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Call number: | TA350.B35523::1977 Show nearby items on shelf |
Title: | Solutions Manual to Accompany Vector Mechanics for Engineers : Dynamics |
Author(s): |
Ferdinand Pierre Beer 1915- E. Russell (Elwood Russell) Johnston 1925- |
Date: | 1977 |
Publisher: | McGraw - Hill |
Note: | 3rd. ed. |
ISBN: | 0070042829 |
Keywords: | Mechanics, Applied , Vector Analysis , Mechanics, Applied - Problems, Exercises, etc. , Dynamics |
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Call number: | TA350.B3552::1988 Show nearby items on shelf |
Title: | Vector mechanics for engineers: Dynamics |
Author(s): |
Ferdinand P. Beer E. Russell Johnston |
Date: | 1988 |
Edition: | 5th ed. |
Publisher: | New York : McGraw-Hill |
Size: | 459-1047 p |
Note: | part two of Vector mechanics for engineers |
Contents: | Kinematics of particles -- Kinetics of particles: Newton's second law -- Kinetics of particles: energy and momentum methods -- Systems of particles -- Kinematics of rigid bodies -- Plane motion of rigid bodies: forces and accelerations -- Plane moti on of rigid bodies: energy and momentum methods -- Kinetics of rigid bodies in three dimensions -- Mechanical vibrations -- Some useful definitions and properties of Vector algebra -- Moments of inertia of masses. |
ISBN: | 9780070799264 |
Keywords: | Mechanics, Applied. , Vector analysis , Mechanics, Applied, Problems, exercises |
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Call number: | TA350.B3552::1977 Show nearby items on shelf |
Title: | Vector Mechanics for Engineers: Statics and Dynamics |
Author(s): |
Ferdinand Pierre Beer 1915- E. Russell Johnston 1925- |
Date: | 1977 |
Publisher: | McGraw - Hill |
Note: | 3rd. ed. |
ISBN: | 0070042772 |
Keywords: | Mechanics, Applied , Vector Analysis , Mechanics, Applied - Problems, Exercises, etc. |
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Location: | MAIN |
Call number: | SPRINGER-2014-9783319053110:ONLINE Show nearby items on shelf |
Title: | Inequalities [electronic resource] : With Applications to Engineering |
Author(s): |
Michael J Cloud Byron C Drachman Leonid P Lebedev |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This book offers a concise introduction to mathematical inequalities for graduate students and researchers in the fields of engineering and applied mathematics. It begins by reviewing essential facts from algebra andcalculusandproceeds with a present ation of the central inequalities of applied analysis, illustrating a wide variety of practical applications. The text provides a gentle introduction to abstract spaces, such as metric, normed, andinner product spaces. It also provides full coverage of th e central inequalities of applied analysis, such as Young's inequality, the inequality of the means, Hlder's inequality, Minkowski's inequality, the CauchySchwarzinequality, Chebyshev's inequality, Jensen's inequality, and the triangle inequality. The sec ond edition features extended coverage of applications, including continuum mechanics and interval analysis. It also includes many additionalexamples and exercises with hints and full solutions that may appeal to upper-level undergraduate and graduate stu dents, as well asresearchers in engineering, mathematics, physics, chemistry, or any other quantitative science |
Contents: | Preface |
1. Basic Review and Elementary Facts | |
2. Methods from the Calculus | |
3. Some Standard Inequalities | |
4. Inequalities in Abstract Spaces | |
5. Some Applications | |
6. Inequalities for Differential Equations | |
7. Brief Introduction to Interval Analysis | |
Hints for Selected Problems | |
References | |
Appendix | |
ISBN: | 9783319053110 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functions, special , Engineering mathematics |
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Call number: | SPRINGER-2013-9781461458685:ONLINE Show nearby items on shelf |
Title: | Functional Analysis in Mechanics [electronic resource] |
Author(s): |
Leonid P Lebedev Iosif I Vorovich Michael J Cloud |
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 book offers a brief, practically complete, and relatively simple introduction to functional analysis. It also illustrates the application of functional analytic methods to the science of continuum mechanics. Abstract butpowerful mathematical not ions are tightly interwoven with physical ideas in the treatment of nontrivial boundary value problems for mechanical objects. This second edition includes more extended coverage of the classical andabstract portions of functional analysis. Taken togethe r, the first three chapters now constitute a regular text on applied functional analysis. This potential use of the book is supported by a significantly extended set of exerciseswith hints and solutions. A new appendix, providing a convenient listing of e ssential inequalities and imbedding results, has been added. The book should appeal to graduate students and researchers in physics, engineering, andapplied mathematics. Reviews of first edition: This book covers functional analysis and its application s to continuum mechanics. The presentation is concise but complete, and is intended for readers in continuum mechanics whowish to understand the mathematical underpinnings of the discipline. . . . Detailed solutions of the exercises are provided in an app endix. (LEnseignment Mathematique, Vol. 49 (1-2), 2003) The reader comes away with aprofound appreciation both of the physics and its importance, and of the beauty of the functional analytic method, which, in skillful hands, has the power to dissolve and clarify these difficult problems as peroxide does clotted blood.Numerous exercises. . .test the readers comprehension at every stage. Summing Up: Recommended. (F. E. J. Linton, Choice, September, 2003) |
Note: | Springer eBooks |
Contents: | Introduction |
Metric, Banach, and Hilbert Spaces | |
Mechanics Problems from the Functional Analysis Viewpoint | |
Some Spectral Problems of Mechanics | |
Elements of Nonlinear Functional Analysis | |
Summary of Inequalities and Imbeddings | |
Hints for Selected Problems | |
References | |
In Memoriam: Iosif I. Vorovich | |
Index | |
ISBN: | 9781461458685 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Differential equations, partial , Mechanics , Materials |
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Call number: | SPRINGER-2013-9781447148203:ONLINE Show nearby items on shelf |
Title: | Functional Analysis, Calculus of Variations and Optimal Control [electronic resource] |
Author(s): |
Francis Clarke |
Date: | 2013 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such asnonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis andincludes many novel elements as well as the stan dard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. Theauthor provides a comprehensive course on these subjects, from their inc eption through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximumprinciple, which appear here for the first time in a textbook. Other major themes include existen ce and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscositysolutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They a lso touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering.Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or secon d-year graduate level, on functional analysis, on the calculus of variations and optimalcontrol, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its ad vanced results in the calculus of variations and optimal control,its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth a |
Note: | Springer eBooks |
Contents: | Normed Spaces |
Convex sets and functions | |
Weak topologies | |
Convex analysis | |
Banach spaces | |
Lebesgue spaces | |
Hilbert spaces | |
Additional exercises for Part I | |
Optimization and multipliers | |
Generalized gradients | |
Proximal analysis | |
Invariance and monotonicity | |
Additional exercises for Part II | |
The classical theory | |
Nonsmooth extremals | |
Absolutely continuous solutions | |
The multiplier rule | |
Nonsmooth Lagrangians | |
Hamilton | |
Jacobi methods | |
Additional exercises for Part III | |
Multiple integrals | |
Necessary conditions | |
Existence and regularity | |
Inductive meth | |
ISBN: | 9781447148203 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v264 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Systems theory , Mathematical optimization |
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Call number: | SPRINGER-2012-9783642273056:ONLINE Show nearby items on shelf |
Title: | Complex Hamiltonian Dynamics [electronic resource] |
Author(s): |
Tassos Bountis Haris Skokos |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion.The role of nonlinear n ormal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena anddistinguish order from strongly and weakly chaoti c regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored inparticular in the concrete setting of one-dimensional Hamiltonian lat tices and physical applications in condensed matter systems. The self-contained and pedagogical approach is blended with a unique balance between mathematicalrigor, physics insights and concrete applications. End of chapter exercises and (more demanding) research oriented problems provide many opportunities to deepen the readers insights into specific aspects of the subject matter. Addressing a broad audience of graduate students, theoretical physicists and applied mathematicians, this text combines the b enefits of a reference work with those of a self-study guide for newcomers to the field |
Note: | Springer eBooks |
Contents: | Hamiltonian Systems of Few Degrees of Freedom |
Equilibrium Points, Periodic Orbits and Local Stability | |
Efficient Indicators of Stable and Chaotic Motion | |
FPU Recurrences and the Transition from Weak to Strong Chaos | |
Localization and Diffusion in Nonlinear 1 | |
Dimensional Lattices | |
The Statistical Mechanics of Quasi | |
Stationary States | |
Conclusion, Open Problems and Future Outlook | |
ISBN: | 9783642273056 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Series in Synergetics, 0172-7389 : v10 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Mathematical physics , Mechanics , Engineering |
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Call number: | SPRINGER-2012-9780817682651:ONLINE Show nearby items on shelf |
Title: | Nonlinear Partial Differential Equations for Scientists and Engineers [electronic resource] |
Author(s): |
Lokenath Debnath |
Date: | 2012 |
Edition: | Third Edition |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | An exceptionally complete overview of the latest developments in the field of PDEs. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something foreveryone here. Applied Mec hanics Review (Review of First Edition) Overall, it is a useful book for teaching, a rich source of examples, and I am happy to have it on a shelf of my library. UK Nonlinear News (Review of SecondEdition) The revised and enlarged third edition of this su ccessful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their various current applications. In an effort tomake the book more useful for a diverse readership, updated modern examples of ap plicationshave beenchosen from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics,acoustics, and wave propagation. The book gives thorough coverage of the derivation and solution methods for all fundamental nonlinear model equations, such as Kortewegde Vries, CamassaHolm, DegasperisProcesi,EulerPoincar, Toda lattice, Boussinesq, Burgers, Fisher, Whitham, nonlinear KleinGordon, sine-Gordon, nonlinear Schrdinger, nonlinear reaction-diffusion, and E ulerLagrange equations. Other topics and key featuresinclude: * Improved presentations of results, solution methods, and proofs. * Solitons, gravity-capillary solitary waves, and the Inverse Scattering Transform. * Special emphasis on compactons, intrinsi c localized modes, andnonlinear instability of dispersive waves with applications to water waves and wave breaking phenomena. * New section on the Lorenz nonlinear system, the Lorenz attractor, and deterministic chaos, and new examples of nonlinearquasi-h armonic waves, modulational instability, nonlinear lattices, and the Toda lattice equation. * Over 1000 worked-out examples and end-of-chapter exercises with expa |
Note: | Springer eBooks |
Contents: | Preface to the Third Edition |
Preface | |
Linear Partial Differential Equations | |
Nonlinear Model Equations and Variational Principles | |
First | |
Order, Quasi | |
Linear Equations and Method of Characteristics | |
First | |
Order Nonlinear Equations and Their Applications | |
Conservation Laws and Shock Waves | |
Kinematic Waves and Real | |
World Nonlinear Problems | |
Nonlinear Dispersive Waves and Whitham's Equations | |
Nonlinear Diffusion | |
Reaction Phenomena | |
Solitons and the Inverse Scattering Transform | |
The Nonlinear Schroedinger Equation and Solitary Waves | |
Nonlinear Klein | |
Gordon and Sine | |
Gordon | |
ISBN: | 9780817682651 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2012-9780817649449:ONLINE Show nearby items on shelf |
Title: | Stochastic Models, Information Theory, and Lie Groups, Volume 2 [electronic resource] : Analytic Methods and Modern Applications |
Author(s): |
Gregory S Chirikjian |
Date: | 2012 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The subjects of stochastic processes, information theory, and Lie groups are usually treated separately from each other. This unique two-volume set presents these topics in a unified setting, thereby building bridges betweenfields that are rarely stu died by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, andgroup-theoretic concepts in the modeling of physical p henomena. Volume 1 establishes the geometric and statistical foundations required to understand the fundamentals of continuous-time stochastic processes, differential geometry, andthe probabilistic foundations of information theory. Volume 2 delves deeper into relationships between these topics, including stochastic geometry, geometric aspects of the theory of communications and coding, multivariate statisticalanalysis, and error propagation on Lie groups. Key features and topics of Volume 2: * The author reviews the concept ofandfunctions and integration onLie groups with many concrete examples. * Extensive exercises andmotivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes on Lie groups or geometric aspects of probability and statistics. *Specific application areas are explored,including biomolecular statistical mechanics and information-driven motion in robotics. * The concrete presentation style makes it easy for readers to obtain numeri cal solutions for their own problems the emphasis is on how tocalculate quantities rather than how to prove theorems. * Modern problems at the interface of mechanics, control theory, and communications are handled in a unified framework and multiple direc tions for future research are explored.Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practition |
Note: | Springer eBooks |
Contents: | Lie Groups I: Introduction and Examples |
Lie Groups II: Differential Geometric Properties | |
Lie Groups III: Integration, Convolution, and Fourier Analysis | |
Variational Calculus on Lie Groups | |
Statistical Mechanics and Ergodic Theory | |
Parts Entropy and the Principal Kinematic Formula | |
Estimation and Multivariate Analysis in R^n | |
Information, Communication, and Group Therapy | |
Algebraic and Geometric Coding Theory | |
Information Theory on Lie Groups | |
Stochastic Processes on Lie Groups | |
Locomotion and Perception as Communication over Principal Fiber Bundles and A Survey of Addi | |
ISBN: | 9780817649449 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied and Numerical Harmonic Analysis |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Global differential geometry , Distribution (Probability theory) , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2010-9783642053702:ONLINE Show nearby items on shelf |
Title: | Mechanics [electronic resource] : From Newton's Laws to Deterministic Chaos |
Author(s): |
Florian Scheck |
Date: | 2010 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book covers all topics in mechanics from elementary Newtonian mechanics, the principles of canonical mechanics and rigid body mechanics to relativistic mechanics and nonlinear dynamics. It was among the first textbooks toinclude dynamical system s and deterministic chaos in due detail. As compared to the previous editions the present fifth edition is updated and revised with more explanations, additional examples and sections on Noether's theorem.Symmetries and invariance principles, the basic ge ometric aspects of mechanics as well as elements of continuum mechanics also play an important role. The book will enable the reader to develop general principles from which equationsof motion follow, to understand the importance of canonical mechanics an d of symmetries as a basis for quantum mechanics, and to get practice in using general theoretical concepts and tools that are essential for all branches ofphysics. The book contains more than 120 problems with complete solutions, as well as some practica l examples which make moderate use of personal computers. This will be appreciated in particular by students using this textbook toaccompany lectures on mechanics. The book ends with some historical notes on scientists who made important contributions to the development of mechanics |
Note: | Springer eBooks |
Contents: | Elementary Newtonian Mechanics |
The Principles of Canonical Mechanics | |
The Mechanics of Rigid Bodies | |
Relativistic Mechanics | |
Geometric Aspects of Mechanics | |
Stability and Chaos | |
Continuous Systems | |
Exercises | |
Solution of Exercises | |
ISBN: | 9783642053702 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Physics, 1868-4513 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Differentiable dynamical systems , Mathematics , Mathematical physics , Mechanics , Mechanics, applied |
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Call number: | SPRINGER-2010-9783642034343:ONLINE Show nearby items on shelf |
Title: | Classical Mechanics [electronic resource] : Systems of Particles and Hamiltonian Dynamics |
Author(s): |
Walter Greiner |
Date: | 2010 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This textbook Classical Mechanics provides a complete survey on all aspects of classical mechanics in theoretical physics. An enormous number of worked examples and problems show students how to apply the abstract principles torealistic problems. The textbook covers Newtonian mechanics in rotating coordinate systems, mechanics of systems of point particles, vibrating systems and mechanics of rigid bodies. It thoroughly introduces and explains the Lagrangeand Hamilton equations and the Hamilton-Jacobi theory. A large section on nonlinear dynamics and chaotic behavior of systems takes Classical Mechanics to newest development in physics. The new edition is completely revised and updated.New exercises and new sections in canonical transformation and Ham iltonian theory have been added |
Note: | Springer eBooks |
Contents: | Part I. Newtonian mechanics in moving co |
ordinate systems | |
Newton's Equations in a Rotating Coordinate System | |
Free fall on the rotating earth | |
Foucault's pendulum | |
Part II. Mechanics of Particle Systems | |
Degrees of Freedom | |
Centre of gravity. Mechanical fundamental quantities of systems of mass points | |
Part III. Vibrating systems | |
Vibrations of coupled mass points | |
The vibrating string | |
Fourier series | |
The vibrating membrane | |
Part IV. Mechanics of Rigid Bodies | |
Rotation about fixed axis | |
Rotation about a point. Theory of the top | |
Part V. Lagrange equations | |
Gen | |
ISBN: | 9783642034343 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Differentiable dynamical systems , Mathematics , Mathematical physics , Mechanics , Mechanics, applied |
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Call number: | SPRINGER-2010-9780817646752:ONLINE Show nearby items on shelf |
Title: | Distributions [electronic resource] : Theory and Applications |
Author(s): |
J.J Duistermaat J.A.C Kolk |
Date: | 2010 |
Edition: | 1 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differentialequations and Fourier a nalysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. Throughout the book, methods are developed to deal with formal calculations involving functions, series,and integrals that cannot be mathematically justified within the classical framework. Key features: Many examples, exercises, hints, and solutions guide the reader throughout the text. Includes an introduction to distributions,differentiation, convergence, convolution, the Fourier transform, and spaces of distributions having special properties. Original proofs, which may be difficult to locate elsewhere, are given for many well-known results. TheFourier transform is transparently treated and applied to provide a new proof of the Kernel Theorem , which in turn is used to efficiently derive numerous important results. The systematic use of pullback and pushforward introducesconcise notation. Emphasizes the role of symmetry in obtaining short arguments and investigates distributions that are inv ariant under the actions of various groups of transformations. Distributions: Theory and Applications isaimed at advanced undergraduates and graduate students in mathematics, theoretical physics, and engineering, who will find this textbook a welcome intr oduction to the subject, requiring only a minimal mathematical background. The workmay also serve as an excellent self-study guide for researchers who use distributions in various fields |
Note: | Springer eBooks |
Contents: | Preface |
Motivation | |
Test Functions | |
Distributions | |
Differentiation of Distributions | |
Convergence of Distributions | |
Taylor Expansion in Several Variables | |
Localization | |
Distributions with Compact Support | |
Multiplication by Functions | |
Transposition, Pullback and Push forward | |
Convolution of Distributions | |
Fundamental Solutions | |
Fractional Integration and Differentiation | |
Fourier Transformation | |
Fourier Series | |
Fundamental Solutions and Fourier Transformation | |
Supports and Fourier Transformation | |
Sobolev Spaces | |
Appendix: Results from Measure Theory in the C | |
ISBN: | 9780817646752 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Cornerstones |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Differential Equations , Differential equations, partial |
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Call number: | SPRINGER-2010-9780387709147:ONLINE Show nearby items on shelf |
Title: | Functional Analysis, Sobolev Spaces and Partial Differential Equations [electronic resource] |
Author(s): |
Haim Brezis |
Date: | 2010 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Uniquely, this book presents a coherent, concise and unified way of combining elements from two distinct worlds, functional analysis (FA) and partial differential equations (PDEs), and is intended for students who have agood background in real analys is. This text presents a smooth transition from FA to PDEs by analyzing in great detail the simple case of one-dimensional PDEs (i.e., ODEs), a more manageable approach for the beginner. Although there aremany books on functional analysis and many on PDEs , this is the first to cover both of these closely connected topics. Moreover, the wealth of exercises and additional material presented, leads the reader to the frontier of research.This book has its roots in a celebrated course taught by the author for many years and is a completely revised, updated, and expanded English edition of the important Analyse Fonctionnelle (1983). Since the French book was firstpublished, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chin ese. The English version is a welcome addition to this list. The first part of the text deals with abstract results in FA and operatortheory. The second part is concerned with the study of spaces of functions (of one or more real variables) having specifi c differentiability properties, e.g., the celebrated Sobolev spaces, which lie at the heart of the modern theoryof PDEs. The Sobolev spaces occur in a wide range of questions, both in pure and applied mathematics, appearing in linear and nonlinear PDEs wh ich arise, for example, in differential geometry, harmonic analysis, engineering, mechanics,physics etc. and belong in the toolbox of any graduate student studying analysis |
Note: | Springer eBooks |
Contents: | Preface |
1. The HahnBanach Theorems. Introduction to the Theory of Conjugate Convex Functions | |
2. The Uniform Boundedness Principle and the Closed Graph Theorem. Unbounded Operators. Adjoint. Characterization of Surjective Operators | |
3. Weak Topologies. Reflexive Spaces. Separable Spaces. Uniform Convexity | |
4. L^p Spaces | |
5. Hilbert Spaces | |
6. Compact Operators. Spectral Decomposition of Self | |
Adjoint Compact Operators | |
7. The HilleYosida Theorem | |
8. Sobolev Spaces and the Variational Formulation of Boundary Value Problems in One Dimension | |
9. Sobolev Spaces and the Vari | |
ISBN: | 9780387709147 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Differential equations, partial |
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Call number: | SPRINGER-2009-9780387877655:ONLINE Show nearby items on shelf |
Title: | Introduction to the Foundations of Applied Mathematics [electronic resource] |
Author(s): |
Mark H Holmes |
Date: | 2009 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The objective of this textbook is the construction, analysis, and interpretation of mathematical models to help us understand the world we live in. Rather than follow a case study approach it develops the mathematical and physicalideas that are funda mental in understanding contemporary problems in science and engineering. Science evolves, and this means that the problems of current interest continually change. What does not change as quickly is the approachused to derive the relevant mathematical mod els, and the methods used to analyze the models. Consequently, this book is written in such a way as to establish the mathematical ideas underlying model development independently of aspecific application. This does not mean applications are not considere d, they are, and connections with experiment are a staple of this book. The book, as well as the individual chapters, is written in such a way that the materialbecomes more sophisticated as you progress. This provides some flexibility in how the book is u sed, allowing consideration for the breadth and depth of the material covered. Moreover, there are a wide spectrum of exercises and detailedillustrations that significantly enrich the material. Students and researchers interested in mathematical modelling in mathematics, physics, engineering and the applied sciences will find this text useful |
Note: | Springer eBooks |
Contents: | Dimensional Analysis |
Perturbation Methods | |
Kinetics | |
Diffusion | |
Traffic Flow | |
Continuum Mechanics: One Spatial Dimension | |
Elastic and Viscoelastic Materials | |
Continuum Mechanics: Three Spatial Dimensions | |
Fluids | |
Taylor's Theorem | |
Fourier Analysis | |
Stochastic Differential Equations | |
Identities | |
Equations for a Newtonian Fluid | |
References | |
Index | |
ISBN: | 9780387877655 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Texts in Applied Mathematics, 0939-2475 : v56 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Mathematical physics , Mechanics |
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Call number: | SPRINGER-2008-9780387759340:ONLINE Show nearby items on shelf |
Title: | The Mathematical Theory of Finite Element Methods [electronic resource] |
Author(s): |
Susanne C Brenner L. Ridgway Scott |
Date: | 2008 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. The third edition contains four new sections: the BDDC domain decompositionpreconditioner, convergence analysis of an adaptive algorithm, interior penalty methods and Poincara\'e-Friedrichs inequalities for piecewise W^1_p functions. New exercises have also been added throughout. The initial chapter providesan introducton to the entire subject, developed i n the one-dimensional case. Four subsequent chapters develop the basic theory in the multidimensional case, and a fifth chapter presents basic applications of this theory. Subsequentchapters provide an introduction to: - multigrid methods and domain decom position methods - mixed methods with applications to elasticity and fluid mechanics - iterated penalty and augmented Lagrangian methods - variational crimesincluding nonconforming and isoparametric methods, numerical integration and interior penalty meth ods - error estimates in the maximum norm with applications to nonlinear problems - error estimators, adaptive meshes and convergenceanalysis of an adaptive algorithm - Banach-space operator-interpolation techniques The book has proved useful to mathemati cians as well as engineers and physical scientists. It can be used for a course that provides an introduction tobasic functional analysis, approximation theory and numerical analysis, while building upon and applying basic techniques of real variable theo ry. It can also be used for courses that emphasize physical applications or algorithmicefficiency. Reviews of earlier editions: This book represents an important contribution to the mathematical literature of finite elements. It is both a well-done text a nd a good reference. (Mathematical Reviews, 1995) This is anexcellent, though demanding, introduction to key mathematical topics in the finite element method, and at the same time a valuable refere |
Note: | Springer eBooks |
Contents: | Preface(3rdEd) |
Preface(2ndEd) | |
Preface(1stED) | |
Basic Concepts | |
Sobolev Spaces | |
Variational Formulation of Elliptic Boundary Value Problems | |
The Construction of a Finite Element of Space | |
Polynomial Approximation Theory in Sobolev Spaces | |
n | |
Dimensional Variational Problems | |
Finite Element Multigrid Methods | |
Additive Schwarz Preconditioners | |
Max | |
norm Estimates | |
Adaptive Meshes | |
Variational Crimes | |
Applications to Planar Elasticity | |
Mixed Methods | |
Iterative Techniques for Mixed Methods | |
Applications of Operator | |
Interpolation Theory | |
References | |
Index | |
ISBN: | 9780387759340 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Texts in Applied Mathematics, 0939-2475 : v15 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Computer science Mathematics , Engineering , Mechanics, applied |
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Call number: | SPRINGER-2007-9780817645601:ONLINE Show nearby items on shelf |
Title: | Linear Partial Differential Equations for Scientists and Engineers [electronic resource] |
Author(s): |
Tyn Myint-U Lokenath Debnath |
Date: | 2007 |
Edition: | Fourth Edition |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena. PDEs have a wide range of interesting and important applicationsin every branch of app lied mathematics, physics, and engineering, including fluid dynamics, elasticity, and optics. This significantly expanded fourth edition is designed as an introduction to the theory and applications of linearPDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new materialthat is not usually covered in similar texts and reference books, incl uding conservation laws, the spherical wave equation, the cylindrical wave equation, higher-dimensional boundary-value problems, the finite element method,fractional partial differential equations, and nonlinear partial differential equations with applica tions. Key features include: * Applications to a wide variety of physical problems in numerous interdisciplinary areas * Over 900worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biol ogy, and chemistry * Historical comments on partial differential equations * Solutions and hints to selectedexercises * A comprehensive bibliographycomprised of many standard texts and reference books, as well as a set of selected classic and recent paper sfor readers interested in learning more about the modern treatment of the subjectLinear Partial Differential Equations for Scientists and Engineers, Fourth Edition will primarily serve as a textbook for the first two courses in PDEs, or in a course on ad vanced engineering mathematics. The book may also be used as areference for graduate students, researchers, and professionals in modern applied mathematics, mathematical physics, and engineering |
Note: | Springer eBooks |
Contents: | Preface to the Fourth Edition |
Preface to the Third Edition | |
Introduction | |
First | |
Order, Quasi | |
Linear Equations and Method of Characteristics | |
Mathematical Models | |
Classification of Second | |
Order Linear Equations | |
The Cauchy Problem and Wave Equations | |
Fourier Series and Integrals with Applications | |
Method of Separation of Variables | |
Eigenvalue Problems and Special Functions | |
Boundary | |
Value Problems and Applications | |
Higher | |
Dimensional Boundary | |
Value Problems | |
Green's Functions and Boundary | |
Value Problems | |
Integral Transform Methods with Applications | |
Nonlinear Partia | |
ISBN: | 9780817645601 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial , Computer science , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2007-9780387491592:ONLINE Show nearby items on shelf |
Title: | An Introduction to Scientific Computing [electronic resource] Twelve Computational Projects Solved with MATLAB |
Author(s): |
Ionut Danaila Pascal Joly Sidi Mahmoud Kaber Marie Postel |
Date: | 2007 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book provides twelve computational projects aimed at numerically solving problems from a broad range of applications including Fluid Mechanics, Chemistry, Elasticity, Thermal Science, Computer Aided Design, Signal and ImageProcessing. For each p roject the reader is guided through the typical steps of scientific computing from physical and mathematical description of the problem, to numerical formulation and programming and finally to critical discussionof numerical results. Considerable emphasis is placed on practical issues of computational methods. The last section of each project contains the solutions to all proposed exercises and guides the reader in using the MATLAB scripts.The mathematical framework provides a basic foundation in the subj ect of numerical analysis of partial differential equations and main discretization techniques, such as finite differences, finite elements, spectral methods andwavelets). The book is primarily intended as a graduate-level text in applied mathematics, but it may also be used by students in engineering or physical sciences. It will also be a useful reference for researchers and practicingengineers |
Note: | Springer eBooks |
Contents: | Numerical Approximation of Model Partial Differential Equations |
Nonlinear Differential Equations: Application to Chemical Kinetics | |
Polynomial Approximation | |
Solving an Advection | |
Diffusion Equation by A Finite Element Method | |
Solving A Differential Equation by A Spectral Method | |
Signal Processing: Multiresolution Analysis | |
Elasticity: Elastic Deformation of A Thin Plate | |
Domain Decomposition Using A Schwarz Method | |
Geometrical Design: Bezier Curves and Surfaces | |
Gas Dynamics: Riemann Problem and Discontinuous Solutions: Application to The Shock Tube Problem | |
Thermal Engineer | |
ISBN: | 9780387491592 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science Mathematics , Numerical analysis , Mathematical physics |
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Call number: | SPRINGER-2007-9780387489476:ONLINE Show nearby items on shelf |
Title: | Applied Linear Algebra and Matrix Analysis [electronic resource] |
Author(s): |
Thomas S Shores |
Date: | 2007 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, AppliedLinear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text isindependent of specific hardware or software pl atforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises. The student will develop a solid foundation in thefollowing topics *Gaussian elimination and other operations with matric es *basic properties of matrix and determinant algebra *standard Euclidean spaces, both real and complex *geometrical aspects of vectors, such as norm, dot product,and angle *eigenvalues, eigenvectors, and discrete dynamical systems *general norm and inne r-product concepts for abstract vector spaces For many students, the tools of matrix and linear algebra will be as fundamental in theirprofessional work as the tools of calculus thus it is important to ensure that students appreciate the utility and beaut y of these subjects as well as the mechanics. By including applied mathematics and mathematical modeling, this newtextbook will teach students how concepts of matrix and linear algebra make concrete problems workable. Thomas S. Shores is Professor of Math ematics at the University of Nebraska, Lincoln, where he has received awards for his teaching.His research touches on group theory, commutative algebra, mathematical modeling, numerical analysis, and inverse theory |
Note: | Springer eBooks |
Contents: | Preface |
Linear Systems of Equations | |
Matrix Algebra | |
Vector Spaces | |
Geometrical Aspects of Standard Spaces | |
The Eigenvalue Problem | |
Geometrical Aspects of Abstract Spaces | |
Table of Symbols | |
Answers to Selected Exercises | |
References | |
Index | |
ISBN: | 9780387489476 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Undergraduate Texts in Mathematics, 0172-6056 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory |
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Call number: | SPRINGER-2007-9780387377483:ONLINE Show nearby items on shelf |
Title: | Variational Principles in Physics [electronic resource] |
Author(s): |
Jean-Louis Basdevant |
Date: | 2007 |
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: | Optimization under constraints is an essential part of everyday life. Indeed, we routinely solve problems by striking a balance between contradictory interests, individual desires and material contingencies. This notion ofequilibrium was dear to thin kers of the enlightenment, as illustrated by Montesquieus famous formulation: In all magistracies, the greatness of the power must be compensated by the brevity of the duration. Astonishingly, naturallaws are guided by a similar principle. Variational pri nciples have proven to be surprisingly fertile. For example, Fermat used variational methods to demonstrate that light follows the fastest route from one point to another, an ideawhich came to be known as Fermats principle, a cornerstone of geometrical op tics. Variational Principles in Physics explains variational principles and charts their use throughout modern physics. The heart of the book is devoted tothe analytical mechanics of Lagrange and Hamilton, the basic tools of any physicist. Prof. Basdevant also offers simple but rich first impressions of Einsteins General Relativity, Feynmans Quantum Mechanics, and more revealingand amazing interconnections between various fields of physics. A graduate of the Ecole Normale Superieure, Jean-Louis Basdevant is Professor and former Chair of the Department of Physics at the Ecole Polytechnique, and Director ofResearch for the CNRS. Specializing in the theoretical physics of elementary particles, quantum field theory and astrophysics, Prof. Basdevant works in t he Leprince-Ringuet Laboratory at the Ecole Polytechnique |
Note: | Springer eBooks |
Contents: | Foreword |
Variational Principles | |
The Analytical Mechanics of Lagrange | |
The Canonical Formalism of Hamilton | |
The Lagrangian Theory of Fields | |
Movement in a Curved Space | |
Feynmans Path Integrals in Quantum Mechanics | |
Solutions to Exercises | |
Bibliography | |
Index | |
ISBN: | 9780387377483 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematical optimization , Mathematical physics , Mechanics , Mechanics, applied |
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Call number: | SPRINGER-2005-9780817644185:ONLINE Show nearby items on shelf |
Title: | Nonlinear Partial Differential Equations for Scientists and Engineers [electronic resource] |
Author(s): |
Lokenath Debnath |
Date: | 2005 |
Edition: | Second Edition |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | An exceptionally complete overview. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here. This reviewer feels that it is avery hard act to follow, a nd recommends it strongly. [This book] is a jewel. ---Applied Mechanics Review (Review of First Edition) This expanded and revised second edition is a comprehensive and systematic treatment of linear andnonlinear partial differential equations and their v aried applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from areas of fluid dynamics, gas dynamics,plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions are presented, along with their physical significance, making the book more useful for adiverse readership. Topics and key features: * Thorough coverage of derivation and methods of sol utions for all fundamental nonlinear model equations, which include Korteweg--de Vries, Boussinesq, Burgers, Fisher, nonlinearreaction-diffusion, Euler--Lagrange, nonlinear Klein--Gordon, sine-Gordon, nonlinear Schrdinger, Euler, Water Waves, Camassa and Holm, Johnson, Davey-Stewartson, Kolmogorov, Petrovsky and Piscunov, Kadomtsev and Petviashivilli,Benjamin, Bona and Mahony, Harry Dym, Lax, and Whitman equations * Systematic presentation and explanation of conservation laws, weak solutions, and shock wa ves * Solitons, compactons, intrinsic localized modes, and the InverseScattering Transform * Special emphasis on nonlinear instability of dispersive waves with applications to water waves * Over 600 worked examples and end-of-chapter exercises with hints and selected solutions New features of the SecondEdition include: * Improved presentation of results, methods of solutions, and proofs * New section on Sturm--Liouville systems and their fundamental |
Note: | Springer eBooks |
Contents: | Linear Partial Differential Equations |
Nonlinear Model Equations and Variational Principles | |
First | |
Order, Quasi | |
Linear Equations and Method of Characteristics | |
First | |
Order Nonlinear Equations and Their Applications | |
Conservation Laws and Shock Waves | |
Kinematic Waves and Real | |
World Nonlinear Problems | |
Nonlinear Dispersive Waves and Whithams Equations | |
Nonlinear Diffusion | |
Reaction Phenomena | |
Solitons and the Inverse Scattering Transform | |
The Nonlinear Schrdinger Equation and Solitary Waves | |
Nonlinear Klein | |
Gordon and Sine | |
Gordon Equations | |
Asymptotic Methods and Nonlin | |
ISBN: | 9780817644185 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2005-9780387276496:ONLINE Show nearby items on shelf |
Title: | Nonlinear Problems of Elasticity [electronic resource] |
Author(s): |
Stuart S Antman |
Date: | 2005 |
Edition: | Second Edition |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This second edition is an enlarged, completely updated, and extensively revised version of the authoritative first edition. It is devoted to the detailed study of illuminating specific problems of nonlinear elasticity, directedtoward the scientist, e ngineer, and mathematician who wish to see careful treatments of precisely formulated problems. Special emphasis is placed on the role of nonlinear material response. The mathematical tools from nonlinearanalysis are given self-contained presentations whe re they are needed. This book begins with chapters on (geometrically exact theories of) strings, rods, and shells, and on the applications of bifurcation theory and the calculus ofvariations to problems for these bodies. The book continues with chapters o n tensors, three-dimensional continuum mechanics, three-dimensional elasticity, large-strain plasticity, general theories of rods and shells, and dynamicalproblems. Each chapter contains a wealth of interesting, challenging, and tractable exercises. Revie ws of the first edition: ``A scholarly work, it is uncompromising in its approach to model formulation, while achieving strikinggenerality in the analysis of particular problems. It will undoubtedly become a standard research reference in elasticity but w ill be appreciated also by teachers of both solid mechanics and applied analysis for its clear derivation ofequations and wealth of examples.'' --- J. M. Ball, (Bulletin of the American Mathematical Society), 1996. ``It is destined to become a standard re ference in the field which belongs on the bookshelf of anyone working on the applicationof mathematics to continuum mechanics. For graduate students, it provides a fascinating introduction to an active field of mathematical research.'' --- M. Renardy, (SI AM Review), 1995. ``The monograph is a masterpiece for writing amodern theoretical treatise on a field of natural sciences. It is highly recommended to all scientists, engineers and mathematicians inter |
Note: | Springer eBooks |
Contents: | Preface |
Background | |
The Equations of Motion for Extensible Strings | |
Elementary Problems for Elastic Strings | |
Planar Steady | |
State Problems for Elastic Rods | |
Introduction to Bifurcation Theory and it's Applications to Elasticity | |
Global Bifurcation Problems for Strings and Rods | |
Variational Methods | |
Theory of Rods Deforming in Space | |
Spatial Problems for Rods | |
Axisymmetric Equilibria of Shells | |
Tensors | |
3 | |
Dimensional Continuum | |
3 | |
Dimensional Theory of Nonlinear Elasticity | |
Problems in Nonlinear Elasticity | |
Large | |
Strain Plasticity | |
General Theories of Rods | |
Gene | |
ISBN: | 9780387276496 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied Mathematical Sciences, 0066-5452 : v107 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Mathematical physics |
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Call number: | SPRINGER-2003-9781461200475:ONLINE Show nearby items on shelf |
Title: | Perturbation Methods for Differential Equations |
Author(s): |
Bhimsen K Shivamoggi |
Date: | 2003 |
Size: | 1 online resource (354 p.) |
Note: | 10.1007/978-1-4612-0047-5 |
Contents: | 1 Asymptotic Series and Expansions -- 1.1 Introduction -- 1.2 Taylor Series Expansions -- 1.3 Gauge Functions -- 1.4 Asymptotic Series and Expansions -- 1.5 Asymptotic Solutions of Differential Equations -- 1.6 Exercises -- 2 Regular |
Perturbation Methods -- 2.1 Introduction -- 2.2 Algebraic Equations -- 2.3 Ordinary Differential Equations -- 2.4 Partial Differential Equations -- 2.5 Applications to Fluid Dynamics: Decay of a Line Vortex -- 2.6 Exercises -- 2.7 | |
Appendix. Review of Partial Differential Equations -- 3 The Method of Strained Coordinates/Parameters -- 3.1 Introduction -- 3.2 Poincaré-Lindstedt-Lighthill Method of Perturbed Eigenvalues -- 3.3 Eigenfunction Expansion Method -- 3.4 | |
Lighthill’s Method of Shifting Singularities -- 3.5 Pritulo’s Method of Renormalization -- 3.6 Wave Propagation in an Inhomogeneous Medium -- 3.7 Applications to Solid Mechanics: Nonlinear Buckling of Elastic Columns -- 3.8 | |
Applications to Fluid Dynamics -- 3.9 Applications to Plasma Physics -- 3.10 Limitations of the Method of Strained Parameters -- 3.11 Exercises -- 3.12 Appendix 1. Fredholm’s Alternative Theorem -- 3.13 Appendix 2. Floquet Theory -- | |
3.14 Appendix 3. Bifurcation Theory -- 4 Method of Averaging -- 4.1 Introduction -- 4.2 Krylov-Bogoliubov Method of Averaging -- 4.3 Krylov-Bogoliubov-Mitropolski Generalized Method of Averaging -- 4.4 Whitham’s Averaged Lagrangian | |
Method -- 4.5 Hamiltonian Perturbation Method -- 4.6 Applications to Fluid Dynamics: Nonlinear Evolution of Modulated Gravity Wave Packet on the Surface of a Fluid -- 4.7 Exercises -- 4.8 Appendix 1. Review of Calculus of Variations -- | |
4.9 Appendix 2. Hamilton-Jacobi Theory -- 5 The Method of Matched Asymptotic Expansions -- 5.1 Introduction -- 5.2 Physical Motivation -- 5.3 The Inner and Outer Expansions -- 5.4 Hyperbolic Equations -- 5.5 Elliptic Equations -- 5.6 | |
Parabolic Equations -- 5.7 Interior Layers -- 5.8 Latta’s Method of Composite Expansions -- 5.9 Turning Point Problems -- 5.10 Applications to Fluid Dynamics: Boundary-Layer Flow Past a Flat Plate -- 5.11 Exercises -- 5.12 Appendix 1. | |
Initial-Value Problem for Partial Differential Equations -- 5.13 Appendix 2. Review of Nonlinear Hyperbolic Equations -- 6 Method of Multiple Scales -- 6.1 Introduction -- 6.2 Differential Equations with Constant Coefficients -- 6.3 | |
Struble’s Method -- 6.4 Differential Equations with Slowly Varying Coefficients -- 6.5 Generalized Multiple-Scale Method -- 6.6 Applications to Solid Mechanics: Dynamic Buckling of a Thin Elastic Plate -- 6.7 Applications to Fluid | |
Dynamics -- 6.8 Applications to Plasma Physics -- 6.9 Exercises -- 7 Miscellaneous Perturbation Methods -- 7.1 A Quantum-Field-Theoretic Perturbative Procedure -- 7.2 A Perturbation Method for Linear Stochastic Differential Equations | |
-- 7.3 Exercises | |
ISBN: | 9781461200475 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Differential equations , Applied mathematics , Engineering mathematics , Computer mathematics , Computational intelligence , Mathematics , Ordinary Differential Equations , Computational Mathematics and Numerical Analysis , Applications of Mathematics , Computational Intelligence |
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Call number: | SPRINGER-2002-9780817681302:ONLINE Show nearby items on shelf |
Title: | A Distributional Approach to Asymptotics Theory and Applications |
Author(s): |
Ricardo Estrada |
Date: | 2002 |
Edition: | Second Edition |
Size: | 1 online resource (454 p.) |
Note: | 10.1007/978-0-8176-8130-2 |
Contents: | 1 Basic Results in Asymptotics -- 1.1 Introduction -- 1.2 Order Symbols -- 1.3 Asymptotic Series -- 1.4 Algebraic and Analytic Operations -- 1.5 Existence of Functions with a Given Asymptotic Expansion -- 1.6 Asymptotic Power Series |
in a Complex Variable -- 1.7 Asymptotic Approximation of Partial Sums -- 1.8 The Euler-Maclaurin Summation Formula -- 1.9 Exercises -- 2 Introduction to the Theory of Distributions -- 2.1 Introduction -- 2.2 The Space of Distributions | |
D? -- 2.3 Algebraic and Analytic Operations -- 2.4 Regularization, Pseudofunction and Hadamard Finite Part -- 2.5 Support and Order -- 2.6 Homogeneous Distributions -- 2.7 Distributional Derivatives of Discontinuous Functions -- 2.8 | |
Tempered Distributions and the Fourier Transform -- 2.9 Distributions of Rapid Decay -- 2.10 Spaces of Distributions Associated with an Asymptotic Sequence -- 2.11 Exercises -- 3 A Distributional Theory for Asymptotic Expansions -- 3.1 | |
Introduction -- 3.2 The Taylor Expansion of Distributions -- 3.3 The Moment Asymptotic Expansion -- 3.4 Expansions in the Space P? -- 3.5 Laplace’s Asymptotic Formula -- 3.6 The Method of Steepest Descent -- 3.7 Expansion of | |
Oscillatory Kernels -- 3.8 Time-Domain Asymptotics -- 3.9 The Expansion of f (?x) as ? ? ? in Other Cases -- 3.10 Asymptotic Separation of Variables -- 3.11 Exercises -- 4 Asymptotic Expansion of Multidimensional Generalized Functions | |
-- 4.1 Introduction -- 4.2 Taylor Expansion in Several Variables -- 4.3 The Multidimensional Moment Asymptotic Expansion -- 4.4 Laplace’s Asymptotic Formula -- 4.5 Fourier Type Integrals -- 4.6 Time-Domain Asymptotics -- 4.7 Further | |
Examples -- 4.8 Tensor Products and Partial Asymptotic Expansions -- 4.9 An Application in Quantum Mechanics -- 4.10 Expansion of Kernels of the Type f (?x, x) -- 4.11 Exercises -- 5 Asymptotic Expansion of Certain Series Considered by | |
Ramanujan -- 5.1 Introduction -- 5.2 Basic Formulas -- 5.3 Lambert Type Series -- 5.4 Distributionally Small Sequences -- 5.5 Multiple Series -- 5.6 Unrestricted Partitions -- 5.7 Exercises -- 6 Cesàro Behavior of Distributions -- 6.1 | |
Introduction -- 6.2 Summability of Series and Integrals -- 6.3 The Behavior of Distributions in the (C) Sense -- 6.4 The Cesàro Summability of Evaluations -- 6.5 Parametric Behavior -- 6.6 Characterization of Tempered Distributions -- | |
6.7 The Space K? -- 6.8 Spherical Means -- 6.9 Existence of Regularizations -- 6.10 The Integral Test -- 6.11 Moment Functions -- 6.12 The Analytic Continuation of Zeta Functions -- 6.13 Fourier Series -- 6.14 Summability of | |
Trigonometric Series -- 6.15 Distributional Point Values of Fourier Series -- 6.16 Spectral Asymptotics -- 6.17 Pointwise and Average Expansions -- 6.18 Global Expansions -- 6.19 Asymptotics of the Coincidence Limit -- 6.20 Exercises | |
-- 7 Series of Dirac Delta Functions -- 7.1 Introduction -- 7.2 Basic Notions -- 7.3 Several Problems that Lead to Series of Deltas -- 7.4 Dual Taylor Series as Asymptotics of Solutions of Equations -- 7.5 Boundary Layers -- 7.6 | |
Spectral Content Asymptotics -- 7.7 Exercises -- References | |
ISBN: | 9780817681302 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Applied mathematics , Engineering mathematics , Statistics , Mathematics , Analysis , Applications of Mathematics , Statistical Theory and Methods |
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Call number: | SPRINGER-1999-9781475758672:ONLINE Show nearby items on shelf |
Title: | Modern Analytic Mechanics |
Author(s): |
Richard K Cooper |
Date: | 1999 |
Size: | 1 online resource (341 p.) |
Note: | 10.1007/978-1-4757-5867-2 |
Contents: | 1 Newtonian Mechanics -- 2 Hamilton’s Principle -- 3 Gravitational Law and Planetary Motion -- 4 Hamiltonian Description -- 5 Oscillations I -- 6 Oscillations II -- 7 Rigid Bodies -- 8 Waves in Mechanical Systems -- 9 Special |
Relativity -- 10 Problems -- Appendix A Linear Algebra -- A.1. Properties of Determinants -- A.2. Matrix Notation -- A.3. Matrix Operations -- A.4. Types of Matrices -- A.5. Eigenvalue Analysis -- Appendix B Linear Differential | |
Equations -- Appendix C Numerical Methods -- C.1. Numerical Evaluation of Integrals -- C.2. Numerical Integration of Ordinary Differential Equations -- Appendix D Fourier Series -- D.1. Series Representation of Periodic Functions -- | |
D.2. Evaluation of Series -- D.3. Numerical Evaluation of Series Coefficients -- D.4. Complex Series -- Appendix E Computer Exercises in Classical Mechanics -- E.1. Using the Computer -- E.2. Starting Out -- Appendix F FORTRAN -- F.1. | |
Basic Elements of a FORTRAN Program -- F.2. Other Data Types -- F.3. FORTRAN Functions -- F.4. Looping -- F.5. Variables with Many Values -- F.6. Subroutines -- Appendix G Mathcad | |
ISBN: | 9781475758672 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Applied mathematics , Engineering mathematics , Physics , Mechanics , Mathematics , Applications of Mathematics , Mechanics , Theoretical, Mathematical and Computational Physics |
Availability: | Click here to see Library holdings or inquire at
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Call number: | SPRINGER-1992-9789401126526:ONLINE Show nearby items on shelf |
Title: | Exercises in Quantum Mechanics A Collection of Illustrative Problems and Their Solutions |
Author(s): |
Harry Mavromatis |
Date: | 1992 |
Edition: | Second Revised Edition |
Size: | 1 online resource (333 p.) |
Note: | 10.1007/978-94-011-2652-6 |
Contents: | 1 Wilson-Sommerfeld Quantization Condition -- 2 The Delta Function, Completeness, and Closure -- 3 Momentum Space -- 4 Wavepackets and the Uncertainty Principle -- 5 Uncertainty Principle and Ground-State Energies of |
Quantum-Mechanical Systems -- 6 Free Particles Incident on Potentials, Time Delay,Phase Shifts, and the Born Approximation -- 7 Heisenberg Representation -- 8 Two-, Three-, and N-, Versus One-Dimensional Problems -- 9 ‘Kramers’ Type | |
Expressions, The Virial Theorem,and Generalizations -- 10 Upper Bounds and Parity Considerations -- 11 Perturbation Theory -- 12 Degeneracy -- 13 The Inverse Problem -- 14 The Dalgarno-Lewis Technique -- 15 Angular Momentum and Coupled | |
States -- 16 Tensor Operators, and Evaluation of Matrix Elements -- 17 Applications of Quantum Mechanics | |
ISBN: | 9789401126526 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Kluwer Texts in the Mathematical Sciences: 6 |
Keywords: | Physics , Applied mathematics , Engineering mathematics , Quantum physics , Physics , Quantum Physics , Applications of Mathematics |
Availability: | Click here to see Library holdings or inquire at
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Call number: | SPRINGER-1989-9789400925540:ONLINE Show nearby items on shelf |
Title: | Rock Rheology |
Author(s): |
N Cristescu |
Date: | 1989 |
Size: | 1 online resource (336 p.) |
Note: | 10.1007/978-94-009-2554-0 |
Contents: | 1. Introduction -- 2. Mechanical Properties of Rocks -- 2.1. Diagnostic tests -- 2.2. Unconfined uniaxial compressive tests -- 2.3. Other mechanical tests -- 2.4. Triaxial tests -- Exercises -- 3. Creep of Rocks -- 3.1. History of |
creep tests -- 3.2. Uniaxial creep -- 3.3. Mathematical model -- 3.4. Examples -- 3.5. Creep in triaxial stress-state -- Exercises -- 4. Volume Deformation -- 4.1. Dilatancy and/or compressibility -- 4.2. Volume compressibility -- 4.3. | |
Mathematical models for the hydrostatic compressibility of volume -- 4.4. Volume dilatancy -- 4.5. Rock dilatancy during creep -- Exercises -- 5. Classical Constitutive Equations -- 5.1. The linear elastic model -- 5.2. Plane strain | |
elasticity in cylindrical coordinates -- 5.3. Thick-walled tube subjected to internal and external pressures -- 5.4. The general linear viscoelastic model -- Exercises -- 6. Rock ‘Elasticity’ at High Pressures -- 6.1. The elastic | |
moduli -- 6.2. Determination of elastic moduli by dynamic procedures -- 6.3. Longitudinal and shear waves in the case of high stresses and finite strains -- 6.4. Restrictions concerning the elastic parameters -- Exercises -- 7. Rock | |
Plasticity -- 7.1. Historical outline -- 7.2. Constitutive hypotheses -- 7.3. Constitutive equation -- 7.4. Yield function and plastic potential -- 7.5. Example for a dilatant rock -- 7.6. Example of compressible/dilatant rock -- 7.7. | |
Generalization of the model for finite rotations -- Exercises -- 8. Elastic/Viscoplastic Constitutive Equations -- 8.1. General considerations -- 8.2. Experimental foundation -- 8.3. Constitutive hypotheses -- 8.4. Constitutive | |
equations -- 8.5. An example for a compressible/dilatant hard rock -- 8.6. Examples for softer rocks -- 8.7. A uniaxial example -- 8.8. Acoustic emission -- Exercises -- 9. Damage and Failure of Rocks -- 9.1. Classical short-time | |
failure-strength criteria -- 9.2. Some experimental evidence -- 9.3. The energetic damage parameter -- 9.4. Numerical examples -- Exercises -- 10. Stress states In-Situ -- 10.1. Primary stress-state -- 10.2. Secondary and relative | |
stress fields -- 10.3. Initial stresses and strains for the linear elastic model -- 10.4. Primary states for the elasto-plastic constitutive equation -- 10.5. Primary states for the linear viscoelastic model -- 10.6. Primary states for | |
the elastic/viscoplastic model -- 10.7. Stresses and strains around underground openings -- Exercises -- 11. Creep and Dilatancy/Compressibility of Rocks Around Vertical Shafts and Oil Wells -- 11.1. Formulation of the problem -- 11.2. | |
The linear elastic solution -- 11.3. The linear viscoelastic rock -- 11.4. The elastic/viscoplastic rock -- 11.5. Dilatancy/compressibility and damage around a well -- 11.6. A more general primary stress-state -- Exercises -- 12. Creep | |
and Dilatancy/Compressibility of Rocks Around Horizontal Tunnels -- 12.1. Formulation of the problem -- 12.2. The elastic approach -- 12.3. Creep around a tunnel according to a linear viscoelastic model -- 12.4. Creep according to an | |
elastic/viscoplastic model -- 12.5. Creep, dilatancy/compressibility, damage, and failure around a tunnel -- Exercises -- 13. Tunnel Support Analysis -- 13.1. Formulation of the problem -- 13.2. Linear elastic support linear | |
viscoelastic rock -- 13.3. Non-linear self-adjusting supports linear viscoelastic rock -- 13.4. Non-linear self-adjusting support elastic/viscoplastic rock -- Exercises -- Appendix 1. A Short Introduction to Fracture Mechanics -- A1.1. | |
Introduction -- A1.2. The fundamental relations of the plane theory of elasticity -- A1.4. The main boundary-value problems -- A1.5. The influence functions corresponding to the elementary crack -- A1.6. The Griffith crack in the plane | |
problem -- A1.7. Stress intensity factors and criteria for the propagation of the crack -- A1.8. Systems of rectilinear cracks -- A1.9. Application to the crack kinking problem -- A1.10. Some numerical and experimental results -- | |
Appendix 2. Creep and Stress Variation Around a Well or a Tunnel. A Numerical Approach -- References -- Author Index | |
ISBN: | 9789400925540 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mechanics of Elastic and Inelastic Solids: 7 |
Keywords: | Earth sciences , Geotechnical engineering , Earth Sciences , Geotechnical Engineering & Applied Earth Sciences |
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Call number: | SPRINGER-1987-9789401577717:ONLINE Show nearby items on shelf |
Title: | Exercises in Quantum Mechanics A Collection of Illustrative Problems and Their Solutions |
Author(s): |
Harry A Mavromatis |
Date: | 1987 |
Size: | 1 online resource (181 p.) |
Note: | 10.1007/978-94-015-7771-7 |
Contents: | 1 / Wilson-Sommerfeld Quantization Condition -- 2 / The Delta Function, Completeness and Closure -- 3 / Momentum Space -- 4 / Wavepackets and the Uncertainty Principle -- 5 / Uncertainty Principle and Ground-State Energies of |
Quantum-Mechanical Systems -- 6 / Free Particles Incident on Potentials, Time Delay, Phase Shiffs and the Born Approximation -- 7 / Heisenberg Representation -- 8 / Two and Three Versus One-Dimensional Problems -- 9 / ‘Kramer’ Type | |
Expressions. The Virial Theorem and Generalizations -- 10 / Upper Bounds and Parity Considerations -- 11 / Perturbation Theory -- 12 / Degeneracy -- 13 / The Inverse problem -- 14 / The Dalgarno-Lewis Technique | |
ISBN: | 9789401577717 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Reidel Texts in the Mathematical Sciences, A Graduate-Level Book Series: 2 |
Keywords: | Physics , Applied mathematics , Engineering mathematics , Quantum physics , Physics , Quantum Physics , Applications of Mathematics |
Availability: | Click here to see Library holdings or inquire at
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