A First Course in Differential Equations with Modeling Applications (with CD-ROM and iLrn Tutorial)

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  • Edition: 8th
  • Format: Hardcover
  • Copyright: 2004-10-20
  • Publisher: Brooks Cole
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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.

Table of Contents

Prefacep. ix
Acknowledgmentsp. xv
Introduction to Differential Equationsp. 1
Definitions and Terminologyp. 2
Initial-Value Problemsp. 15
Differential Equations as Mathematical Modelsp. 22
Chapter 1 in Reviewp. 37
First-Order Differential Equationsp. 39
Solution Curves Without the Solutionp. 40
Separable Variablesp. 51
Linear Equationsp. 60
Exact Equationsp. 72
Solutions by Substitutionsp. 80
A Numerical Solutionp. 86
Chapter 2 in Reviewp. 92
Modeling with First-Order Differential Equationsp. 95
Linear Equationsp. 96
Nonlinear Equationsp. 109
Systems of Linear and Nonlinear Differential Equationsp. 121
Chapter 3 in Reviewp. 130
Project Module: Harvesting of Renewable Natural Resourcesp. 133
Higher-Order Differential Equationsp. 138
Preliminary Theory: Linear Equationsp. 139
Initial-Value and Boundary-Value Problemsp. 139
Homogeneous Equationsp. 142
Nonhomogeneous Equationsp. 148
Reduction of Orderp. 154
Homogeneous Linear Equations with Constant Coefficientsp. 158
Undetermined Coefficients--Superposition Approachp. 167
Undetermined Coefficients--Annihilator Approachp. 178
Variation of Parametersp. 188
Cauchy-Euler Equationp. 193
Solving Systems of Linear Equations by Eliminationp. 201
Nonlinear Equationsp. 207
Chapter 4 in Reviewp. 212
Modeling with Higher-Order Differential Equationsp. 215
Linear Equations: Initial-Value Problemsp. 216
Spring/Mass Systems: Free Undamped Motionp. 216
Spring/Mass Systems: Free Damped Motionp. 220
Spring/Mass Systems: Driven Motionp. 224
Series Circuit Analoguep. 227
Linear Equations: Boundary-Value Problemsp. 237
Nonlinear Equationsp. 247
Chapter 5 in Reviewp. 259
Project Module: The Collapse of the Tacoma Narrows Suspension Bridgep. 263
Series Solutions of Linear Equationsp. 267
Solutions About Ordinary Pointsp. 268
Review of Power Seriesp. 268
Power Series Solutionsp. 271
Solutions About Singular Pointsp. 280
Two Special Equationsp. 292
Chapter 6 in Reviewp. 304
The Laplace Transformp. 306
Definition of the Laplace Transformp. 307
Inverse Transform and Transforms of Derivativesp. 314
Translation Theoremsp. 324
Translation on the s-Axisp. 324
Translation on the t-Axisp. 328
Additional Operational Propertiesp. 338
Dirac Delta Functionp. 351
Systems of Linear Equationsp. 354
Chapter 7 in Reviewp. 361
Systems of Linear First-Order Differential Equationsp. 364
Preliminary Theoryp. 365
Homogeneous Linear Systems with Constant Coefficientsp. 375
Distinct Real Eigenvaluesp. 376
Repeated Eigenvaluesp. 380
Complex Eigenvaluesp. 384
Variation of Parametersp. 393
Matrix Exponentialp. 399
Chapter 8 in Reviewp. 404
Project Module: Earthquake Shaking of Multistory Buildingsp. 406
Numerical Solutions of Ordinary Differential Equationsp. 410
Euler Methods and Error Analysisp. 411
Runge-Kutta Methodsp. 417
Multistep Methodsp. 424
Higher-Order Equations and Systemsp. 427
Second-Order Boundary-Value Problemsp. 433
Chapter 9 in Reviewp. 438
Appendixesp. 1
Gamma Functionsp. 1
Introduction to Matricesp. 3
Laplace Transformsp. 25
Selected Answers for Odd-Numbered Problemsp. 1
Indexp. 1
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