Second Course in Elementary Differential Equations

ISBN-10: 0486434788
ISBN-13: 9780486434780
Edition: 2004
Authors: Paul Waltman
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Description: Focusing on applicable rather than applied mathematics, this text begins with an examination of linear systems of differential equations and 2-dimensional linear systems and then explores the use of polar coordinate techniques, Liapunov stability  More...

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Book details

List price: $18.95
Copyright year: 2004
Publisher: Dover Publications, Incorporated
Publication date: 3/23/2004
Binding: Paperback
Pages: 272
Size: 5.75" wide x 9.25" long x 0.40" tall
Weight: 1.034
Language: English

Focusing on applicable rather than applied mathematics, this text begins with an examination of linear systems of differential equations and 2-dimensional linear systems and then explores the use of polar coordinate techniques, Liapunov stability and elementary ideas from dynamic systems. Features an in-depth treatment of existence and uniqueness theorems, more. 1986 edition. Includes 39 figures.

Preface
Systems of Linear Differential Equations
Introduction
Some Elementary Matrix Algebra
The Structure of Solutions of Homogeneous Linear Systems
Matrix Analysis and the Matrix Exponential
The Constant Coefficient Case: Real and Distinct Eigenvalues
The Constant Coefficient Case: Complex and Distinct Eigenvalues
The Constant Coefficient Case: The Putzer Algorithm
General Linear Systems
Some Elementary Stability Considerations
Periodic Coefficients
Scalar Equations
An Application: Coupled Oscillators
Two-Dimensional Autonomous Systems
Introduction
The Phase Plane
Critical Points of Some Special Linear Systems
Critical Points of General Two-Dimensional Linear Systems
Behavior of Nonlinear Two-Dimensional Systems Near a Critical Point
Elementary Liapunov Stability Theory
Limit Cycles and the Poincare-Bendixon Theorem
An Example: Lotka-Volterra Competition
An Example: The Simple Pendulum
Existence Theory
Introduction
Preliminaries
The Contraction Mapping Theorem
The Initial Value Problem for One Scalar Differential Equation
The Initial Value Problem for Systems of Differential Equations
An Existence Theorem for a Boundary Value Problem
Boundary Value Problems
Introduction
Linear Boundary Value Problems
Oscillation and Comparison Theorems
Sturm-Liouville Problems
The Existence of Eigenvalues for Sturm-Liouville Problems
Two Properties of Eigenfunctions
An Alternate Formulation - Integral Equations
Eigenfunction Expansions
The Inhomogeneous Sturm-Liouville Problem
Some Standard Applications of Sturm-Liouville Theory
Nonlinear Boundary Value Problems
Index

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