Mathematical Physics with Partial Differential Equations, Second Edition is designed for upper division undergraduate and beginning graduate students taking a course on mathematical physics taught out of 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 in 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 TO THIS EDITION: Features novel and illustrative examples from physics including the 1- dimensional quantum mechanical oscillator, the hydrogen atom and the rigid rotor modelChapter-length discussion of relevant functions, including the Hermite polynomials, Legendre polynomials, Laguerre polynomials and Bessel functionsAll-new focus on complex examples only solvable by multiple methods Introduces and evaluates numerous physical and engineering concepts in a rigorous mathematical frameworkProvides extremely detailed mathematical derivations and solutions with extensive proofs, weighting for application potentialExplores an array of detailed examples from physics that give direct application to rigorous mathematicsOffers instructors useful resources for teaching, including an illustrated Instructors Manual, chapter powerpoint presentations, and a solutions manual INDICE: 1. Preliminaries 2. Vector Calculus 3. Green's Function 4. Fourier Series 5. Three Important Equations 6. Sturm-Liouville Theory 7. Solving PDE's in Cartesian Coordinates by Separation of Variables 8. Generating Functions 9. Solving PDE's in Cylindrical Coordinates by Separation of Variables 10. Solving PDE's in spherical coordinates w/Sep. of Variables 11. The Fourier Transform 12. The Laplace Transform 13. Solving PDE's using Green's Functions
- ISBN: 978-0-12-814759-7
- Editorial: Academic Press
- Encuadernacion: Rústica
- Páginas: 576
- Fecha Publicación: 01/03/2018
- Nº Volúmenes: 1
- Idioma: Inglés