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 66
Página viii
73 6.3 Diagonalizing M 75 6.4 The Loaded String 78 6.5 Difference Operators 79 PART TWO. SYSTEMS WITH AN INFINITE NUMBER OF DEGREES OF FREEDOM Chapter 7 The Transition to Continuous Systems .
73 6.3 Diagonalizing M 75 6.4 The Loaded String 78 6.5 Difference Operators 79 PART TWO. SYSTEMS WITH AN INFINITE NUMBER OF DEGREES OF FREEDOM Chapter 7 The Transition to Continuous Systems .
Página ix
The Infinite Domain, — 00 < x < + w The Semi-infinite Domain, 0 g x < + 00 The Finite Domain, 0 s x s L . The Circular Domain The Method of Images Chapter 10 The Laplacian (V2) in Two Dimensions . 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 ...
The Infinite Domain, — 00 < x < + w The Semi-infinite Domain, 0 g x < + 00 The Finite Domain, 0 s x s L . The Circular Domain The Method of Images Chapter 10 The Laplacian (V2) in Two Dimensions . 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 ...
Página xi
Infinite One-dimensional Transforms . . . . . Infinite Multidimensional Transforms—Cartesian Coordinates Finite One-dimensional Transforms The Fourier-Bessel Integral The Fourier-Bessel Expansion Appendix 2C The Cylindrical Functions .
Infinite One-dimensional Transforms . . . . . Infinite Multidimensional Transforms—Cartesian Coordinates Finite One-dimensional Transforms The Fourier-Bessel Integral The Fourier-Bessel Expansion Appendix 2C The Cylindrical Functions .
Página 20
Using the infinite series expressions for e”, cos x, and sin x, show that 0 1 0 1 exp t = cos t + sin I. ——1 0 —1 0 References von Karman, T., and M. A. Biot: “Mathematical Methods in Engineering,” chap. 5, McGraw-Hill Book Company, ...
Using the infinite series expressions for e”, cos x, and sin x, show that 0 1 0 1 exp t = cos t + sin I. ——1 0 —1 0 References von Karman, T., and M. A. Biot: “Mathematical Methods in Engineering,” chap. 5, McGraw-Hill Book Company, ...
Página 21
... just as well when A is a matrix and u a column as they do when A and u are scalars, as is clear from the definition of the various matrix operations involved, at least in such cases as when the infinite series in (2.3) converges.
... just as well when A is a matrix and u a column as they do when A and u are scalars, as is clear from the definition of the various matrix operations involved, at least in such cases as when the infinite series in (2.3) converges.
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 |