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A First Course in Differential Equations With Modeling Applications,9780534379995
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A First Course in Differential Equations With Modeling Applications

by
Edition:
7th
ISBN13:

9780534379995

ISBN10:
0534379990
Format:
Paperback
Pub. Date:
10/5/2000
Publisher(s):
Brooks Cole
List Price: $125.66

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This is the 7th edition with a publication date of 10/5/2000.
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Summary

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.

Table of Contents

Preface ix
Acknowledgments xv
Introduction To Differential Equations
1(38)
Definitions and Terminology
2(13)
Initial-Value Problems
15(7)
Differential Equations as Mathematical Models
22(17)
Chapter 1 in Review
37(2)
First-Order Differential Equations
39(56)
Solution Curves Without the Solution
40(11)
Separable Variables
51(9)
Linear Equations
60(12)
Exact Equations
72(8)
Solutions by Substitutions
80(6)
A Numerical Solution
86(9)
Chapter 2 in Review
92(3)
Modeling With First-Order Differential Equations
95(43)
Linear Equations
96(13)
Nonlinear Equations
109(12)
Systems of Linear and Nonlinear Differential Equations
121(17)
Chapter 3 in Review
130(3)
Project Module: Harvesting of Renewable Natural Resources
133(5)
Gilbert N. Lewis
Higher-Order Differential Equations
138(77)
Preliminary Theory: Linear Equations
139(15)
Initial-Value and Boundary-Value Problems
139(3)
Homogeneous Equations
142(6)
Nonhomogeneous Equations
148(6)
Reduction of Order
154(4)
Homogeneous Linear Equations with Constant Coefficients
158(9)
Undetermined Coefficients--Superposition Approach
167(11)
Undetermined Coefficients--Annihilator Approach
178(10)
Variation of Parameters
188(5)
Cauchy-Euler Equation
193(8)
Solving Systems of Linear Equations by Elimination
201(6)
Nonlinear Equations
207(8)
Chapter 4 in Review
212(3)
Modeling with Higher-Order Differential Equations
215(52)
Linear Equations: Initial-Value Problems
216(21)
Spring/Mass Systems: Free Undamped Motion
216(4)
Spring/Mass Systems: Free Damped Motion
220(4)
Spring/Mass Systems: Driven Motion
224(3)
Series Circuit Analogue
227(10)
Linear Equations: Boundary-Value Problems
237(10)
Nonlinear Equations
247(20)
Chapter 5 in Review
259(4)
Project Module: The Collapse of the Tacoma Narrows Suspension Bridge
263(4)
Gilbert N. Lewis
Series Solutions of Linear Equations
267(39)
Solutions About Ordinary Points
268(12)
Review of Power Series
268(3)
Power Series Solutions
271(9)
Solutions About Singular Points
280(12)
Two Special Equations
292(14)
Chapter 6 in Review
304(2)
The Laplace Transform
306(58)
Definition of the Laplace Transform
307(7)
Inverse Transform and Transforms of Derivatives
314(10)
Translation Theorems
324(14)
Translation on the s-Axis
324(4)
Translation on the t-Axis
328(10)
Additional Operational Properties
338(13)
Dirac Delta Function
351(3)
Systems of Linear Equations
354(10)
Chapter 7 in Review
361(3)
Systems of Linear First-Order Differential Equations
364(46)
Preliminary Theory
365(10)
Homogeneous Linear Systems with Constant Coefficients
375(18)
Distinct Real Eigenvalues
376(4)
Repeated Eigenvalues
380(4)
Complex Eigenvalues
384(9)
Variation of Parameters
393(6)
Matrix Exponential
399(11)
Chapter 8 in Review
404(2)
Project Module: Earthquake Shaking of Multistory Buildings
406(4)
Gilbert N. Lewis
Numerical Solutions of Ordinary Differential Equations
410
Euler Methods and Error Analysis
411(6)
Runge-Kutta Methods
417(7)
Multistep Methods
424(3)
Higher-Order Equations and Systems
427(6)
Second-Order Boundary-Value Problems
433
Chapter 9 in Review
438
APPENDIXES 1(1)
I Gamma Functions
1(2)
II Introduction to Matrices
3(22)
III Laplace Transforms
25
Selected Answers for Odd-Numbered Problems 1(1)
Index 1


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