## Product Description

**Description**

This text introduces elementary ordinary differential equations in a clear and concise fashion. Designed around a single-semester undergraduate course, Ordinary Differential Equations explores key concepts along with various real-world applications. In particular, we discuss common techniques for solving first-order differential equations, basic numerical methods, second-order homogeneous and nonhomogeneous differential equations, the generalization to higher-order linear differential equations, the Laplace transform method, linear systems of differential equations, and nonlinear systems of differential equations.

The Second Edition contains several new sections, and several new subsections, additional discussion on certain topics, additional exercises, and a number of corrections. This new edition contains approximately 80 additional pages.

** Table of Contents**

- First Order Differential Equations
- Separable Equations and Exponential Growth
- Linear Equations and Integrating Factors
- Autonomous Equations and Population Dynamics
- Numerical Solutions

- Homogenous Linear Equations
- Particle Dynamics
- Theory of Homogeneous Second-Order Linear Equations
- Homogeneous Equations with Constant Coefficients
- Complex Roots and Oscillations
- Mechanical and Electrical Systems
- Theory of Higher Order Differential Equations

- Nonhomogeneous Linear Equations
- Method of Undetermined Coefficients
- Forced Vibrations and Resonance
- Variation of Parameters
- Theory of Higher Order Differential Equations

- Laplace Transform
- Laplace Transform
- Initial Value Problems
- Steps and Impulses
- Convolution Integrals

- Linear Algebra
- Vectors and Matrices
- Matrix Multiplication
- Eigenvalues and Eigenvectors

- Systems of Differential Equations
- Linear Systems of Differential Equations
- Linear Systems with Complex Eigenvalues
- Nonlinear Systems I–Local Linearization
- Nonlinear Systems II–Population Dynamics

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