最 低 价：￥146.00
定 价：￥162.27
作 者：Paul D. Ritger 著 著
出 版 社：Oversea Publishing House
出版时间：2002-9-1
I S B N：9780486411545
| Prefaee Chap. I Basic Concepts 1-1 Introduction 1-2 Classificationa and Examples of Differential Equations 1-3 The Motion of a Particle 1-4 The Solution of a Differential Equation 1-5 Initial- and Boundary-value Problems 1-6 The Differential Equation y' = f(z) 1-7 Integrals as Function, s of Parameters 1-8 Elementary and Non-elementary Functions 1-9 The Gamma Function Appendix Chap. 2 Special Methods for First.order Equations 2-1 Introduction 2-2 Separation of Variables 2-3 The First-order Linear Differential Equation 2-4 Exact Differential Equations 2-5 Integrating Factors 2-6 Use of Substitutions 2-7 Second-order Equations Reducible to First-order 2-8 Summary Chap. 3 Applications of First-order Equations 3-1 Introduction 3-2 Falling Bodies with Air Resistance 3-3 Motion on a Given Curve 3-4 Linear Motion wish Variable Mass 3-5 Newton's Law of Cooling 3-6 Dilution Problems 3-7 Chemical Reactions 3-8 Population Growth 3-9 A Simple Electrical Circuit 3-10 Families of Curves and Orthogonal Trajectories Chap. 4 Existence and Uniqueness and Methods of Approximation 95 4-1 Introduction 4-2 The Direction Field 4-3 Existence and Uniqueness o.f Solutions 4-4 The Picard Method 4-5 The Cauchy-Euler Method 4-6 Taylor Series 4-7 Existence and Uniqueness Theorems for Systems of Equations and Higher-order Equations 4-8 Existence and Uniqueness Theorems for Linear Equations Appendix: Proof of existence and uniqueness theorems Chap. 5 Linear Differential Equations 5-1 Introduction 5-2 Fundamental Theory of Second-order Linear Equations 5-3 Complex-valued Solutions 5-4 Homogeneous Linear Equations with Constant Coejacients 5-5 Undetermined Coefficients 5-6 Variation of Parameters 5-7 Euler' s Equation 5-8 Formulas of Lagrange and Abel 5-9 Linear Equations of the nth Order Chap. 6 Applications of Second-order Linear Differential Equations 6-1 Introduction 6-2 Free Vibrations 6-3 Forced Vibrations 6-4 Electrical Circuits 6-5 The Equations of Planetary Motion Chap. 7 Linear Differential Equations with Variable Coefficients 7-1 Introduction 7-2 Solution by Power Series …… Chap 8 Systems of Linear Differential Epuations Chap 9 The Laplace Transforn Chap 10 Nonlinear Differential Epuations Chap 11 Linear Difference Epuations Chap 12 Numerical Methods Chap 13 Boubdary-value Problems Chap 14 Partial Differential Epuations of Mathematical Physics Chap 15 Further Applications of Partial Differential Epuations Appendix A Infinite Series Appendix B Functions of a Complex Variable References Answers and Hints Index |
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