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    Brian Doyle 9780870717543

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Differential Equations (2ND 06 Edition)


Differential Equations (2ND 06 Edition) Cover


Synopses & Reviews

Publisher Comments:

Combining traditional material with a modern systems approach, this handbook provides a thorough introduction to differential equations, tempering its classic "pure math" approach with more practical applied aspects. Features up-to-date coverage of key topics such as first order equations, matrix algebra, systems, and phase plane portraits. Illustrates complex concepts through extensive detailed figures. Focuses on interpreting and solving problems through optional technology projects. For anyone interested in learning more about differential equations.


This package contains the following components:

-0131437380: Differential Equations

-0131456792: Ordinary Differential Equations Using MATLAB

Table of Contents

Chapter 1: Introduction to Differential Equations

Differential Equation Models. The Derivative. Integration.

  Chapter 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 2.10 The Daredevil Skydiver.

  Chapter 3: Modeling and Applications

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.

  Chapter 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 4.8 Nonlinear Oscillators.

  Chapter 5: The Laplace Transform

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.

  Chapter 6: Numerical Methods

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

Project 6.6 Numerical Error Comparison.

  Chapter 7: Matrix Algebra

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.



Product Details

Polking, John
Polking, John C.
Cram101 Textbook Reviews
Arnold, David
Boggess, Al
Boggess, Albert
Polking, John
Differential Equations
Mathematics-Differential Equations
Edition Number:
Edition Description:
Trade paper
Featured Titles for Differential Equations
Publication Date:
June 2005
Grade Level:
College/higher education:
10.1 x 8 x 1.1 in 1229 gr

Related Subjects

Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » General

Differential Equations (2ND 06 Edition) New Hardcover
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$164.40 In Stock
Product details 656 pages Prentice Hall - English 9780131437388 Reviews:
"Synopsis" by , This package contains the following components:

-0131437380: Differential Equations

-0131456792: Ordinary Differential Equations Using MATLAB

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