参加工业合作须知

Contents
Chapter 1: Basic Concepts
Differential Equations
Notation
Solutions
Initial-Value and Boundary-Value Problems
Chapter 2: Classifications of First-Order Differential Equations
Standard Form and Differential Form
Linear Equations
Bernoulli Equations
Homogeneous Equations
Separable Equations
Exact Equations
Chapter 3: Separable First-Order Differential Equations
General Solution
Solutions to the Initial-Value Problem
Reduction of Homogeneous Equations
Chapter 4: Exact First-Order Differential Equations
Defining Properties
Method of Solution
Integrating Factors
Chapter 5: Linear First-Order Differential Equations
Method of Solution
Reduction of Bernoulli Equations
Chapter 6: Applications of First-Order Differential Equations
Growth and Decay Problems
Temperature Problems
Falling Body Problems
Dilution Problems
Electrical Circuits
Orthogonal Trajectories
Chapter 7: Linear Differential Equations: Theory of Solutions
Linear differential equations
Linearly independent solutions
The Wronskian
Nonhomogeneous equations
Chapter 8: Second-Order Linear Homogeneous Differential Equations with Constant Coefficients
The characteristic equation
The general solution
Chapter 9: nth-Order Linear Homogeneous Differential Equations with Constant Coefficients
The Characteristic Equation
The General Solution
Chapter 10: The Method of Undetermined Coefficients
Simple Form of the Method
Generalizations
Modifications
Limitations of the Method
Chapter 11: Variation of Parameters
The Method
Scope of the Method
Chapter 12: Initial-Value Problems
Chapter 13: Applications of Second-Order Linear Differential Equations
Spring Problems
Electrical Circuit Problems
Buoyancy Problems
Classifying Solutions
Chapter 14: The Laplace Transform
Definition
Properties of Laplace Transforms
Functions of Other Independent Variables
Chapter 15: Inverse Laplace Transforms
Definition
Manipulating Denominators
Manipulating Numerators
Chapter 16: Convolutions and the Unit Step Function
Convolutions
Unit Step Function
Translations
Chapter 17: Solutions of Linear Differential Equations with Constant Coefficients by Laplace Transforms
Laplace Transforms of Derivatives
Solutions of Differential Equations
Chapter 18: Solutions of Linear Systems by Laplace Transforms
The Method
Chapter 19: Matrices
Matrices and Vectors
Matrix Addition
Scalar and Matrix Multiplication
Powers of a Square Matrix
Differentiation and Integration of Matrices
The Characteristic Equation
Chapter 20: e[sup(At)]
Definition
Computation of e[sup(At)]
Chapter 21: Reduction of Linear Differential Equations to a First-Order System
Reduction of one equation
Reduction of a system
Chapter 22: Solutions of Linear Differential Equations with Constant Coefficients by Matrix Methods
Solution of the Initial-Value Problem
Solution with No Initial Conditions
Chapter 23: Linear Differential Equations with Variable Coefficients
Second-Order Equations
Analytic Functions and Ordinary Points
Solutions around the Origin of Homogeneous Equations
Solutions around the Origin of Nonhomogeneous Equations
Initial-Value Problems
Solutions around Other Points
Chapter 24: Regular Singular Points and the Method of Frobenius
Regular Singular Points
Method of Frobenius
General Solution
Chapter 25: Gamma and Bessel Functions
Gamma Function
Bessel Functions
Algebraic Operations on Infinite Series
Chapter 26: Graphical Methods for Solving First-Order Differential Equations
Direction Fields
Euler\\u0027s Method
Stability
Chapter 27: Numerical Methods for Solving First-Order Differential Equations
General Remarks
Modified Euler\\u0027s Method
Runge-Kutta Method
Adams-Bashforth-Moulton Method
Milne\\u0027s Method
Starting Values
Order of a Numerical Method
Chapter 28: Numerical Methods for Systems
First-Order Systems
Euler\\u0027s Method
Runge-Kutta Method
Adams-Bashforth-Moulton Method
Chapter 29: Second-Order Boundary-Value Problems
Standard Form
Solutions
Eigenvalue Problems
Sturm-Liouville Problems
Properties of Sturm-Liouville Problems
Chapter 30: Eigenfunction Expansions
Piecewise Smooth Functions
Fourier Sine Series
Fourier Cosine Series
Appendix A: Laplace Transforms
Answers to Supplementary Problems
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
R
S
T
U
V
W
Z