Mathematical Physics with Partial Differential Equations

Mathematical Physics with Partial Differential Equations
Author: James Kirkwood
Publsiher: Academic Press
Total Pages: 492
Release: 2018-02-26
Genre: Mathematics
ISBN: 9780128147603

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Mathematical Physics with Partial Differential Equations, Second Edition, is designed for upper division undergraduate and beginning graduate students taking mathematical physics taught out by math departments. The new edition is based on the success of the first, with a continuing focus on clear presentation, detailed examples, mathematical rigor and a careful selection of topics. It presents the familiar classical topics and methods of mathematical physics with more extensive coverage of the three most important partial differential equations in the field of mathematical physics—the heat equation, the wave equation and Laplace’s equation. The book presents the most common techniques of solving these equations, and their derivations are developed in detail for a deeper understanding of mathematical applications. Unlike many physics-leaning mathematical physics books on the market, this work is heavily rooted in math, making the book more appealing for students wanting to progress in mathematical physics, with particularly deep coverage of Green’s functions, the Fourier transform, and the Laplace transform. A salient characteristic is the focus on fewer topics but at a far more rigorous level of detail than comparable undergraduate-facing textbooks. The depth of some of these topics, such as the Dirac-delta distribution, is not matched elsewhere. New features in this edition include: novel and illustrative examples from physics including the 1-dimensional quantum mechanical oscillator, the hydrogen atom and the rigid rotor model; chapter-length discussion of relevant functions, including the Hermite polynomials, Legendre polynomials, Laguerre polynomials and Bessel functions; and all-new focus on complex examples only solvable by multiple methods. Introduces and evaluates numerous physical and engineering concepts in a rigorous mathematical framework Provides extremely detailed mathematical derivations and solutions with extensive proofs and weighting for application potential Explores an array of detailed examples from physics that give direct application to rigorous mathematics Offers instructors useful resources for teaching, including an illustrated instructor's manual, PowerPoint presentations in each chapter and a solutions manual

Partial Differential Equations of Mathematical Physics

Partial Differential Equations of Mathematical Physics
Author: S. L. Sobolev
Publsiher: Elsevier
Total Pages: 440
Release: 2016-06-06
Genre: Mathematics
ISBN: 9781483181363

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Pure and Applied Mathematics, Volume 56: Partial Differential Equations of Mathematical Physics provides a collection of lectures related to the partial differentiation of mathematical physics. This book covers a variety of topics, including waves, heat conduction, hydrodynamics, and other physical problems. Comprised of 30 lectures, this book begins with an overview of the theory of the equations of mathematical physics that has its object the study of the integral, differential, and functional equations describing various natural phenomena. This text then examines the linear equations of the second order with real coefficients. Other lectures consider the Lebesgue–Fubini theorem on the possibility of changing the order of integration in a multiple integral. This book discusses as well the Dirichlet problem and the Neumann problem for domains other than a sphere or half-space. The final lecture deals with the properties of spherical functions. This book is a valuable resource for mathematicians.

Partial Differential Equations in Classical Mathematical Physics

Partial Differential Equations in Classical Mathematical Physics
Author: Isaak Rubinstein,Lev Rubinstein
Publsiher: Cambridge University Press
Total Pages: 677
Release: 1998-04-28
Genre: Mathematics
ISBN: 0521558468

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The book's combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs.

Mathematical Methods in Physics

Mathematical Methods in Physics
Author: Victor Henner,Tatyana Belozerova,Kyle Forinash
Publsiher: CRC Press
Total Pages: 859
Release: 2009-06-18
Genre: Science
ISBN: 9781568813356

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This book is a text on partial differential equations (PDEs) of mathematical physics and boundary value problems, trigonometric Fourier series, and special functions. This is the core content of many courses in the fields of engineering, physics, mathematics, and applied mathematics. The accompanying software provides a laboratory environment that allows the user to generate and model different physical situations and learn by experimentation. From this standpoint, the book along with the software can also be used as a reference book on PDEs, Fourier series and special functions for students and professionals alike.

Kernel Functions and Elliptic Differential Equations in Mathematical Physics

Kernel Functions and Elliptic Differential Equations in Mathematical Physics
Author: Stefan Bergman,Menahem Schiffer
Publsiher: Courier Corporation
Total Pages: 464
Release: 2013-01-23
Genre: Mathematics
ISBN: 9780486154657

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Covers the theory of boundary value problems in partial differential equations and discusses a portion of the theory from a unifying point of view while providing an introduction to each branch of its applications. 1953 edition.

Partial Differential Equations of Mathematical Physics

Partial Differential Equations of Mathematical Physics
Author: Arthur Godon Webster
Publsiher: Courier Dover Publications
Total Pages: 464
Release: 2016-06-15
Genre: Mathematics
ISBN: 9780486805153

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A classic treatise on partial differential equations, this comprehensive work by one of America's greatest early mathematical physicists covers the basic method, theory, and application of partial differential equations. In addition to its value as an introductory and supplementary text for students, this volume constitutes a fine reference for mathematicians, physicists, and research engineers. Detailed coverage includes Fourier series; integral and elliptic equations; spherical, cylindrical, and ellipsoidal harmonics; Cauchy's method; boundary problems; the Riemann-Volterra method; and many other basic topics. The self-contained treatment fully develops the theory and application of partial differential equations to virtually every relevant field: vibration, elasticity, potential theory, the theory of sound, wave propagation, heat conduction, and many more. A helpful Appendix provides background on Jacobians, double limits, uniform convergence, definite integrals, complex variables, and linear differential equations.

Partial Differential Equations for Mathematical Physicists

Partial Differential Equations for Mathematical Physicists
Author: Bijan Kumar Bagchi
Publsiher: CRC Press
Total Pages: 224
Release: 2019-07-02
Genre: Mathematics
ISBN: 9781000228939

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Partial Differential Equations for Mathematical Physicists is intended for graduate students, researchers of theoretical physics and applied mathematics, and professionals who want to take a course in partial differential equations. This book offers the essentials of the subject with the prerequisite being only an elementary knowledge of introductory calculus, ordinary differential equations, and certain aspects of classical mechanics. We have stressed more the methodologies of partial differential equations and how they can be implemented as tools for extracting their solutions rather than dwelling on the foundational aspects. After covering some basic material, the book proceeds to focus mostly on the three main types of second order linear equations, namely those belonging to the elliptic, hyperbolic, and parabolic classes. For such equations a detailed treatment is given of the derivation of Green's functions, and of the roles of characteristics and techniques required in handling the solutions with the expected amount of rigor. In this regard we have discussed at length the method of separation variables, application of Green's function technique, and employment of Fourier and Laplace's transforms. Also collected in the appendices are some useful results from the Dirac delta function, Fourier transform, and Laplace transform meant to be used as supplementary materials to the text. A good number of problems is worked out and an equally large number of exercises has been appended at the end of each chapter keeping in mind the needs of the students. It is expected that this book will provide a systematic and unitary coverage of the basics of partial differential equations. Key Features An adequate and substantive exposition of the subject. Covers a wide range of important topics. Maintains mathematical rigor throughout. Organizes materials in a self-contained way with each chapter ending with a summary. Contains a large number of worked out problems.

Partial Differential Equations and Mathematical Physics

Partial Differential Equations and Mathematical Physics
Author: Kunihiko Kajitani,Jean Vaillant
Publsiher: Springer Science & Business Media
Total Pages: 243
Release: 2002-12-13
Genre: Mathematics
ISBN: 0817643095

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A wide range of topics in partial differential equations, complex analysis, and mathematical physics are presented to commemorate the memory of the great French mathematician Jean Leray. The 17 research articles are written by some of the world's leading mathematicians who explore important current subjects. Most articles contain complete proofs and excellent bibliographies. For graduate students and mathematical physicists as well as mathematicians in analysis and PDEs.

Equations of Mathematical Physics

Equations of Mathematical Physics
Author: A. N. Tikhonov,A. A. Samarskii
Publsiher: Courier Corporation
Total Pages: 800
Release: 2013-09-16
Genre: Science
ISBN: 9780486173368

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DIVThorough, rigorous advanced-undergraduate to graduate-level treatment of problems leading to partial differential equations. Hyperbolic, parabolic, elliptic equations; wave propagation in space, heat conduction in space, more. Problems. Appendixes. /div

Partial Differential Equations of Mathematical Physics

Partial Differential Equations of Mathematical Physics
Author: Harry 1882-1946 Bateman
Publsiher: Hassell Street Press
Total Pages: 552
Release: 2021-09-09
Genre: Electronic Book
ISBN: 101359097X

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This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Partial Differential Equations

Partial Differential Equations
Author: Walter A. Strauss
Publsiher: John Wiley & Sons
Total Pages: 464
Release: 2007-12-21
Genre: Mathematics
ISBN: 9780470054567

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Partial Differential Equations presents a balanced and comprehensive introduction to the concepts and techniques required to solve problems containing unknown functions of multiple variables. While focusing on the three most classical partial differential equations (PDEs)—the wave, heat, and Laplace equations—this detailed text also presents a broad practical perspective that merges mathematical concepts with real-world application in diverse areas including molecular structure, photon and electron interactions, radiation of electromagnetic waves, vibrations of a solid, and many more. Rigorous pedagogical tools aid in student comprehension; advanced topics are introduced frequently, with minimal technical jargon, and a wealth of exercises reinforce vital skills and invite additional self-study. Topics are presented in a logical progression, with major concepts such as wave propagation, heat and diffusion, electrostatics, and quantum mechanics placed in contexts familiar to students of various fields in science and engineering. By understanding the properties and applications of PDEs, students will be equipped to better analyze and interpret central processes of the natural world.

Differential Equations on Manifolds and Mathematical Physics

Differential Equations on Manifolds and Mathematical Physics
Author: Vladimir M. Manuilov,Alexander S. Mishchenko,Vladimir E. Nazaikinskii,Bert-Wolfgang Schulze,Weiping Zhang
Publsiher: Birkhäuser
Total Pages: 338
Release: 2022-01-22
Genre: Mathematics
ISBN: 3030373258

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This is a volume originating from the Conference on Partial Differential Equations and Applications, which was held in Moscow in November 2018 in memory of professor Boris Sternin and attracted more than a hundred participants from eighteen countries. The conference was mainly dedicated to partial differential equations on manifolds and their applications in mathematical physics, geometry, topology, and complex analysis. The volume contains selected contributions by leading experts in these fields and presents the current state of the art in several areas of PDE. It will be of interest to researchers and graduate students specializing in partial differential equations, mathematical physics, topology, geometry, and their applications. The readers will benefit from the interplay between these various areas of mathematics.

Methods of Mathematical Physics

Methods of Mathematical Physics
Author: Richard Courant,David Hilbert
Publsiher: John Wiley & Sons
Total Pages: 852
Release: 2008-09-26
Genre: Science
ISBN: 9783527617241

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Since the first volume of this work came out in Germany in 1937, this book, together with its first volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's final revision of 1961.

Partial Differential Equations in Physics

Partial Differential Equations in Physics
Author: Arnold Sommerfeld
Publsiher: Sarat Book Distributors
Total Pages: 335
Release: 1961
Genre: Differential equations, Partial
ISBN: 8187169494

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Partial Differential Equations I

Partial Differential Equations I
Author: Michael E. Taylor
Publsiher: Springer Science & Business Media
Total Pages: 654
Release: 2010-10-29
Genre: Mathematics
ISBN: 9781441970558

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The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations.The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.