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 vii
... . . . . . . . . . 38 3.2 The Cauchy-integral Formula . . . . . . . 38 3.3 Application to Matrices . . . . . . . . 39 3.4 Evaluation of f(A) with Illustrations . . . . . . 40 3.5 The Inversion Formula 43 3.6 Laplace Transforms . 44 VII.
... . . . . . . . . . 38 3.2 The Cauchy-integral Formula . . . . . . . 38 3.3 Application to Matrices . . . . . . . . 39 3.4 Evaluation of f(A) with Illustrations . . . . . . 40 3.5 The Inversion Formula 43 3.6 Laplace Transforms . 44 VII.
Página viii
Gerald Goertzel, Nunzio Tralli. 3.5 The Inversion Formula 43 3.6 Laplace Transforms . 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 ...
Gerald Goertzel, Nunzio Tralli. 3.5 The Inversion Formula 43 3.6 Laplace Transforms . 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 ...
Página ix
... Laplacian (V') in One Dimension 9.1 9.2 9.3 9.4 9.5 9.6 Introduction . . . . 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 ...
... Laplacian (V') in One Dimension 9.1 9.2 9.3 9.4 9.5 9.6 Introduction . . . . 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 ...
Página 43
... l—bd) enough, q(Z) may be obtained from (3.8). Analytic continuation takes care of other values of Z. 3.6 Laplace Transforms According to (3.6) and (3.7), the solution. EVALUATION OF FUNCTION OF MATRIX FOR AN ARBITRARY MATRIX 43.
... l—bd) enough, q(Z) may be obtained from (3.8). Analytic continuation takes care of other values of Z. 3.6 Laplace Transforms According to (3.6) and (3.7), the solution. EVALUATION OF FUNCTION OF MATRIX FOR AN ARBITRARY MATRIX 43.
Página 44
... Laplace transform of u(t). It may be obtained by solving Eq. (3.1la). The main reason for the introduction of the Laplace transform U(Z) is that Eq. (3.1 la) for U(Z) is often easier to solve than is Eq. (3.9) for u(t). In such cases ...
... Laplace transform of u(t). It may be obtained by solving Eq. (3.1la). The main reason for the introduction of the Laplace transform U(Z) is that Eq. (3.1 la) for U(Z) is often easier to solve than is Eq. (3.9) for u(t). In such cases ...
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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