematical Preliminaries |
I Finite | |
Dimensional Vector Spaces | |
1 Vectors and Linear Maps | |
2 Algebras | |
3 Operator Algebra | |
4 Matrices | |
5 Spectral Decomposition | |
II Infinite | |
Dimensional Vector Spaces | |
6 Hilbert Spaces | |
7 Classical Orthogonal Polynomials | |
8 Fourier Analysis | |
III Complex Analysis | |
9 Complex Calculus | |
10 Calculus of Residues | |
11 Advanced Topics | |
IV Differential Equations | |
12 Separation of Variables in Spherical Coordinates | |
13 Second | |
Order Linear Differential Equations | |
14 Complex Analysis of SOLDEs | |
15 Integral Transforms and Differential Equ | |
ISBN: | 9783319011950 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Mathematical physics |
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Call number: | SPRINGER-2013-9783319004013:ONLINE Show nearby items on shelf |
Title: | Computational Physics [electronic resource] : Simulation of Classical and Quantum Systems |
Author(s): |
Philipp O.J Scherer |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | Heidelberg : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This textbook presents basic and advanced computational physics in a very didactic style. It contains very-well-presented and simple mathematical descriptions of many of the most important algorithms used in computational physics.Many clear mathemati cal descriptions of important techniques in computational physics are given. The first part of the book discusses the basic numerical methods. A large number of exercises and computer experiments allows to study theproperties of these methods. The second part concentrates on simulation of classical and quantum systems. It uses a rather general concept for the equation of motion which can be applied to ordinary and partial differential equations.Several classes of integration methods are discussed includin g not only the standard Euler and Runge Kutta method but also multistep methods and the class of Verlet methods which is introduced by studying the motion in Liouville space.Besides the classical methods, inverse interpolation is discussed, together with the popular combined methods by Dekker and Brent and a not so well known improvement by Chandrupatla. A general chapter on the numerical treatment ofdifferential equations provides methods of finite differences, finite volumes, finite elements and boundar y elements together with spectral methods and weighted residual based methods. A comparison of several methods for quantumsystems is performed, containing pseudo-spectral methods, finite differences methods, rational approximation to the time evolution op erator, second order differencing and split operator methods. The book gives simple but non trivialexamples from a broad range of physical topics trying to give the reader insight into the numerical treatment but also the simulated problems. Rotational mo tion is treated in much detail to describe the motion of rigid rotors which canbe just a simple spinning top or a collection of molecules or planets. The behaviour of simple quantum systems is studied t |
Note: | Springer eBooks |
Contents: | Part I Numerical Methods |
Error Analysis | |
Interpolation | |
Numerical Differentiation | |
Numerical Integration | |
Systems of Inhomogeneous Linear Equations | |
Roots and Extremal Points | |
Fourier Transformation | |
Random Numbers and Monte | |
Carlo Methods | |
Eigenvalue Problems | |
Data Fitting | |
Discretization of Differential Equations | |
Equations of Motion | |
Part II Simulation of Classical and Quantum Systems | |
Rotational Motion | |
Molecular Dynamics | |
Thermodynamic Systems | |
Random Walk and Brownian Motion | |
Electrostatics | |
Waves | |
Diffusion | |
Nonlinear Systems | |
Simple Quantum S | |
ISBN: | 9783319004013 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Physics, 1868-4513 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Chemistry , Engineering mathematics |
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Call number: | SPRINGER-2013-9783034806039:ONLINE Show nearby items on shelf |
Title: | Quaternion and Clifford Fourier Transforms and Wavelets [electronic resource] |
Author(s): |
Eckhard Hitzer Stephen J Sangwine |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Quaternion andClifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering.This edited volume pres ents the state of the art in these hypercomplex transformations. The Clifford algebras unify Hamiltons quaternions with Grassmann algebra. A Clifford algebra is a complete algebra of a vector space and all itssubspaces including the measurement of volumes and dihedral angles between any pair of subspaces. Quaternion and Clifford algebras permit the systematic generalization of many known concepts. This book provides comprehensiveinsights into current developments and applications including their performa nce and evaluation. Mathematically, it indicates where further investigation is required. For instance, attention is drawn to the matrix isomorphisms forhypercomplex algebras, which will help readers to see that software implementations are within our gra sp. It also contributes to a growing unification of ideas and notation across the expanding field of hypercomplex transforms andwavelets. The first chapter provides a historical background and an overview of the relevant literature, and shows how the con tributions that follow relate to each other and to prior work. The book will be a valuable resource forgraduate students as well as for scientists and engineers |
Note: | Springer eBooks |
Contents: | Preface |
History of Quaternion and Clifford | |
Fourier Transforms and Wavelets | |
Part I: Quaternions | |
1 Quaternion Fourier Transform: Re | |
tooling Image and Signal Processing Analysis | |
2 The Orthogonal 2D Planes Split of Quaternions and Steerable Quaternion Fourier Transformations | |
3 Quaternionic Spectral Analysis of Non | |
Stationary Improper Complex Signals | |
4 Quaternionic Local Phase for Low | |
level Image Processing Using Atomic Functions | |
5 Bochners Theorems in the Framework of Quaternion Analysis | |
6 Bochner | |
Minlos Theorem and Quaternion Fourier Transform | |
Part II: Clifford Algeb | |
ISBN: | 9783034806039 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Trends in Mathematics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer vision , Matrix theory , Fourier analysis , Numerical analysis , Number theory |
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Call number: | SPRINGER-2013-9783034802949:ONLINE Show nearby items on shelf |
Title: | The Weyl Operator and its Generalization [electronic resource] |
Author(s): |
Leon Cohen |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book deals with the theory and application of associating a function of two variables with a function of two operators that do not commute. The concept of associating ordinary functions with operators has arisen in many areasof science and mathe matics, and up to the beginning of the twentieth century many isolated results were obtained. These developments were mostly based on associating a function of one variable with one operator, the operator generallybeing the differentiation operator. With the discovery of quantum mechanics in the years 1925-1930, there arose, in a natural way, the issue that one has to associate a function of two variables with a function of two operators that donot commute. Methods to do so became known as rules of associ ation, correspondence rules, or ordering rules. This has led to a wonderfully rich mathematical development that has found applications in many fields. Subsequently it wasrealized that for every correspondence rule there is a corresponding phase-space dis tribution. Now the fields of correspondence rules and phase-space distributions are intimately connected. A similar development occurred in the fieldof time-frequency analysis where the aim is to understand signals with changing frequencies. The Weyl Oper ator and Its Generalization aims at bringing together the basic results of the field in a unified manner. A wide audience isaddressed, particularly students and researchers who want to obtain an up-to-date working knowledge of the field. The mathematics i s accessible to the uninitiated reader and is presented in a straightforward manner |
Note: | Springer eBooks |
Contents: | Introduction |
The Fundamental Idea, Terminology, and Operator Algebra | |
The Weyl Operator | |
The Algebra of the Weyl Operator | |
Product of Operators, Commutators, and the Moyal Sin Bracket | |
Some Other Ordering Rules | |
Generalized Operator Association | |
The Fourier, Monomial, and Delta Function Associations | |
Transformation Between Associations | |
Path Integral Approach | |
The Distribution of a Symbol and Operator | |
The Uncertainty Principle | |
Phase | |
Space Distributions | |
Amplitude, Phase, Instantaneous Frequency, and the Hilbert Transform | |
Time | |
Frequency Analysis | |
The Transfor | |
ISBN: | 9783034802949 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Pseudo-Differential Operators, Theory and Applications : v9 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Operator theory , Differential equations, partial |
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Call number: | SPRINGER-2013-9781461485261:ONLINE Show nearby items on shelf |
Title: | Hermitian Analysis [electronic resource] : From Fourier Series to Cauchy-Riemann Geometry |
Author(s): |
John P D'Angelo |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry provides a coherent, integrated look at various topics from analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transformon the real line, an d then turns to the heart of the book: geometric considerations in several complex variables. The final chapter includes complex differential forms, geometric inequalities from one and several complex variables,finite unitary groups, proper mappings, and naturally leads to the Cauchy-Riemann geometry of the unit sphere. The book thus takes the reader from the unit circle to the unit sphere. This textbook will be a useful resource forupper-undergraduate students who intend to continue with mathematics, gra duate students interested in analysis, and researchers interested in some basic aspects of CR Geometry. It will also be useful for students in physics andengineering, as it includes topics in harmonic analysis arising in these subjects.The inclusion of an appendix and more than 270 exercises makes this book suitable for a capstone undergraduate Honors class |
Note: | Springer eBooks |
Contents: | Preface |
Introduction to Fourier series | |
Hilbert spaces | |
Fourier transform on R | |
Geometric considerations | |
Appendix | |
References | |
Index. | |
ISBN: | 9781461485261 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Cornerstones, 2197-182X |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Differential Equations , Global differential geometry |
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Call number: | SPRINGER-2013-9781461482598:ONLINE Show nearby items on shelf |
Title: | Prolate Spheroidal Wave Functions of Order Zero [electronic resource] : Mathematical Tools for Bandlimited Approximation |
Author(s): |
Andrei Osipov Vladimir Rokhlin Hong Xiao |
Date: | 2013 |
Publisher: | Boston, MA : Springer US : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Prolate Spheroidal Wave Functions (PSWFs) are the eigenfunctions of the bandlimited operator in one dimension. As such, they play an important role in signal processing, Fourier analysis, and approximation theory. Whilehistorically the numerical eval uation of PSWFs presented serious difficulties, the developments of the last fifteen years or so made them as computationally tractable as any other class of special functions. As a result, PSWFs havebeen becoming a popular computational tool. The present book serves as a complete, self-contained resource for both theory and computation. It will be of interest to a wide range of scientists and engineers, from mathematiciansinterested in PSWF as an analytical tool to electrical engineers designing filters and antennas |
Note: | Springer eBooks |
Contents: | Introduction |
Mathematical and Numerical Preliminaries | |
Overview | |
Analysis of the Differential Operator | |
Analysis of the Integral Operator | |
Rational Approximations of PSWFs | |
Miscellaneous Properties of PSWFs | |
Asymptotic Analysis of PSWFs | |
Quadrature Rules and Interpolation via PSWFs | |
Numerical Algorithms | |
ISBN: | 9781461482598 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied Mathematical Sciences, 0066-5452 : v187 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Numerical analysis , Engineering mathematics |
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Call number: | SPRINGER-2013-9781461482086:ONLINE Show nearby items on shelf |
Title: | Distributions, Partial Differential Equations, and Harmonic Analysis [electronic resource] |
Author(s): |
Dorina Mitrea |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis. Thebook is written in a for mat suitable for a graduate course spanning either over one-semester, when the focus is primarily on the foundational aspects, or over a two-semester period that allows for the proper amount of time to coverall intended applications as well. It presents a balanced treatment of the topics involved, and contains a large number of exercises (upwards of two hundred, more than half of which are accompanied by solutions), which have beencarefully chosen to amplify the effect, and substantiate the power and scop e, of the theory of distributions. Graduate students, professional mathematicians, and scientifically trained people with a wide spectrum of mathematicalinterests will find this book to be a useful resource and complete self-study guide. Throughout, a spe cial effort has been made to develop the theory of distributions not as an abstract edifice but rather give the reader a chance tosee the rationale behind various seemingly technical definitions, as well as the opportunity to apply the newly developed too ls (in the natural build-up of the theory) to concrete problems in partial differential equations and harmonicanalysis, at the earliest opportunity |
Note: | Springer eBooks |
Contents: | Introduction |
Summary of Topological and Functional Analysis Results | |
Weak Derivatives | |
The Space D0() of Distributions | |
The Fourier Transform | |
The Space of Tempered Distributions | |
Fundamental Solution | |
The Laplace Operator | |
The Heat Operator | |
The Wave Operator | |
The Lame Operator | |
Fundamental Solutions for Other Operators | |
Hypoelliptic operators | |
Sobolev spaces | |
Appendix | |
References. | |
ISBN: | 9781461482086 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Functional analysis , Differential equations, partial , Potential theory (Mathematics) |
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Call number: | SPRINGER-2013-9781461479727:ONLINE Show nearby items on shelf |
Title: | Harmonic Analysis on Symmetric SpacesEuclidean Space, the Sphere, and the Poincar Upper Half-Plane [electronic resource] |
Author(s): |
Audrey Terras |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincar upper half plane. This book is intended for beginning graduate students inmathematics or researchers in phy sics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, andengineering. Many corrections, new topics, and updates have be en incorporated in this new edition. These include discussions of the work of P. Sarnak and others making progress on various conjectures on modular forms, the work of T.Sunada, Marie-France Vignras, Carolyn Gordon, and others on Mark Kac's question Can y ou hear the shape of a drum?, Ramanujan graphs, wavelets, quasicrystals, modular knots, triangle and quaternion groups, computations of Maasswaveforms, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summationformula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon tr ansform, non-Euclidean geometry on the Poincar upper half plane H or unit disc andapplications to microwave engineering, fundamental domains in H for discrete groups , tessellations of H from such discrete group actions, automorphic forms, the Selberg tra ce formula and its applications in spectral theory as wellas number theory |
Note: | Springer eBooks |
Contents: | Chapter1 Flat Space. Fourier Analysis on R^m |
1.1 Distributions or Generalized Functions | |
1.2 Fourier Integrals | |
1.3 Fourier Series and the Poisson Summation Formula | |
1.4 Mellin Transforms, Epstein and Dedekind Zeta Functions | |
1.5 Finite Symmetric Spaces, Wavelets, Quasicrystals, Weyls Criterion for Uniform Distribution | |
Chapter2 A Compact Symmetric Space | |
The Sphere | |
2.1 Fourier Analysis on the Sphere | |
2.2 O(3) and R^3. The Radon Transform | |
Chapter 3 The Poincar Upper Half | |
Plane | |
3.1 Hyperbolic Geometry | |
3.2 Harmonic Analysis on H | |
3.3 Fundamental Domains for | |
ISBN: | 9781461479727 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , Topological Groups , Harmonic analysis , Fourier analysis , Functions of complex variables , Functions, special |
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Call number: | SPRINGER-2013-9781461467861:ONLINE Show nearby items on shelf |
Title: | Principles of Musical Acoustics [electronic resource] |
Author(s): |
William M Hartmann |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Principles of Musical Acoustics focuses on the basic principles in the science and technology of music. Musical examples and specific musical instruments demonstrate the principles. The book begins with a study of vibrations andwaves, in that order. These topics constitute the basic physical properties of sound, one of two pillars supporting the science of musical acoustics. The second pillar is the human element, the physiological and psychological aspectsof acoustical science. The perceptual topics include loudness, pitch, tone color, and localization of sound. With these two pillars in place, it is possible to go in a variety of directions. The book treats in turn, the topics of roomacoustics, audio both analog and digital, broadcasting, and speec h. It ends with chapters on the traditional musical instruments, organized by family. The mathematical level of this book assumes that the reader is familiar withelementary algebra. Trigonometric functions, logarithms and powers also appear in the book, b ut computational techniques are included as these concepts are introduced, and there is further technical help in appendices |
Note: | Springer eBooks |
Contents: | Sound, Music, and Science |
Vibrations 1 | |
Vibrations 2 | |
Instrumentation | |
Sound Waves | |
Wave Properties | |
Standing Waves | |
Standing Waves in Pipes | |
Fourier Analysis and Synthesis | |
Sound Intensity | |
The Auditory System | |
Loudness Perception | |
Pitch | |
Localization of Sound | |
Sound Environments | |
Audio Transducers | |
Distortion and Noise | |
Audio Systems | |
Loudspeakers | |
Digital Audio | |
Broadcasting | |
Speech | |
Brass Musical Instruments | |
Woodwind Instruments | |
String Instruments | |
Percussion Instruments | |
Electronic Music | |
ISBN: | 9781461467861 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Undergraduate Lecture Notes in Physics, 2192-4791 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Neurobiology , Acoustics , Acoustics in engineering |
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Call number: | SPRINGER-2013-9781461466604:ONLINE Show nearby items on shelf |
Title: | Approximation Theory and Harmonic Analysis on Spheres and Balls [electronic resource] |
Author(s): |
Feng Dai Yuan Xu |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book containsmainstream material on the s ubject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part ofthe book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate studentsin analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewiczmultiplier theorem, the Riesz transform, and doubling weights are all familiar tools to re searchers in this area |
Note: | Springer eBooks |
Contents: | 1 Spherical Harmonics |
2 Convolution and Spherical Harmonic Expansion | |
3 Littlewood | |
Paley Theory and Multiplier Theorem | |
4 Approximation on the Sphere | |
5 Weighted Polynomial Inequalities | |
6 Cubature Formulas on Spheres | |
7 Harmonic Analysis Associated to Reflection Groups | |
8 Boundedness of Projection Operator and Cesro Means | |
9 Projection Operators and Cesro Means in L^p Spaces | |
10 Weighted Best Approximation by Polynomials | |
11 Harmonic Analysis on the Unit Ball | |
12 Polynomial Approximation on the Unit Ball | |
13 Harmonic Analysis on the Simplex | |
14 Applications | |
ISBN: | 9781461466604 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Fourier analysis , Functions, special |
Availability: | Click here to see Library holdings or inquire at
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Call number: | SPRINGER-2013-9781461460060:ONLINE Show nearby items on shelf |
Title: | Wavelets Made Easy [electronic resource] |
Author(s): |
Yves Nievergelt |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Originally published in 1999, Wavelets Made Easyoffers a lucid and concise explanation of mathematical wavelets.Written at the level of a first course in calculus and linear algebra, its accessible presentation is designedfor undergraduates in a vari ety of disciplinescomputer science, engineering, mathematics, mathematical sciencesas well as for practicing professionals in these areas. The presentsoftcover reprintretainsthecorrectionsfromthesecond printing (2001) andmakesthis uniquetext available to a wider audience. The first chapter startswith a description of the key features and applications of wavelets, focusing on Haar's wavelets but using onlyhigh-school mathematics. The next two chapters introduce one-, two-, and three-dimensional wavelets, with only the occasional use of matrix algebra. The second part of this book provides the foundations of least-squaresapproximation, the discrete Fourier transform, and Fourier series. The third part explains the Fourier transform and then demonstrates h ow to apply basic Fourier analysis to designing and analyzing mathematical wavelets. Particularattention is paid to Daubechies wavelets. Numerous exercises, a bibliography, and a comprehensive index combine to make this book an excellent text for the cla ssroom as well as a valuable resource for self-study |
Note: | Springer eBooks |
Contents: | Preface |
Outline | |
A. Algorithms for Wavelet Transforms | |
Haar's Simple Wavelets | |
Multidimensional Wavelets and Applications | |
Algorithms for Daubechies Wavelets | |
B. Basic Fourier Analysis | |
Inner Products and Orthogonal Projections | |
Discrete and Fast Fourier Transforms | |
Fourier Series for Periodic Functions | |
C. Computation and Design of Wavelets | |
Fourier Transforms on the Line and in Space | |
Daubechies Wavelets Design | |
Signal Representations with Wavelets. D. Directories | |
Acknowledgements | |
Collection of Symbols | |
Bibliography | |
Index. | |
ISBN: | 9781461460060 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Computer science Mathematics , Computer engineering |
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Location: | ONLINE |
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