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.

Suitable for advanced undergraduate and beginning graduate students taking a course on mathematical physics, this title presents some of the most important topics and methods of mathematical physics. It contains mathematical derivations and solutions - reinforcing the material through repetition of both the equations and the techniques.

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.

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.

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

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