First Course in Differential Equations : With Modeling Applications

by Zill, Dennis G.

• ISBN13: 9780495108245
• ISBN10: 0495108243
• Edition: 9th
• Format: Hardcover
• Copyright: 2008-05-14
• Publisher: Brooks Cole

Summary

A First Course in Differential Equations with Modeling Applications, 9th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible text speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.

Table of Contents

Introduction to Differential Equations

Definitions and Terminology

Initial-Value Problems

Differential Equations as Mathematical Models

Chapter 1 in Review

First-Order Differential Equations

Solution Curves Without a Solution

Separable Variables

Linear Equations

Exact Equations and Integrating Factors

Solutions by Substitutions

A Numerical Method

Chapter 2 in Review

Modeling with First-Order Differential Equations

Linear Models

Nonlinear Models

Modeling with Systems of First-Order Differential Equations

Chapter 3 in Review

Higher-Order Differential Equations

Preliminary Theory- Linear Equations

Reduction of Order

Homogeneous Linear Equations with Constant Coefficients

Undetermined Coefficients- Superposition Approach

Undetermined Coefficients- Annihilator Approach

Variation of Parameters

Cauchy-Euler Equation

Solving Systems of Linear Differential Equations by Elimination

Nonlinear Differential Equations

Chapter 4 in Review

Modeling with Higher-Order Differential Equations

Linear Models: Initial-Value Problems

Linear Models: Boundary-Value Problems

Nonlinear Models

Chapter 5 in Review

Series Solutions of Linear Equations

Solutions About Ordinary Points

Solutions About Singular Points

Special Functions

Chapter 6 in Review

Laplace Transform

Definition of the Laplace Transform

Inverse Transform and Transforms of Derivatives

Operational Properties I

Operational Properties II

Dirac Delta Function

Systems of Linear Differential Equations

Chapter 7 in Review

Systems of Linear First-Order Differential Equations

Preliminary Theory

Homogeneous Linear Systems

Nonhomogeneous Linear Systems

Matrix Exponential

Chapter 8 in Review

Numerical Solutions of Ordinary Differential Equations

Euler Methods

Runge-Kutta Methods

Multistep Methods

Higher-Order Equations and Systems

Second-Order Boundary-Value Problems

Chapter 9 in Review

Gamma Function

Matrices

Laplace Transforms

Answers for Selected Odd-Numbered Problems

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