A Course in Ordinary Differential Equations (Hardcover, 2)

Traditional First-Order Differential Equations
Introduction to First-Order Equations
Separable Differential Equations
Linear Equations
Some Physical Models Arising as Separable Equations
Exact Equations
Special Integrating Factors and Substitution Methods

Geometrical and Numerical Methods for First-Order Equations
Direction Fields?the Geometry of Differential Equations
Existence and Uniqueness for First-Order Equations
First-Order Autonomous Equations?Geometrical Insight
Modeling in Population Biology
Numerical Approximation: Euler and Runge-Kutta Methods
An Introduction to Autonomous Second-Order Equations

Elements of Higher-Order Linear Equations
Introduction to Higher-Order Equations
Linear Independence and the Wronskian
Reduction of Order?the Case n = 2
Numerical Considerations for nth-Order Equations
Essential Topics from Complex Variables
Homogeneous Equations with Constant Coefficients
Mechanical and Electrical Vibrations

Techniques of Nonhomogeneous Higher-Order Linear Equations
Nonhomogeneous Equations
Method of Undetermined Coefficients via Superposition
Method of Undetermined Coefficients via Annihilation
Exponential Response and Complex Replacement
Variation of Parameters
Cauchy-Euler (Equidimensional) Equation
Forced Vibrations

Fundamentals of Systems of Differential Equations
Useful Terminology
Gaussian Elimination
Vector Spaces and Subspaces
Eigenvalues and Eigenvectors
A General Method, Part I: Solving Systems with Real & Distinct or Complex Eigenvalues
A General Method, Part II: Solving Systems with Repeated Real Eigenvalues
Matrix Exponentials
Solving Linear Nonhomogeneous Systems of Equations

Geometrical and Numerical Methods for First-Order Equations
An Introduction to the Phase Plane
Nonlinear Equations and Phase Plane Analysis
Bifurcations
Epidemiological Models
Models in Ecology

Laplace Transforms
Introduction
Fundamentals of the Laplace Transform
The Inverse Laplace Transform
Translated Functions, Delta Function, and Periodic Functions
The s-Domain and Poles
Solving Linear Systems using Laplace Transforms
The Convolution

Series Methods
Power Series Representations of Functions
The Power Series Method
Ordinary and Singular Points
The Method of Frobenius
Bessel Functions

A Review, Computer Labs, and Projects appear at the end of each chapter.