微分方程及邊值問題計算與模型（第3版

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2006年9月6日 17:34

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微分方程及邊值問題計算與模型（第3版）

作者：（美）愛德華茲（Edwards,C.H.）,（美）彭尼（Penney,D.E.）編著

出版社：清華大學出版社
ISBN：7302099782
印次：1

紙張：膠版紙

出版日期：2004-12-1
版次：1

定價：79元當當價：63.2元
折扣：80折

鉆石VIP價：63.20元

該圖書已被瀏覽了 77次共有顧客評論0條

內容提要：

本書以一些模型問題為背景，借助于數學軟件Maple，Mathematica 及MATLAB，利用符號運算、圖像表示和數值解法等手段，系統地介紹了（線性與非線性）微分方程的基本概念和基本方法。通過40多個實際模型的討論，使讀者對建模、求解、分析解所反映的性質這一過程進行全面的了解。利用Maple，Mathematica及MATLAB在圖形顯示、符號計算、數值計算方面的功能，定性地分析了微分方程解的性質，700余幅圖將方向場、解曲線、相平面等概念形象直觀地表示出來。另外，書中選配了1900余道習題供讀者使用。
本書可供學習數學建模或微分方程的學生作為參考書，對于從事計算與建模的科技人員，本書也具有很高的價值。

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
……
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

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