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Some Mathematical Methods of Physics.

Author: Gerald Goertzel
Publisher: Dover Publications, 2014.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Gerald Goertzel
ISBN: 130655344X 9781306553445 9780486793320 048679332X
OCLC Number: 875636227
Description: 1 online resource
Contents: Cover; Title Page; Copyright Page; Preface; Contents; References; Part One. Systems with a Finite Number of Degrees of Freedom; Chapter 1 Formulation of the Problem and Development of Notation.; 1.1 Introduction; 1.2 Standardization of Notation; 1.3 Matrices; 1.4 Elementary Arithmetic Operations with Matrices; 1.5 The Row-Column Rule; 1.6 Warnings.; 1.7 Some Properties of Determinants; 1.8 Inverses; 1.9 Linear Independence; Chapter 2 Solution for Diagonalizable Matrices; 2.1 Solution by Taylor Series; 2.2 Eigenvalues and Eigencolumns; 2.3 Superposition; 2.4 Completeness. 2.5 Diagonalization of Nondegenerate Matrices2.6 Outline of Computation Procedure with Examples; 2.7 Change of Variable; 2.8 The Steady-state Solution; 2.9 The Inhomogeneous Problem; Chapter 3 The Evaluation of a Function of a Matrix for an Arbitrary Matrix; 3.1 Introduction; 3.2 The Cauchy-integral Formula; 3.3 Application to Matrices; 3.4 Evaluation of f(A) with Illustrations; 3.5 The Inversion Formula; 3.6 Laplace Transforms; 3.7 Inhomogeneous Equations; 3.8 The Convolution Theorem; Chapter 4 Vector Spaces and Linear Operators; 4.1 Introduction; 4.2 Base Vectors and Basis. 4.3 Change of Basis4.4 Linear Operators; 4.5 The Representation of Linear Operators by Matrices; 4.6 The Operator in the Dual Space; 4.7 Effect of Change of Basis on the Representation of an Operator.; 4.8 The Spectral Representation of an Operator; 4.9 The Formation of a Basis by Eigenvectors of a Linear Operator.; 4.10 The Diagonalization of Normal Matrices; Chapter 5 The Dirac Notation; 5.1 Introduction; 5.2 The Change of Basis; 5.3 Linear Operators in the Dirac Notation; 5.4 Eigenvectors and Eigenvalues; 5.5 The Spectral Representation of an Operator; 5.6 Theorems on Hermitian Operators. Chapter 6 Periodic Structures6.1 Motivation; 6.2 The RC Line; 6.3 Diagonalizing M; 6.4 The Loaded String; 6.5 Difference Operators; Part Two. Systems with an Infinite Number of Degrees of Freedom; Chapter 7 The Transition to Continuous Systems; 7.1 Introduction; 7.2 The RC Line-Change of Notation; 7.3 The RC Line-Transition to the Continuous Case; 7.4 Solution of the Discrete Problem; 7.5 Solution in the Limit (Continuous Problem); 7.6 The Fourier Transform; Chapter 8 Operators in Continuous Systems; 8.1 Introduction; 8.2 Operators on Functions; 8.3 The Dirac <U+0065> Function. 8.4 Coordinate Transformations8.5 Adjoints; 8.6 Orthogonality of Eigenfunctions; 8.7 Functions of Operators; 8.8 Three-dimensional Continuous Systems; 8.9 Differential Operators; Chapter 9 The Laplacian (∇2) in One Dimension; 9.1 Introduction; 9.2 The Infinite Domain, − ∞ < x < + ∞; 9.3 The Semi-infinite Domain, 0 ≤ x < + ∞; 9.4 The Finite Domain, 0 ≤ x ≤ L; 9.5 The Circular Domain; 9.6 The Method of Images; Chapter 10 The Laplacian (∇2) in Two Dimensions; 10.1 Introduction; 10.2 Conduction of Heat in an Infinite Insulated Plate. Cartesian Coordinates; 10.3 The Vibrating Rectangular Membrane.

Abstract:

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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