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基础微分方程与边值问题（第2版）影印版

样章
作者：
Werner Kohler, Lee Johnson
定价：
118.00 元
版面字数：
1260.00千字
开本：
16开
装帧形式：
平装
版次：
1
最新版次
印刷时间：
2026-01-13
ISBN：
978-7-04-067158-2
物料号：
67158-00
出版时间：
2026-05-21
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
暂无
  • 前辅文
  • Chapter 1 Introduction to Differential Equations
    • 1.1 Introduction
    • 1.2 Examples of Differential Equations
    • 1.3 Direction Fields
  • 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
  • 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
    • 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
  • 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
    • 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
  • 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
  • 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
  • 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
  • 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
  • Chapter 9 Second Order Partial Differential Equations and Fourier Series
    • 9.1 Introduction
    • 9.2 Heat Flow in a Thin Bar
    • 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
    • Project
  • 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
  • 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
  • Answers
  • Index
  • A BRIEF TABLE OF INTEGRALS
  • A BRIEF TABLE OF LAPLACE TRANSFORMS

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