图书信息
图书目录
基础微分方程与边值问题（第2版）影印版
暂无简介
作者：
Werner Kohler, Lee Johnson
定价：
118.00 元
出版时间：
2026-05-21
ISBN：
978-7-04-067158-2
物料号：
67158-00
读者对象：
高等教育
一级分类：
数学与统计学类
二级分类：
数学与应用数学专业课
三级分类：
偏微分方程
重点项目：
暂无
版面字数：
1260千字
开本：
16开
装帧形式：
平装
页数：
暂无
最新印次时间：
2026年01月
- 目录
- 前辅文
- Chapter 1 Introduction to Differential Equations
- 1.1 Introduction
- 1.2 Examples of Differential Equations
- 1.3 Direction Fields
- 1.1 Introduction
- Chapter 2 First Order Differential Equations
- 2.1 Introduction
- 2.2 First Order Linear Differential Equations
- 2.3 Introduction to Mathematical Models
- 2.4 Population Dynamics and Radioactive Decay
- 2.5 First Order Nonlinear Differential Equations
- 2.6 Separable First Order Equations
- 2.7 Exact Differential Equations
- 2.8 The Logistic Population Model
- 2.9 Applications to Mechanics
- 2.10 Euler’s Method
- Review Exercises
- Projects
- 2.1 Introduction
- Chapter 3 Second and Higher Order Linear Differential Equations
- 3.1 Introduction
- 3.2 The General Solution of Homogeneous Equations
- 3.3 Constant Coefficient Homogeneous Equations
- 3.4 Real Repeated Roots; Reduction of Order
- 3.5 Complex Roots
- 3.6 Unforced Mechanical Vibrations
- 3.7 The General Solution of a Linear Nonhomogeneous Equation
- 3.8 The Method of Undetermined Coefficients
- 3.9 The Method of Variation of Parameters
- 3.10 Forced Mechanical Vibrations, Electrical Networks, and Resonance
- 3.11 Higher Order Linear Homogeneous Differential Equations
- 3.12 Higher Order Homogeneous Constant Coefficient Differential Equations
- 3.13 Higher Order Linear Nonhomogeneous Differential Equations
- Review Exercises
- Projects
- 3.1 Introduction
- Chapter 4 First Order Linear Systems
- 4.1 Introduction
- 4.2 Existence and Uniqueness
- 4.3 Homogeneous Linear Systems
- 4.4 Constant Coefficient Homogeneous Systems; the Eigenvalue Problem
- 4.5 Real Eigenvalues and the Phase Plane
- 4.6 Complex Eigenvalues
- 4.7 Repeated Eigenvalues
- 4.8 Nonhomogeneous Linear Systems
- 4.9 Numerical Methods for Systems of Linear Differential Equations
- 4.10 The Exponential Matrix and Diagonalization
- Review Exercises
- Projects
- 4.1 Introduction
- Chapter 5 Laplace Transforms
- 5.1 Introduction
- 5.2 Laplace Transform Pairs
- 5.3 The Method of Partial Fractions
- 5.4 Laplace Transforms of Periodic Functions and System Transfer Functions
- 5.5 Solving Systems of Differential Equations
- 5.6 Convolution
- 5.7 The Delta Function and Impulse Response
- Projects
- 5.1 Introduction
- Chapter 6 Nonlinear Systems
- 6.1 Introduction
- 6.2 Equilibrium Solutions and Direction Fields
- 6.3 Conservative Systems
- 6.4 Stability
- 6.5 Linearization and the Local Picture
- 6.6 Two-Dimensional Linear Systems
- 6.7 Predator-Prey Population Models
- Projects
- 6.1 Introduction
- Chapter 7 Numerical Methods
- 7.1 Introduction
- 7.2 Euler’s Method, Heun’s Method, and the Modified Euler’s Method
- 7.3 Taylor Series Methods
- 7.4 Runge-Kutta Methods
- Appendix 1: Convergence of One-Step Methods
- Appendix 2: Stability of One-Step Methods
- Projects
- 7.1 Introduction
- Chapter 8 Series Solutions of Linear Differential Equations
- 8.1 Introduction
- 8.2 Series Solutions Near an Ordinary Point
- 8.3 The Euler Equation
- 8.4 Solutions Near a Regular Singular Point and the Method of Frobenius
- 8.5 The Method of Frobenius Continued: Special Cases and a Summary
- Projects
- 8.1 Introduction
- Chapter 9 Second Order Partial Differential Equations and Fourier Series
- 9.1 Introduction
- 9.2 Heat Flow in a Thin Bar; Separation of Variables
- 9.3 Series Solutions
- 9.4 Calculating the Solution
- 9.5 Fourier Series
- 9.6 The Wave Equation
- 9.7 Laplace’s Equation
- 9.8 Higher-Dimensional Problems; Nonhomogeneous Equations
- Project
- 9.1 Introduction
- Chapter 10 First Order Partial Differential Equations and the Method of Characteristics
- 10.1 Introduction
- 10.2 The Cauchy Problem
- 10.3 Existence and Uniqueness
- 10.4 The Method of Characteristics
- Projects
- 10.1 Introduction
- Chapter 11 Linear Two-Point Boundary Value Problems
- 11.1 Introduction
- 11.2 Existence and Uniqueness
- 11.3 Two-Point Boundary Value Problems for Linear Systems
- 11.4 Sturm-Liouville Boundary Value Problems
- Project
- 11.1 Introduction
- Answers
- Index
- A BRIEF TABLE OF INTEGRALS
- A BRIEF TABLE OF LAPLACE TRANSFORMS
- 前辅文
