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First Course in Differential Equations with Modeling Applications

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ISBN-10: 0534418783

ISBN-13: 9780534418786

Edition: 8th 2005

Authors: Dennis G. Zill

List price: $360.95
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Master differential equations and succeed in your course with A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS with accompanying CD-ROM and technology! Straightfoward and readable, this mathematics text provides you with tools such as examples, explanations, definitions, and applications designed to help you succeed. The accompanying DE Tools CD-ROM makes helps you master difficult concepts through twenty-one demonstration tools such as Project Tools and Text Tools. Studying is made easy with iLrn Tutorial, a text-specific, interactive tutorial software program that gives the practice you need to succeed.
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Book details

List price: $360.95
Edition: 8th
Copyright year: 2005
Publisher: Brooks/Cole
Publication date: 10/20/2004
Binding: Hardcover
Pages: 472
Size: 8.50" wide x 11.00" long x 0.75" tall
Weight: 2.684
Language: English

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 the Solution
Separable Variables
Linear Equations
Exact Equations
Solutions by Substitutions
A Numerical Solution
Chapter 2 in Review
Modeling with First-Order Differential Equations
Linear Equations
Nonlinear Equations
Systems of Linear and Nonlinear Differential Equations
Chapter 3 in Review
Project Module: Harvesting of Renewable Natural Resources
Higher-Order Differential Equations
Preliminary Theory: Linear Equations
Initial-Value and Boundary-Value Problems
Homogeneous Equations
Nonhomogeneous 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 Equations by Elimination
Nonlinear Equations
Chapter 4 in Review
Modeling with Higher-Order Differential Equations
Linear Equations: Initial-Value Problems
Spring/Mass Systems: Free Undamped Motion
Spring/Mass Systems: Free Damped Motion
Spring/Mass Systems: Driven Motion
Series Circuit Analogue
Linear Equations: Boundary-Value Problems
Nonlinear Equations
Chapter 5 in Review
Project Module: The Collapse of the Tacoma Narrows Suspension Bridge
Series Solutions of Linear Equations
Solutions About Ordinary Points
Review of Power Series
Power Series Solutions
Solutions About Singular Points
Two Special Equations
Chapter 6 in Review
The Laplace Transform
Definition of the Laplace Transform
Inverse Transform and Transforms of Derivatives
Translation Theorems
Translation on the s-Axis
Translation on the t-Axis
Additional Operational Properties
Dirac Delta Function
Systems of Linear Equations
Chapter 7 in Review
Systems of Linear First-Order Differential Equations
Preliminary Theory
Homogeneous Linear Systems with Constant Coefficients
Distinct Real Eigenvalues
Repeated Eigenvalues
Complex Eigenvalues
Variation of Parameters
Matrix Exponential
Chapter 8 in Review
Project Module: Earthquake Shaking of Multistory Buildings
Numerical Solutions of Ordinary Differential Equations
Euler Methods and Error Analysis
Runge-Kutta Methods
Multistep Methods
Higher-Order Equations and Systems
Second-Order Boundary-Value Problems
Chapter 9 in Review
Gamma Functions
Introduction to Matrices
Laplace Transforms
Selected Answers for Odd-Numbered Problems