基础微分方程与边值问题（第2版，影印版）
定价：￥118.00
作者： Werner Kohler，Lee Johnson
出版社：高等教育出版社
“101计划”核心教材
- 高等教育出版社
- 9787040671582
- 2版
- 64270505-7
- 特殊
- 1260
- 理学
- 数学类
- 数学类
- 本科 研究生及以上
内容简介
本书全面整合微分方程的理论、方法与计算，结构清晰，力求帮助读者掌握微分方程理论与应用技巧，并深入理解核心内容。教材特色有：1.系统讲解线性和非线性微分方程。注重基础理论与解题方法的无缝衔接，将数值与计算方法贯穿始终。2.数学建模与物理背景的深入引导。覆盖物理、生命科学等多领域案例，将模型推导与物理原理紧密结合，鼓励读者将理论应用于科学问题，具备跨学科视野。3.提倡批判性思维与数学结果解释能力。注意常识与直觉的合理运用，培养严谨科学态度，提升实际应用能力。4.紧密衔接后续课程，确保学习连贯性和知识体系完整性，助力读者顺利过渡到更高级课程，并奠定扎实学术基础。5.提供数学软件的创新支持，可作为工程与科学领域的重要参考资料。
目录
目录
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; 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
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
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; 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
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
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; 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
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
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; 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
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
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; 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
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
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; 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
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
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; 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
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
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; 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
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
