Some Mathematical Methods of PhysicsThis well-rounded, thorough treatment for advanced undergraduates and graduate students introduces basic concepts of mathematical physics involved in the study of linear systems. The text emphasizes eigenvalues, eigenfunctions, and Green's functions. Prerequisites include differential equations and a first course in theoretical physics. The three-part presentation begins with an exploration of systems with a finite number of degrees of freedom (described by matrices). In part two, the concepts developed for discrete systems in previous chapters are extended to continuous systems. New concepts useful in the treatment of continuous systems are also introduced. The final part examines approximation methods — including perturbation theory, variational methods, and numerical methods — relevant to addressing most of the problems of nature that confront applied physicists. Two Appendixes include background and supplementary material. 1960 edition. |
Dentro del libro
Resultados 1-5 de 96
Página vii
16 1.9 Linear Independence 17 Chapter 2 Solution for Diagonalizable Matrices . . . 21 2.1 Solution by Taylor Series . . . . . . . . 21 2.2 Eigenvalues and Eigencolumns . . . . . . . 22 2.3 Superposition .
16 1.9 Linear Independence 17 Chapter 2 Solution for Diagonalizable Matrices . . . 21 2.1 Solution by Taylor Series . . . . . . . . 21 2.2 Eigenvalues and Eigencolumns . . . . . . . 22 2.3 Superposition .
Página viii
35 7.3 The RC Line—Transition to the Continuous Case 87 7.4 Solution of the Discrete Problem . . 87 7.5 Solution in the Limit (Continuous Problem) 89 7.6 The Fourier Transform . . 92 Chapter 8 Operators in Continuous Systems .
35 7.3 The RC Line—Transition to the Continuous Case 87 7.4 Solution of the Discrete Problem . . 87 7.5 Solution in the Limit (Continuous Problem) 89 7.6 The Fourier Transform . . 92 Chapter 8 Operators in Continuous Systems .
Página ix
Solution of (V2 + k2)tp = 0 . . . . Recurrence Relations for the Spherical Harmonics Some Expansion Theorems Solution of the Wave Equation . 11.10 Heat Conduction in an Infinite Solid Chapter 12 12.1 12.2 12.3 12.4 12.5 Green's ...
Solution of (V2 + k2)tp = 0 . . . . Recurrence Relations for the Spherical Harmonics Some Expansion Theorems Solution of the Wave Equation . 11.10 Heat Conduction in an Infinite Solid Chapter 12 12.1 12.2 12.3 12.4 12.5 Green's ...
Página 5
... thus has to solve 0 I <1» To find the steady-state solution of (1.8) one need merely solve kxl : k0(x2 — x1) + F! (L10) kxz : ko(x1 _ x2) + F2 1.2 Standardization of Notation In order to focus attention on the form of the problems ...
... thus has to solve 0 I <1» To find the steady-state solution of (1.8) one need merely solve kxl : k0(x2 — x1) + F! (L10) kxz : ko(x1 _ x2) + F2 1.2 Standardization of Notation In order to focus attention on the form of the problems ...
Página 6
These equations are to be solved for prescribed values of the dependent variables at zero time. Equations (1.1), (1.2), (1.5), and (1.6), when written in the form of (1.1 1), become _ __1_ E_ RCE (1.12) NI:T-11\r,+01v2+01va T1 .
These equations are to be solved for prescribed values of the dependent variables at zero time. Equations (1.1), (1.2), (1.5), and (1.6), when written in the form of (1.1 1), become _ __1_ E_ RCE (1.12) NI:T-11\r,+01v2+01va T1 .
Comentarios de la gente - Escribir un comentario
No encontramos ningún comentario en los lugares habituales.
Otras ediciones - Ver todas
Términos y frases comunes
applied approximate arbitrary base vectors basis Bessel function boundary conditions Chap chapter coefficients column commute complete consider constant continuous systems contour corresponding cylindrical functions defined definition denoted determinant diagonal diagonalizable differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector elements evaluate expansion find finite number first follows formula Fourier given Green’s function Hence Hermitian matrix Hermitian operator infinite integral Introduction inverse Laplacian linear operator linearly independent lowest eigenvalue matrix McGraw-Hill Book Company membrane method multiplication nonsingular normal normal matrix Note number of degrees obtained orthonormality conditions perturbation plane procedure QUANTUM MECHANICS relations representation result Ritz method satisfies satisfy scattering solve specified spherical spherical harmonics string Substitution theorem theory tion trial functions vanish variable vector space verified wave write written yields York zero
Información bibliográfica
| Título | Some Mathematical Methods of Physics Dover Books on Physics |
| Autores | Gerald Goertzel, Nunzio Tralli |
| Editor | Courier Corporation, 2014 |
| ISBN | 048679332X, 9780486793320 |
| Largo | 320 páginas |
| Exportar cita | BiBTeX EndNote RefMan |