Differential Equations and Linear Algebra Global Edition 4e Edwards 9781292356952

Differential Equations and Linear Algebra provides the conceptual development and geometric visualization of a modern differential equations and linear algebra course that is essential to science and engineering students. It balances traditional manual methods with the new, computer-based methods that illuminate qualitative phenomena – a comprehensive approach that makes accessible a wider range of more realistic applications.

The book combines core topics in elementary differential equations with concepts and methods of elementary linear algebra. It starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout.

Table of Contents

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

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

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

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

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

6. Eigenvalues and Eigenvectors

6.1 Introduction to Eigenvalues

6.2 Diagonalization of Matrices

6.3 Applications Involving Powers of Matrices

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 A Gallery of Solution Curves of Linear Systems

7.5 Second-Order Systems and Mechanical Applications

7.6 Multiple Eigenvalue Solutions

7.7 Numerical Methods for Systems

8. Matrix Exponential Methods

8.1 Matrix Exponentials and Linear Systems

8.2 Nonhomogeneous Linear Systems

8.3 Spectral Decomposition Methods

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

10. Laplace Transform Methods

11. Power Series Methods