Differential Equations and Linear Algebra, 3rd Edition

C. Henry Edwards
David E. Penney



For courses in Differential Equations and Linear Algebra.

Acclaimed authors Edwards and Penney combine core topics in elementary differential equations with those concepts and methods of elementary linear algebra needed for a contemporary combined introduction to differential equations and linear algebra. Known for its real-world applications and its blend of algebraic and geometric approaches, this text discusses mathematical modeling of real-world phenomena, with a fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications. In the Third Edition, new graphics and narrative have been added as needed—yet the proven chapter and section structure remains unchanged, so that class notes and syllabi will not require revision for the new edition.

Table of Contents

CHAPTER 1. First-Order Differential Equations
1.1 Differential Equations and Mathematical Models
1.2 Integrals as General and Particular Solutions
1.3 Slope Fields and Solution Curves
1.4 Separable Equations and Applications
1.5 Linear First-Order Equations
1.6 Substitution Methods and Exact Equations

CHAPTER 2. Mathematical Models and Numerical Methods
2.1 Population Models
2.2 Equilibrium Solutions and Stability
2.3 Acceleration–Velocity Models
2.4 Numerical Approximation: Euler's Method
2.5 A Closer Look at the Euler Method
2.6 The Runge–Kutta Method

CHAPTER 3. Linear Systems and Matrices
3.1 Introduction to Linear Systems
3.2 Matrices and Gaussian Elimination
3.3 Reduced Row-Echelon Matrices
3.4 Matrix Operations
3.5 Inverses of Matrices
3.6 Determinants
3.7 Linear Equations and Curve Fitting

CHAPTER 4. Vector Spaces
4.1 The Vector Space R3
4.2 The Vector Space Rn and Subspaces
4.3 Linear Combinations and Independence of Vectors
4.4 Bases and Dimension for Vector Spaces
4.5 Row and Column Spaces
4.6 Orthogonal Vectors in Rn
4.7 General Vector Spaces

CHAPTER 5. Higher-Order Linear Differential Equations
5.1 Introduction: Second-Order Linear Equations
5.2 General Solutions of Linear Equations
5.3 Homogeneous Equations with Constant Coefficients
5.4 Mechanical Vibrations
5.5 Nonhomogeneous Equations and Undetermined Coefficients
5.6 Forced Oscillations and Resonance

CHAPTER 6. Eigenvalues and Eigenvectors
6.1 Introduction to Eigenvalues
6.2 Diagonalization of Matrices
6.3 Applications Involving Powers of Matrices

CHAPTER 7. Linear Systems of Differential Equations
7.1 First-Order Systems and Applications
7.2 Matrices and Linear Systems
7.3 The Eigenvalue Method for Linear Systems
7.4 Second-Order Systems and Mechanical Applications
7.5 Multiple Eigenvalue Solutions
7.6 Numerical Methods for Systems

CHAPTER 8. Matrix Exponential Methods
8.1 Matrix Exponentials and Linear Systems
8.2 Nonhomogeneous Linear Systems
8.3 Spectral Decomposition Methods

CHAPTER 9. Nonlinear Systems and Phenomena
9.1 Stability and the Phase Plane
9.2 Linear and Almost Linear Systems
9.3 Ecological Models: Predators and Competitors
9.4 Nonlinear Mechanical Systems

CHAPTER 10. Laplace Transform Methods
10.1 Laplace Transforms and Inverse Transforms
10.2 Transformation of Initial Value Problems
10.3 Translation and Partial Fractions
10.4 Derivatives, Integrals, and Products of Transforms
10.5 Periodic and Piecewise Continuous Input Functions

CHAPTER 11. Power Series Methods
11.1 Introduction and Review of Power Series
11.2 Power Series Solutions
11.3 Frobenius Series Solutions
11.4 Bessel Functions

References for Further Study
Appendix A: Existence and Uniqueness of Solutions
Appendix B: Theory of Determinants
Answers to Selected Problems
Index



  如果你喜欢我分享的书籍，请关注我：
https://bbs.pinggu.org/z_guanzhu.php?action=add&fuid=5975757

订阅我的文库：

【金融 + 经济 + 商学 + 国际政治】
https://bbs.pinggu.org/forum.php?mod=collection&action=view&ctid=3257

【数学 + 统计 + 计算机编程】
https://bbs.pinggu.org/forum.php?mod=collection&action=view&ctid=3258

【历史 + 心理学 + 社会自然科学】
https://bbs.pinggu.org/forum.php?mod=collection&action=view&ctid=3259