A First Course in Differential Equations with Modeling Applications, International Metric Edition

✍ Scribed by Dennis Zill

• Publisher: Cengage Learning.
• Year: 2023
• Tongue: English
• Leaves: 482
• Edition: 12
• Category: Library

✦ Table of Contents

Cover
Contents
Preface for This Metric Edition
Chapter 1: Introduction to Differential Equations
1.1 Definitions and Terminology
1.2 Initial-Value Problems
1.3 Differential Equations as Mathematical Models
Chapter 1 In Review
Chapter 2: First-Order Differential Equations
2.1 Solution Curves without a Solution
2.2 Separable Equations
2.3 Linear Equations
2.4 Exact Equations
2.5 Solutions by Substitutions
2.6 A Numerical Method
Chapter 2 In Review
Chapter 3: Modeling with First-Order Differential Equations
3.1 Linear Models
3.2 Nonlinear Models
3.3 Modeling with Systems of First-Order DEs
Chapter 3 In Review
Chapter 4: Higher-Order Differential Equations
4.1 Theory of Linear Equations
4.2 Reduction of Order
4.3 Homogeneous Linear Equations with Constant Coefficients
4.4 Undetermined Coefficients - Superposition Approach
4.5 Undetermined Coefficients - Annihilator Approach
4.6 Variation of Parameters
4.7 Cauchy-Euler Equations
4.8 Green's Functions
4.9 Solving Systems of Linear DEs by Elimination
4.10 Nonlinear Differential Equations
Chapter 4 In Review
Chapter 5: Modeling with Higher-Order Differential Equations
5.1 Linear Models: Initial-Value Problems
5.2 Linear Models: Boundary-Value Problems
5.3 Nonlinear Models
Chapter 5 In Review
Chapter 6: Series Solutions of Linear Equations
6.1 Review of Power Series
6.2 Solutions about Ordinary Points
6.3 Solutions about Singular Points
6.4 Special Functions
Chapter 6 In Review
Chapter 7: The Laplace Transform
7.1 Definition of the Laplace Transform
7.2 Inverse Transforms and Transforms of Derivatives
7.3 Operational Properties I
7.4 Operational Properties II
7.5 The Dirac Delta Function
7.6 Systems of Linear Differential Equations
Chapter 7 In Review
Chapter 8: Systems of Linear Differential Equations
8.1 Theory of Linear Systems
8.2 Homogeneous Linear Systems
8.3 Nonhomogeneous Linear Systems
8.4 Matrix Exponential
Chapter 8 In Review
Chapter 9: Numerical Solutions of Ordinary Differential Equations
9.1 Euler Methods and Error Analysis
9.2 Runge-Kutta Methods
9.3 Multistep Methods
9.4 Higher-Order Equations and Systems
9.5 Second-Order Boundary-Value Problems
Chapter 9 In Review
Appendices
Appendix A: Integral-Defined Functions
Appendix B: Matrices
Appendix C: Laplace Transforms
Answers for Selected Odd-Numbered Problems
Index