Description

Features

• Unique blend of traditional algebraic and modern qualitative geometric approaches – Tempers the classic pure math approach with the practical, applied aspects of modern DE uses.

• Strong systems approach – Features a full chapter on matrix algebra, followed by three systems chapters. Practical uses of DEs today are not single equations but rather looking at several DEs using a computer.

• Novel modeling approach – Emphasizesproblems and approaches.

• Flexible use of technology – Focuses on solving and interpreting through the inclusion of several optional technology projects. The text is platform-neutral.

New To This Edition

• New Chapter (#11) on Power Series Solutions.

• Updated material throughout – Improved exposition based on current classroom trends as well as the feedback of first edition users. Includes revised coverage of exact first order equations (Ch. 2), matrix algebra (Ch. 7), and systems (Ch. 8).

• Expanded coverage of phase plane portraits – Now covered in two sections, including a new section on the trace-determinant plane.

• Large number of new figures – Help students clearly visualize ideas described in the text. The most geometric text available.

• More application-based examples – Demonstrate to students the broad applications of differential equations.

• Clearly highlighted methods of solution – Make solutions easier to identify throughout the text.

• Extensive new exercises throughout – Including all Chapters 1- 11.

• Appendix on complex numbers and matrices – Gathers information in a single location to make it more readily accessible.

Table of Contents

Chapter 1: Introduction to Differential Equations

Differential Equation Models. The Derivative. Integration.

Differential Equations and Solutions. Solutions to Separable Equations. Models of Motion. Linear Equations.

Mixing Problems. Exact Differential Equations. Existence and Uniqueness of Solutions. Dependence of Solutions on Initial Conditions. Autonomous Equations and Stability.

Project 2.10 The Daredevil Skydiver.

Modeling Population Growth. Models and the Real World. Personal Finance. Electrical Circuits. Project 3.5 The Spruce Budworm. Project 3.6 Social Security, Now or Later.

Definitions and Examples. Second-Order Equations and Systems. Linear, Homogeneous Equations with Constant Coefficients. Harmonic Motion. Inhomogeneous Equations; the Method of Undetermined Coefficients. Variation of Parameters. Forced Harmonic Motion. Project 4.8 Nonlinear Oscillators.

The Definition of the Laplace Transform. Basic Properties of the Laplace Transform 241. The Inverse Laplace Transform

Using the Laplace Transform to Solve Differential Equations. Discontinuous Forcing Terms. The Delta Function. Convolutions. Summary. Project 5.9 Forced Harmonic Oscillators.

Euler’s Method. Runge-Kutta Methods. Numerical Error Comparisons. Practical Use of Solvers. A Cautionary Tale.

Project 6.6 Numerical Error Comparison.

Vectors and Matrices. Systems of Linear Equations with Two or Three Variables. Solving Systems of Equations. Homogeneous and Inhomogeneous Systems. Bases of a subspace. Square Matrices. Determinants.

Chapter 8:  An Introduction to Systems

Definitions and Examples. Geometric Interpretation of Solutions. Qualitative Analysis. Linear Systems. Properties of Linear Systems. Project 8.6 Long-Term Behavior of Solutions.

Chapter 9:  Linear Systems with Constant Coefficients

Overview of the Technique. Planar Systems. Phase Plane Portraits. The Trace-Determinant Plane. Higher Dimensional Systems. The Exponential of a Matrix. Qualitative Analysis of Linear Systems. Higher-Order Linear Equations. Inhomogeneous Linear Systems. Project 9.10 Phase Plane Portraits. Project 9.11 Oscillations of Linear Molecules.

Chapter 10: Nonlinear Systems

The Linearization of a Nonlinear System. Long-Term Behavior of Solutions. Invariant Sets and the Use of Nullclines. Long-Term Behavior of Solutions to Planar Systems. Conserved Quantities. Nonlinear Mechanics. The Method of Lyapunov. Predator—Prey Systems. Project 10.9 Human Immune Response to Infectious Disease. Project 10.10 Analysis of Competing Species.

Chapter 11: Series Solutions to Differential Equations

Review of Power Series. Series Solutions Near Ordinary Points. Legendre’s Equation. Types of Singular Points–Euler’s Equation. Series Solutions Near Regular Singular Points. Series Solutions Near Regular Singular Points – the General Case. Bessel’s Equation and Bessel Functions.

Courses

Differential Equations  (Mathematics)

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Instructor's Solutions Manual for Differential Equations, 2/E
Polking
©2006  |  Pearson  |  Paper; 942 pp  |  Instock
ISBN-10: 0131862359  |  ISBN-13: 9780131862357

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Student Solutions Manual for Differential Equations, 2/E
Polking
©2006  |  Pearson  |  Paper; 498 pp  |  Instock
ISBN-10: 0131437399  |  ISBN-13: 9780131437395
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Ordinary Differential Equations Using MATLAB, 3/E
Polking
©2004  |  Pearson  |  Paper; 264 pp  |  Instock
ISBN-10: 0131456792  |  ISBN-13: 9780131456792
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Allied Health Study Card, 2/E
Forshier
©2006  |  Pearson  |  Study Card  |  Instock
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Basic Math Review Card, 2/E
Addison-Wesley
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Center for Excellence Sticker
Addison Wesley Higher Education Group
©2000  |  Pearson  |  Unknown / Other  |  Instock
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Concept Videos: Algebra
Addison-Wesley
©2008  |  Pearson  |  Multiple Media Package  |  Instock
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Concept Videos: Basic Math & Prealgebra
Addison-Wesley
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Discovering Algebra: Examples with Keystrokes on the TI-83/TI-82 and TI-85/TI-86, A Laboratory Approach
Pirich & Bigliani
©1997  |  Pearson  |  Paper; 195 pp  |  Instock
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Graphing Calculator Tutorial CD
Addison-Wesley
©2006  |  Pearson  |  CD-ROM Only  |  Instock
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Overcoming Math Anxiety, 2/E
Davidson & Levitov
©2000  |  Pearson  |  Paper  |  Instock
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Prealgebra Review Workbook
Wheel
©2006  |  Pearson  |  Paper; 300 pp  |  Instock
ISBN-10: 0321473329  |  ISBN-13: 9780321473325
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Review of Algebra, A
Howard
©2002  |  Pearson  |  Paper; 224 pp  |  Instock
ISBN-10: 0201773473  |  ISBN-13: 9780201773477
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Spanish Basic Math Study Card
Leonarte
©2007  |  Pearson  |  Study Card  |  Instock
ISBN-10: 0321438582  |  ISBN-13: 9780321438584
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TestGen All-in-One 2005 Package
Addison-Wesley
©2005  |  Pearson  |  CD-ROM Only  |  Instock
ISBN-10: 0321334469  |  ISBN-13: 9780321334466
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