Some Mathematical Methods of PhysicsCourier Corporation, 2014 M03 5 - 320 páginas This 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
... Theorem 47 Chapter 4 Vector Spaces and Linear Operators . . . . 50 4.1 Introduction . 50 4.2 Base Vectors and Basis ... Theorems on Hemiitian Operators . 70 Chapter 6 Penod' ic Structures 73 6.1 Motivation 73 6.2 The RC Line . 73 6.3 ...
... Theorem 47 Chapter 4 Vector Spaces and Linear Operators . . . . 50 4.1 Introduction . 50 4.2 Base Vectors and Basis ... Theorems on Hemiitian Operators . 70 Chapter 6 Penod' ic Structures 73 6.1 Motivation 73 6.2 The RC Line . 73 6.3 ...
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
... Theorem and Corollary Singularities . . . . . . Cauchy's Integral Formula . The Theorem of Residues . 184 185 190 192 201 201 202 203 204 205 206 207 211 211 212 213 215 220 221 225 225 229 233 233 233 234 236 236 . 236 . 239 243 252 +u ...
... Theorem and Corollary Singularities . . . . . . Cauchy's Integral Formula . The Theorem of Residues . 184 185 190 192 201 201 202 203 204 205 206 207 211 211 212 213 215 220 221 225 225 229 233 233 233 234 236 236 . 236 . 239 243 252 +u ...
Página xi
... 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.
... 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.
Página 25
... theorem. The problem is that of finding the quantities a,- such that u = 2 54-01 This may be written as u = sa (2.13) where s is the matrix of the eigencolumns of A. Note that sis nonsingular, since its columns are linearly independent ...
... theorem. The problem is that of finding the quantities a,- such that u = 2 54-01 This may be written as u = sa (2.13) where s is the matrix of the eigencolumns of A. Note that sis nonsingular, since its columns are linearly independent ...
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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