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. |
Dentro del libro
Página vii
... Determinants 14 1.8 Inverses . . . . 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 ...
... Determinants 14 1.8 Inverses . . . . 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 ...
Página x
... Determinants . 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 ...
... Determinants . 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 ...
Página 14
... determinants which will be needed in Sec. 1.8 are summarized in Sec. 1.7. 1.7 Some Properties of Determinants The determinant of a square matrix m is a number indicated as |m|, read “determinant of m.” This determinant can be calculated ...
... determinants which will be needed in Sec. 1.8 are summarized in Sec. 1.7. 1.7 Some Properties of Determinants The determinant of a square matrix m is a number indicated as |m|, read “determinant of m.” This determinant can be calculated ...
Página 15
Gerald Goertzel, Nunzio Tralli. The general definition of the determinant of m is given in Appendix 1A. Some properties of determinants as derived in Appendix 1A will be listed below. I. The determinant of a matrix is equal to the ...
Gerald Goertzel, Nunzio Tralli. The general definition of the determinant of m is given in Appendix 1A. Some properties of determinants as derived in Appendix 1A will be listed below. I. The determinant of a matrix is equal to the ...
Página 16
... determinant of m does not vanish) there exists a unique matrix, denoted by m-l, such that mm—1 : m—lm = 1. Thus, it will first be shown that there exists a q such that mq I I, second that there exists a p such that pm = I, and third ...
... determinant of m does not vanish) there exists a unique matrix, denoted by m-l, such that mm—1 : m—lm = 1. Thus, it will first be shown that there exists a q such that mq I I, second that there exists a p such that pm = I, and third ...
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