文档介绍：Mathematical Tools for Physics
by James Nearing
Physics Department
University of Miami
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Copyright 2003, James Nearing
Permission to copy for
individual or classroom
use is granted.
QA
Contents
Introduction . . . . . . . . . . . . . . . . . iv 4 Differential Equations . . . . . . . . . . . . 83
Linear Constant-Coefficient
Bibliography . . . . . . . . . . . . . . . . vi Forced Oscillations
1 Basic Stuff. . . . . . . . . . . . . . . . . 1 Series Solutions
Trigonometry Trigonometry via ODE’s
Parametric Differentiation Green’s Functions
Gaussian Integrals Separation of Variables
erf and Gamma Simultaneous Equations
Differentiating Simultaneous ODE’s
Integrals Legendre’s Equation
Polar Coordinates
5 Fourier Series . . . . . . . . . . . . . . . 118
Sketching Graphs
Examples
2 Infinite Series . . . . . . . . . . . . . . . . puting Fourier Series
The Basics Choice of Basis
Deriving Taylor Series Periodically Forced ODE’s
Convergence Return to Parseval
Series of Series Gibbs Phenomenon
Power series, two variables
Stirling’s Approximation 6 Vector Spaces . . . . . . . . . . . . . . . 142
Useful Tricks The Underlying Idea
Diffraction Axioms
Checking Results Examples of Vector Spaces
Linear Independence
plex Algebra . . . . . . . . . . . . . . 65 Norms
Complex Numbers Scalar Product
Some Functions Bases and Scalar Products
Applications of Euler’s Formula Gram-Schmidt Orthogonalization
Logarithms Cauchy-Schwartz inequality
Mapping Infinite Dimensions
i
7 Operators and Matrices . . . . . . . . . . 168 Integral Representation of Curl
The Idea of an Operator The Gradient
Definition of an Operator Shorter Cut for div and curl
Examples of Operators Identities for Vector Operators
Matrix Multiplication Applications to Gravity
Inverses Gravitational Potential
Areas, Volumes, Determinants Summation Convention
Matrices as Operators plicated Potentials
Eigenvalues and Eigenv