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顾客评论
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目录
Application Modules
Preface
CHAPTER 1 First-Order Differential Equations
1.1 Differential Equations and Mathematical Models
1.2 Integrals as General and Paticular Solutions
1.3 Slope Fields and Solution Curves
1.4 Separable Equations and Applications
1.5 Linear First-Order Equations
1.6 Substifution Methods and Exact Equations
CHAPTER 2 Mathematical Models and Numercal Methods
2.1 Population Models
2.2 Equlilibrium Solutions and Stablility
2.3 Acceleration-Velocity Models
2.4 Numerical Approzimation:Euler''''''''s Method
2.5 A Closer Look at the Euler Method
2.6 The Runge-Kutta Method
CHAPTER 3 Linear Equations of Higher Order
3.1 Introduction:Second-Order Linear Equations
3.2 General Solutions of Linear Equations
3.3 Homogeneous Equations with Constant Coelficients
3.4 Mechanical Vibrations
3.5 Nonhomogeneous Equations and Undetermined Coefficients
3.6 Forced Oscillations and Resonance
3.7 Electrical Ciruits
3.8 Endpoint Problems and Eigenvalues
CHAPTER 4 Introduction to Systems of Differential Equations
4.1 First-Order Systems and Applications
4.2 The Method of Elimination
4.3 Numerical Methods for Systems
CHAPTER 5 Linear Systems of Differential Equtions
5.1 Matrices and Linear Systems
5.2 The Eigenvalue Method for Homogeneous Systems
5.3 Second-Order Systems and Mechanical Applications
5.4 Multiple Eigenvaluve Solutions
5.5 Matrix Exponentials and Linear Systems
5.6 Nonhomogeneous Linear Systems
CHAPTER 6 Nonlinear Systems and Phenomena
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CHATPER 7 Laplace Transform Methods
CHAPTER 8 Power Series Methods
CHAPTER 9 Fourier Series Methods
CHATPER 10 Eigenvalues and Boundary Value Problems
References for Futher Study
Appendix:Existence and Uniqueness of Solutions
Answers to Selected Problems
Index
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