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Differential Equations with Boundary Value Problems
John Polking, Rice University
Albert Boggess
David Arnold, College of the Redwoods

ISBN-10: 0130911062
ISBN-13: 9780130911063

Publisher: Prentice Hall
Copyright: 2002
Format: Cloth; 907 pp
Published: 06/30/2002

This item has been replaced by Differential Equations with Boundary Value Problems, 2/E.

Ideal for one or two term first courses in differential equations for engineering, math, biology, and finance majors.

This text strikes a balance between the traditional and the modern. It combines the traditional material with a modern systems emphasis. It offers flexibility of use that will allow faculty at a variety of institutions to use the book with extensive problem sets.

A unique blend of traditional algebraic approach with the modern qualitative geometric approach—The traditional pure math approach is now modified by practical, applied aspects of modern DE uses.

Strong systems emphasis—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—A whole chapter is devoted to modeling, emphasizing problems, and approaches.

Flexible use of technology—Many optional technology projects are included. There are also a large number of modern graphics that show but do not require technology. The emphasis is on solving and interpreting.

Strong emphasis on numerical techniques throughout.

FREE MATLAB manual available.

1. Introduction to Differential Equations.

Differential Equation Models. The Derivative. Integration.

2. First-Order Equations.

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—The Daredevil Skydiver.

3. Modeling and Applications.

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

4. Second-Order Equations.

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—Nonlinear Harmonic Oscillators.

5. The Laplace Transform.

The Definition of the Laplace Transform. Basic Properties of the Laplace Transform. The Inverse Laplace Transform. Using the Laplace Transform to Solve Differential Equations. Discontinuous Forcing Terms. The Delta Function. Convolutions. Summary. Project—Forced Harmonic Oscillators.

6. Numerical Methods.

Euler's Method. Runge-Kutta Methods. Numerical Error Comparisons. Other Solvers. A Cautionary Tale. Project—Numerical Error Comparison.

7. Matrix Algebra.

Vectors and Matrices. The Geometry of Systems of Linear Equations. Solving Systems of Equations. Properties of Solution Sets. Subspaces. Determinants.

8. An Introduction to Systems.

Definition and Examples. Geometric Interpretation of Solutions. Qualitative Analysis. Linear Systems. Project—Long Term Behavior of Solutions.

9. Linear Systems with Constant Coefficients.

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

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—Human Immune Response to Infectious Disease. Project—Analysis of Competing Species.

11. Power Series Solutions.

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. Solutions in the Exceptional Cases. Bessel's Equation and Bessel Functions.

12. Fourier Series Methods.

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.

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.

Differential Equations (Mathematics)

Differential Equations with Boundary Value Problems, 2/E
Polking, Boggess & Arnold
©2006 | Prentice Hall | Cloth; 768 pp | Instock
ISBN-10: 0131862367 | ISBN-13: 9780131862364
Brief Description | Buy from myPearsonStore

Combining traditional differential equation material with a modern qualitative and systems approach, this new edition continues to deliver flexibility of use and extensive problem sets. The second edition’s refreshed presentation includes extensive new visuals, as well as updated exercises throughout.

Companion Website - Polking
Polking
©2002 | Prentice Hall | On-line Supplement | Estimated Availability : 08/03/2002
ISBN-10: 0130673226 | ISBN-13: 9780130673220

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