Mathematical Physics With Partial Differential Equations

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Mathematical Physics with Partial Differential Equations

Mathematical Physics with Partial Differential Equations
  • Author : James Kirkwood
  • Publisher : Academic Press
  • Release Date : 2018-02-26
  • Total pages : 492
  • ISBN : 9780128147603
  • File Size : 50,8 Mb
  • Total Download : 217
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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
  • Publisher : Courier Corporation
  • Release Date : 1964-01-01
  • Total pages : 452
  • ISBN : 048665964X
  • File Size : 30,6 Mb
  • Total Download : 573
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This volume presents an unusually accessible introduction to equations fundamental to the investigation of waves, heat conduction, hydrodynamics, and other physical problems. Topics include derivation of fundamental equations, Riemann method, equation of heat conduction, theory of integral equations, Green's function, and much more. The only prerequisite is a familiarity with elementary analysis. 1964 edition.

Partial Differential Equations in Classical Mathematical Physics

Partial Differential Equations in Classical Mathematical Physics
  • Author : Isaak Rubinstein,Lev Rubinstein
  • Publisher : Cambridge University Press
  • Release Date : 1998-04-28
  • Total pages : 704
  • ISBN : 0521558468
  • File Size : 16,8 Mb
  • Total Download : 800
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The unique feature of this book is that it considers the theory of partial differential equations in mathematical physics as the language of continuous processes, that is, as an interdisciplinary science that treats the hierarchy of mathematical phenomena as reflections of their physical counterparts. Special attention is drawn to tracing the development of these mathematical phenomena in different natural sciences, with examples drawn from continuum mechanics, electrodynamics, transport phenomena, thermodynamics, and chemical kinetics. At the same time, the authors trace the interrelation between the different types of problems - elliptic, parabolic, and hyperbolic - as the mathematical counterparts of stationary and evolutionary processes. This combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs, one that will be appreciated by both students and researchers alike.

Partial Differential Equations of Mathematical Physics

Partial Differential Equations of Mathematical Physics
  • Author : Arthur Godon Webster
  • Publisher : Courier Dover Publications
  • Release Date : 2016-06-20
  • Total pages : 465
  • ISBN : 9780486805153
  • File Size : 40,8 Mb
  • Total Download : 488
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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.

Equations of Mathematical Physics

Equations of Mathematical Physics
  • Author : A. N. Tikhonov,A. A. Samarskii
  • Publisher : Courier Corporation
  • Release Date : 2013-09-16
  • Total pages : 800
  • ISBN : 9780486173368
  • File Size : 30,6 Mb
  • Total Download : 696
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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

Methods of Mathematical Physics

Methods of Mathematical Physics
  • Author : Richard Courant,David Hilbert
  • Publisher : John Wiley & Sons
  • Release Date : 2008-09-26
  • Total pages : 852
  • ISBN : 9783527617241
  • File Size : 36,9 Mb
  • Total Download : 603
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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.

Mathematical Methods in Physics

Mathematical Methods in Physics
  • Author : Victor Henner,Tatyana Belozerova,Kyle Forinash
  • Publisher : CRC Press
  • Release Date : 2009-06-18
  • Total pages : 861
  • ISBN : 9781568813356
  • File Size : 44,9 Mb
  • Total Download : 374
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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.

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
  • Publisher : Birkhäuser
  • Release Date : 2022-01-22
  • Total pages : 338
  • ISBN : 3030373258
  • File Size : 9,9 Mb
  • Total Download : 741
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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.

Partial Differential Equations for Mathematical Physicists

Partial Differential Equations for Mathematical Physicists
  • Author : Bijan Kumar Bagchi
  • Publisher : CRC Press
  • Release Date : 2019-07-02
  • Total pages : 224
  • ISBN : 9781000228939
  • File Size : 18,5 Mb
  • Total Download : 258
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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

Partial Differential Equations
  • Author : Walter A. Strauss
  • Publisher : John Wiley & Sons
  • Release Date : 2007-12-21
  • Total pages : 468
  • ISBN : 9780470054567
  • File Size : 26,9 Mb
  • Total Download : 243
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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.

Partial Differential Equations, Spectral Theory, and Mathematical Physics

Partial Differential Equations, Spectral Theory, and Mathematical Physics
  • Author : Pavel Exner,Rupert L. Frank,Fritz Gesztesy,Helge Holden,Timo Weidl
  • Publisher : Unknown
  • Release Date : 2021
  • Total pages : 229
  • ISBN : 3985470073
  • File Size : 19,8 Mb
  • Total Download : 488
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PDF book entitled Partial Differential Equations, Spectral Theory, and Mathematical Physics written by Pavel Exner,Rupert L. Frank,Fritz Gesztesy,Helge Holden,Timo Weidl and published by Unknown which was released on 2021 with total hardcover pages 229, the book become popular and critical acclaim.

Partial Differential Equations of Mathematical Physics

Partial Differential Equations of Mathematical Physics
  • Author : Tyn Myint U.
  • Publisher : Unknown
  • Release Date : 1980
  • Total pages : 408
  • ISBN : UOM:39015016367297
  • File Size : 53,8 Mb
  • Total Download : 551
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PDF book entitled Partial Differential Equations of Mathematical Physics written by Tyn Myint U. and published by Unknown which was released on 1980 with total hardcover pages 408, the book become popular and critical acclaim.

Equations in Mathematical Physics

Equations in Mathematical Physics
  • Author : Victor P. Pikulin,Stanislav I. Pohozaev
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-01-05
  • Total pages : 215
  • ISBN : 9783034802673
  • File Size : 52,8 Mb
  • Total Download : 984
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Many physical processes in fields such as mechanics, thermodynamics, electricity, magnetism or optics are described by means of partial differential equations. The aim of the present book is to demontstrate the basic methods for solving the classical linear problems in mathematical physics of elliptic, parabolic and hyperbolic type. In particular, the methods of conformal mappings, Fourier analysis and Green`s functions are considered, as well as the perturbation method and integral transformation method, among others. Every chapter contains concrete examples with a detailed analysis of their solution.The book is intended as a textbook for students in mathematical physics, but will also serve as a handbook for scientists and engineers.

Partial Differential Equations of Mathematical Physics

Partial Differential Equations of Mathematical Physics
  • Author : Harry 1882-1946 Bateman
  • Publisher : Hassell Street Press
  • Release Date : 2021-09-09
  • Total pages : 552
  • ISBN : 1014038391
  • File Size : 37,6 Mb
  • Total Download : 563
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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 and Mathematical Physics

Partial Differential Equations and Mathematical Physics
  • Author : Kunihiko Kajitani,Jean Vaillant
  • Publisher : Springer Science & Business Media
  • Release Date : 2002-12-13
  • Total pages : 260
  • ISBN : 0817643095
  • File Size : 29,6 Mb
  • Total Download : 860
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The 17 invited research articles in this volume, all written by leading experts in their respective fields, are dedicated to the great French mathematician Jean Leray. A wide range of topics with significant new results---detailed proofs---are presented in the areas of partial differential equations, complex analysis, and mathematical physics. Key subjects are: * Treated from the mathematical physics viewpoint: nonlinear stability of an expanding universe, the compressible Euler equation, spin groups and the Leray--Maslov index, * Linked to the Cauchy problem: an intermediate case between effective hyperbolicity and the Levi condition, global Cauchy--Kowalewski theorem in some Gevrey classes, the analytic continuation of the solution, necessary conditions for hyperbolic systems, well posedness in the Gevrey class, uniformly diagonalizable systems and reduced dimension, and monodromy of ramified Cauchy problem. Additional articles examine results on: * Local solvability for a system of partial differential operators, * The hypoellipticity of second order operators, * Differential forms and Hodge theory on analytic spaces, * Subelliptic operators and sub- Riemannian geometry. Contributors: V. Ancona, R. Beals, A. Bove, R. Camales, Y. Choquet- Bruhat, F. Colombini, M. De Gosson, S. De Gosson, M. Di Flaviano, B. Gaveau, D. Gourdin, P. Greiner, Y. Hamada, K. Kajitani, M. Mechab, K. Mizohata, V. Moncrief, N. Nakazawa, T. Nishitani, Y. Ohya, T. Okaji, S. Ouchi, S. Spagnolo, J. Vaillant, C. Wagschal, S. Wakabayashi The book is suitable as a reference text for graduate students and active researchers.

Partial Differential Equations Arising from Physics and Geometry

Partial Differential Equations Arising from Physics and Geometry
  • Author : Anonim
  • Publisher : Unknown
  • Release Date : 2019
  • Total pages : 229
  • ISBN : OCLC:1100480581
  • File Size : 19,8 Mb
  • Total Download : 579
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In this edited volume leaders in the field of partial differential equations present recent work on topics in PDEs arising from geometry and physics. The papers originate from a 2015 research school organized by CIMPA and MIMS in Hammamet, Tunisia to celebrate the 60th birthday of the late Professor Abbas Bahri. The opening chapter commemorates his life and work. While the research presented in this book is cutting-edge, the treatment throughout is at a level accessible to graduate students. It includes short courses offering readers a unique opportunity to learn the state of the art in evolution equations and mathematical models in physics, which will serve as an introduction for students and a useful reference for established researchers. Finally, the volume includes many open problems to inspire the next generation.

Physical Mathematics and Nonlinear Partial Differential Equations

Physical Mathematics and Nonlinear Partial Differential Equations
  • Author : James H. Lightbourne
  • Publisher : CRC Press
  • Release Date : 2020-12-18
  • Total pages : 280
  • ISBN : 9781000154238
  • File Size : 39,6 Mb
  • Total Download : 155
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This volume consists of the proceedings of the conference on Physical Mathematics and Nonlinear Partial Differential Equations held at West Virginia University in Morgantown. It describes some work dealing with weak limits of solutions to nonlinear systems of partial differential equations.

Elements of Partial Differential Equations

Elements of Partial Differential Equations
  • Author : Ian N. Sneddon
  • Publisher : Courier Corporation
  • Release Date : 2013-01-23
  • Total pages : 352
  • ISBN : 9780486162997
  • File Size : 13,8 Mb
  • Total Download : 726
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This text features numerous worked examples in its presentation of elements from the theory of partial differential equations, emphasizing forms suitable for solving equations. Solutions to odd-numbered problems appear at the end. 1957 edition.

Non-Local Partial Differential Equations for Engineering and Biology

Non-Local Partial Differential Equations for Engineering and Biology
  • Author : Nikos I. Kavallaris,Takashi Suzuki
  • Publisher : Springer
  • Release Date : 2017-11-28
  • Total pages : 300
  • ISBN : 9783319679440
  • File Size : 16,5 Mb
  • Total Download : 795
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This book presents new developments in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical tools. Theoretical backgrounds in mechanics, thermo-dynamics, game theory, and theoretical biology are examined in details. It starts off with a review and summary of the basic ideas of mathematical modeling frequently used in the sciences and engineering. The authors then employ a number of models in bio-science and material science to demonstrate applications, and provide recent advanced studies, both on deterministic non-local partial differential equations and on some of their stochastic counterparts used in engineering. Mathematical models applied in engineering, chemistry, and biology are subject to conservation laws. For instance, decrease or increase in thermodynamic quantities and non-local partial differential equations, associated with the conserved physical quantities as parameters. These present novel mathematical objects are engaged with rich mathematical structures, in accordance with the interactions between species or individuals, self-organization, pattern formation, hysteresis. These models are based on various laws of physics, such as mechanics of continuum, electro-magnetic theory, and thermodynamics. This is why many areas of mathematics, calculus of variation, dynamical systems, integrable systems, blow-up analysis, and energy methods are indispensable in understanding and analyzing these phenomena. This book aims for researchers and upper grade students in mathematics, engineering, physics, economics, and biology.

Partial differential equations in physics

Partial differential equations in physics
  • Author : Arnold Sommerfeld
  • Publisher : Sarat Book Distributors
  • Release Date : 1961
  • Total pages : 352
  • ISBN : 8187169494
  • File Size : 41,5 Mb
  • Total Download : 525
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PDF book entitled Partial differential equations in physics written by Arnold Sommerfeld and published by Sarat Book Distributors which was released on 1961 with total hardcover pages 352, the book become popular and critical acclaim.

Differential Geometry, Differential Equations, and Mathematical Physics

Differential Geometry, Differential Equations, and Mathematical Physics
  • Author : Maria Ulan,Eivind Schneider
  • Publisher : Springer Nature
  • Release Date : 2021-02-12
  • Total pages : 231
  • ISBN : 9783030632533
  • File Size : 24,9 Mb
  • Total Download : 918
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This volume presents lectures given at the Wisła 19 Summer School: Differential Geometry, Differential Equations, and Mathematical Physics, which took place from August 19 - 29th, 2019 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures were dedicated to symplectic and Poisson geometry, tractor calculus, and the integration of ordinary differential equations, and are included here as lecture notes comprising the first three chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and mathematical physics. Specific topics covered include: Parabolic geometry Geometric methods for solving PDEs in physics, mathematical biology, and mathematical finance Darcy and Euler flows of real gases Differential invariants for fluid and gas flow Differential Geometry, Differential Equations, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry is assumed.