Second Course in Elementary Differential Equations

Name: Second Course in Elementary Differential Equations
Price: 6.74 USD
Availability: InStock
ISBN: 9780486434780

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 and elementary ideas from dynamic systems. Features an in-depth treatment of existence and uniqueness theorems, more. 1986 edition. Includes 39 figures.

Book details

List price: $18.95
Copyright year: 2004
Publisher: Dover Publications, Incorporated
Publication date: 3/23/2004
Binding: Paperback
Pages: 272
Size: 6.06" wide x 9.21" long x 0.40" tall
Weight: 0.792
Language: English



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