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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 Equations of Higher Order
3.1 Introduction: Second-Order Linear Equation
3.2 General Solutions of Linear Equations
3.3 Homogeneous Equations with Constant Coefficients
3.4 Mechanical Vibrations
3.5 Nonhomogeneous Equations and Undetermined Coefficients
3.6 Forced Oscillations and Resonance
3.7 Electrical Circuits
3.8 Endpoint Problems and Eigenvalues

4. Introduction to Systems of Differential Equations
4.1 First-Order Systems and Applications
4.2 The Method of Elimination
4.3 Numerical Methods for Systems

5. Linear Systems of Differential Equations
5.1 Matrices and Linear Systems
5.2 The Eigenvalue Method for Homogeneous Systems
5.3 A Gallery of Solution Curves of Linear Systems
5.4 Second-Order Systems and Mechanical Applications
5.5 Multiple Eigenvalue Solutions
5.6 Matrix Exponentials and Linear Systems
5.7 Nonhomogeneous Linear Systems

6. Nonlinear Systems and Phenomena
6.1 Stability and the Phase Plane
6.2 Linear and Almost Linear Systems
6.3 Ecological Models: Predators and Competitors
6.4 Nonlinear Mechanical Systems
6.5 Chaos in Dynamical Systems

7. Laplace Transform Methods
7.1 Laplace Transforms and Inverse Transforms
7.2 Transformation of Initial Value Problems
7.3 Translation and Partial Fractions
7.4 Derivatives, Integrals, and Products of Transforms
7.5 Periodic and Piecewise Continuous Input Functions
7.6 Impulses and Delta Functions

Product Details:

Language: English
ISBN-10: 0321816250
ISBN-13: 978-0321816252
ISBN-13: 9780321816252

See more:

Differential Equations and Linear Algebra 4th edition by Goode Solution Manual

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Get Differential Equations Computing and Modeling 5th edition by C. Henry Edwards, David E. Penney, David Calvis

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