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. |
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Página viii
44 3.7 Inhomogeneous Equations 46 3.8 The Convolution Theorem 47 Chapter 4 Vector Spaces and Linear Operators . . . . 50 4.1 Introduction . 50 4.2 Base Vectors and Basis 52 4.3 Change of Basis . . 55 4.4 Linear Operators .
44 3.7 Inhomogeneous Equations 46 3.8 The Convolution Theorem 47 Chapter 4 Vector Spaces and Linear Operators . . . . 50 4.1 Introduction . 50 4.2 Base Vectors and Basis 52 4.3 Change of Basis . . 55 4.4 Linear Operators .
Página ix
Theorems on Cylindrical Functions (of Integral Order n) . . . Conduction of Heat in an Infinite Insulated Plate; Plane Polar Coordinates (Concluded) The Circular Membrane . . . . . The Vibrating Circular Ring and Circular Sector .
Theorems on Cylindrical Functions (of Integral Order n) . . . Conduction of Heat in an Infinite Insulated Plate; Plane Polar Coordinates (Concluded) The Circular Membrane . . . . . The Vibrating Circular Ring and Circular Sector .
Página x
Appendix 18 Convergence of Matrix Power Series . Appendix 1C Remarks on Theory of Functions of Complex Variables . 1C.1 1C.2 1C3 1C.4 1C.5 Analytic Functions . . . . . The Cauchy Integral Theorem and Corollary Singularities .
Appendix 18 Convergence of Matrix Power Series . Appendix 1C Remarks on Theory of Functions of Complex Variables . 1C.1 1C.2 1C3 1C.4 1C.5 Analytic Functions . . . . . The Cauchy Integral Theorem and Corollary Singularities .
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Series Expansions at the Origin . The Asymptotic Expansions . . . The Asymptotic Series of Debye . . The Addition Theorems for Bessel Functions 261 266 266 267 268 272 275 276 280 280 280 283 284 286 287 291 292 295 CONTENTS xi.
Series Expansions at the Origin . The Asymptotic Expansions . . . The Asymptotic Series of Debye . . The Addition Theorems for Bessel Functions 261 266 266 267 268 272 275 276 280 280 280 283 284 286 287 291 292 295 CONTENTS xi.
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If A does have n linearly independent eigencolumns, it is possible to solve specifically for u in terms of the eigencolumns (see the next paragraph), thus completing the proof of the theorem. The problem is that of finding the ...
If A does have n linearly independent eigencolumns, it is possible to solve specifically for u in terms of the eigencolumns (see the next paragraph), thus completing the proof of the theorem. The problem is that of finding the ...
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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 |