Mathematics

• Unique blend of traditional algebraic and modern qualitative geometric approaches – Tempers the classic pure math approach (algebraic) 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.

• 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 Chapters 11, 12, and 13 on power series methods, Fourier series, and partial differential equations.

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

• FREE when shrink-wrapped with the text are manuals for MATLAB, Maple, and Mathematica.

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

Chapter 12: Fourier Series

Computation of Fourier Series. Convergence of Fourier Series. Fourier Cosine and Sine Series. The Complex Form of a Fourier Series. The Discrete Fourier Transform and the FFT.

Chapter 13: Partial Differential Equations

Derivation of the Heat Equation. Separation of Variables for the Heat Equation. The Wave Equation. Laplace’s Equation. Laplace’s Equation on a Disk. Sturm Liouville Problems. Orthogonality and Generalized Fourier Series. Temperature in a Ball–Legendre Polynomials. Time Dependent PDEs in Higher Dimension. Domains with Circular Symmetry–Bessel Functions.

Appendix: Complex Numbers and Matrices

Answers to Odd-Numbered Problems

Index

Differential Equations  (Mathematics)

Companion Website - Polking, 2/E
Polking
©2006 | Pearson | On-line Supplement | Estimated Availability : 07/15/2005
ISBN-10: 0131862383 | ISBN-13: 9780131862388
This online resource is available at no cost at http://www.prenhall.com/polking.

Companion Website - Polking, 2/E
Polking
©2006 | Pearson | On-line Supplement | Estimated Availability : 07/15/2005
ISBN-10: 0131862383 | ISBN-13: 9780131862388
This online resource is available at no cost at http://www.prenhall.com/polking.

Instructor's Solutions Manual, 2/E
Polking
©2006 | Pearson | Paper; 942 pp | Out of Stock
ISBN-10: 0131862359 | ISBN-13: 9780131862357
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Companion Website - Polking, 2/E
Polking
©2006 | Pearson | On-line Supplement | Estimated Availability : 07/15/2005
ISBN-10: 0131862383 | ISBN-13: 9780131862388
This online resource is available at no cost at http://www.prenhall.com/polking.

Student Solutions Manual, 2/E
Polking
©2006 | Pearson | Paper; 498 pp | Instock
ISBN-10: 0131437399 | ISBN-13: 9780131437395
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For Differential Equations

Maple Projects for Differential Equations
Gilbert & Hsiao
©2003 | Pearson | Paper; 200 pp | Instock
ISBN-10: 0130479748 | ISBN-13: 9780130479747
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Addison-Wesley's Algebra Review
Addison-Wesley
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ISBN-10: 0321247086 | ISBN-13: 9780321247087
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Addison-Wesley's Basic Math Review
Addison-Wesley
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Algebra Review Study Card, 2/E
D'Ippolito & Generazzo
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Allied Health Study Card, 2/E
Forshier
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ISBN-10: 0321394747 | ISBN-13: 9780321394743
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Basic Math Review Card, 2/E
Addison-Wesley
©2006 | Pearson | Study Card; 6 pp | Instock
ISBN-10: 0321394763 | ISBN-13: 9780321394767
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Concept Videos: Algebra
Addison-Wesley
©2008 | Pearson | Multiple Media Package | Instock
ISBN-10: 0321517199 | ISBN-13: 9780321517197
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Concept Videos: Basic Math & Prealgebra
Addison-Wesley
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ISBN-10: 032151758X | ISBN-13: 9780321517586
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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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Finite Mathematics Study Card
Addison-Wesley
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Flash Review Series: Algebra
Becker
©2004 | Pearson | Paper | Instock
ISBN-10: 0321143094 | ISBN-13: 9780321143099
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Graphing Calculator Reference Card, 3/E
Ripley
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Graphing Calculator Tutorial CD
Addison-Wesley
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Math for Allied Health Study/Reference Card
Forshier
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Mathematics Spanish Glossary, 2/E
Lara & Peeples
©2000 | Pearson | Paper; 48 pp | Instock
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Overcoming Math Anxiety, 2/E
Davidson & Levitov
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Pearson TI Rebate Coupon $15, 2/E
Pearson
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Prealgebra Review Workbook
Wheel
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Review of Algebra, A
Howard
©2002 | Pearson | Paper; 224 pp | Instock
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Saleable Technology Bundle, 2/E
Pearson
©2009 | Pearson | Multiple Media Package | Estimated Availability : 09/01/2008
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Spanish Basic Math Study Card
Leonarte
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Stand-alone Access Code Tutor Center
Addison-Wesley
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Companion Website - Polking, 2/E
Polking
©2006 | Pearson | On-line Supplement | Estimated Availability : 07/15/2005
ISBN-10: 0131862383 | ISBN-13: 9780131862388
This online resource is available at no cost at http://www.prenhall.com/polking.

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