Mathematical Methods in Physics and Engineering

by Dettman, John W.

• ISBN13: 9780486656496
• ISBN10: 0486656497
• eBook ISBN(s): 9780486169361
• Format: Paperback
• Copyright: 2011-11-30
• Publisher: Dover Publications
• More Book Details

Summary

Algebraically based approach to vectors, mapping, diffraction, and other topics in applied math also covers generalized functions, analytic function theory, and more. Additional topics include sections on linear algebra, Hilbert spaces, calculus of variations, boundary value problems, integral equations, analytic function theory, and integral transform methods. Exercises. 1969 edition.

Table of Contents

Preface
CHAPTER 1. Linear Algebra
1.1 Linear Equations. Summation Convention
1.2 Matrices
1.3 Determinants
1.4 Systems of Linear Algebraic Equations. Rank of a Matrix
1.5 Vector Spaces
1.6 Scalar Product
1.7 Orthonormal Basis. Linear Transformations
1.8 Quadratic Forms. Hermitian Forms
1.9 Systems of Ordinary Differential Equations. Vibration Problems
1.10 Linear Programming
CHAPTER 2. Hilbert Spaces
2.1 Infinite-dimensional Vector Spaces. Function Spaces
2.2 Fourier Series
2.3 Separable Hilbert Spaces
2.4 The Projection Theorem
2.5 Linear Functionals
2.6 Weak Convergence
2.7 Linear Operators
2.8 Completely Continuous Operators
CHAPTER 3. Calculus of Variations
3.1 Maxima and Minima of Functions. Lagrange Multipliers
3.2 Maxima and Minima of Functionals. Euler's Equation
3.3 Hamilton's Principle. Lagrange's Equations
3.4 Theory of Small Vibrations
3.5 The Vibrating String
3.6 Boundary-value Problems of Mathematical Physics
3.7 Eigenvalues and Eigenfunctions
3.8 Eigenfunction Expansions
3.9 Upper and Lower Bounds for Eigenvalues
CHAPTER 4. Boundary-value Problems. Separation of Variables
4.1 Orthogonal Coordinate Systems. Separation of Variables
4.2 Sturm-Liouville Problems
4.3 Series Solutions of Ordinary Differential Equations
4.4 Series Solutions of Boundary-value Problems
CHAPTER 5. Boundary-value Problems. Green's Functions
5.1 Nonhomogeneous Boundary-value Problems
5.2 One-dimensional Green's Functions
5.3 Generalized Functions
5.4 Green's Functions in Higher Dimensions
5.5 Problems in Unbounded Regions
5.6 A Problem in Diffraction Theory
CHAPTER 6. Integral Equations
6.1 Integral-equation Formulation of Boundary-value Problems
6.2 Hilbert-Schmidt Theory
6.3 Fredholm Theory
6.4 Integral Equations of the First Kind
CHAPTER 7. Analytic Function Theory
7.1 Introduction
7.2 Analytic Functions
7.3 Elementary Functions
7.4 Complex Integration
7.5 Integral Representations
7.6 Sequences and Series
7.7 Series Representations of Analytic Functions
7.8 Contour Integration
7.9 Conformal Mapping
7.10 Potential Theory
CHAPTER 8. Integral Transform Methods
8.1 Fourier Transforms
8.2 Applications of Fourier Transforms. Ordinary Differential Equations
8.3 Applications of Fourier Transforms. Partial Differential Equations
8.4 Applications of Fourier Transforms. Integral Equations
8.5 Laplace Transforms. Applications
8.6 Other Transform Techniques
Index