Differential Equations and Linear Algebra, 4th Edition Differential Equations and Linear Algebra, 4th Edition

Differential Equations and Linear Algebra, 4th Edition

4th Edition | ISBN: 9780134497181 / 013449718X


expert-verified solutions in this book

Differential Equations and Linear Algebra, 4th Edition
Buy on Amazon.com

4th Edition | ISBN: 9780134497181 / 013449718X


expert-verified solutions in this book

Buy on Amazon.com

Table of Contents

Chapter 1

First-Order Differential Equations

1-1 Differential Equations and Mathematical Models Problems p.8
1-2 Integrals as General and Particular Solutions Problems p.15
1-3 Slope Fields and Solutions Curves Problems p.25
1-4 Separable equations and Applications Problems p.41
1-5 Linear First-Order Equations Problems p.53
1-6 Substitution Methods and Exact Equations Problems p.70
Review Problems p.74

Chapter 2

Mathematical Models And Numerical Methods

2-1 Population Models Problems p.82
2-2 Equilibrium Solutions and Stability Problems p.92
2-3 Acceleration-Velocity Models Problems p.101
2-4 Numerical Approximation: Euler's Method Problems p.114
2-5 A Closer Look at the Euler Method Problems p.124
2-6 The Runge-Kutta Method Problems p.133

Chapter 3

Linear Systems And Matrices

3-1 Introduction to Linear Systems Problems p.145
3-2 Matrices and Gaussian Elimination Problems p.154
3-3 Reduced Row-Echelon Matrices Problems p.162
3-4 Matrix Operations Problems p.173
3-5 Inverses of Matrices Problems p.185
3-6 Determinants Problems p.201
3-7 Linear Equations and Curve Fitting Problems p.209

Chapter 4

Vector Spaces

4-1 The Vector Space R3 Problems p.220
4-2 The Vector Space Rn and Subspaces Problems p.227
4-3 Linear Combinations and Independence of Vectors Problems p.234
4-4 Bases and Dimension for Vector Spaces Problems p.241
4-5 Row and Column Spaces Problems p.249
4-6 Orthogonal Vectors in Rn Problems p.256
4-7 General Vector Spaces Problems p.263

Chapter 5

Higher-Order Linear Differential Equations

5-1 Introduction: Second-Order Linear Equations Problems p.276
5-2 General Solutions of Linear Equations Problems p.288
5-3 Homogeneous Equations with Constant Coefficients Problems p.300
5-4 Mechanical Vibrations Problems p.311
5-5 Nonhomogeneous Equations and Undetermined Coefficients Problems p.325
5-6 Forced Oscillations and Resonance Problems p.335

Chapter 6

Eigenvalues And Eigenvectors

6-1 Introduction to Eigenvalues Problems p.346
6-2 Diagonalization of Matrices Problems p.353
6-3 Applications Involving Powers of Matrices Problems p.363

Chapter 7

Linear Systems Of Differential Equations

7-1 First-Order Systems and Applications Problems p.371
7-2 Matrices and Linear Systems Problems p.384
7-3 The Eigenvalue Method for Linear Systems Problems p.395
7-4 A Gallery of Solution Curves of Linear Systems Problems p.419
7-5 Second-Order Systems and Mechanical Applications* Problems p.433
7-6 Multiple Eigenvalue Solutions Problems p.451
7-7 Numerical Methods for Systems Problems p.463

Chapter 8

Matrix Exponential Methods

8-1 matrix Exponentials and Linear Systems Problems p.479
8-2 Nonhomogeneous Linear Systems Problems p.489
8-3 Spectral Decomposition Methods Problems p.502

Chapter 9

Nonlinear Systems And Phenomena

9-1 Stability and the Phase Plane Problems p.511
9-2 Linear and Almost Linear Systems Problems p.522
9-3 Ecological Models: Predators and Competitors Problems p.535
9-4 Nonlinear Mechanical Systems Problems p.549

Chapter 10

Laplace Transform Methods

10-1 Laplace Transforms and Inverse Transforms Problems p.565
10-2 Transformation of Initial Value Problem Problems p.576
10-3 Translation and Partial Fractions Problems p.584
10-4 Derivatives, Integrals, and Products of Transforms Problems p.593
10-5 Periodic and Piecewise Continuous Input Functions Problems p.601

Chapter 11

Power Series Methods

11-1 Introduction and Review of Power Series Problems p.615
11-2 Power Series Solutions Problems p.624
11-3 Frobenius Series Solutions Problems p.638
11-4 Bessel Functions Problems p.650

Chapter Appendix A

Existence And Uniqueness Of Solutions

Problems p.666
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