Differential Equations A Concise Course

ISBN-10: 0486406784

ISBN-13: 9780486406787

Edition: N/A

Authors: H. S. Bear

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Book details

List price: $12.95
Publisher: Dover Publications, Incorporated
Publication date: 11/2/2011
Binding: Paperback
Pages: 224
Size: 5.50" wide x 8.75" long x 0.50" tall
Weight: 0.484
Language: English

First Order Equations
Variable separate
Geometric interpretation of first order equations
Existence and uniqueness theorem
Families of curves and envelopes
Clairaut equations
Special Methods for First Order Equations
Homogeneous equations--substitutions
Exact equations
Line integrals
First order linear equations--integrating factors
Orthogonal families
Review of power series
Series solutions
Linear Equations
Two theorems on linear algebraic equations
General theory of linear equations
Second order equations with constant coefficients
Special Methods for Linear Equations
Complex-valued solutions
Linear differential operators
Homogeneous equations with constant coefficients
Method of undetermined coefficients
Inverse operators
Variation of parameters method
The Laplace Transform
Review of improper integrals
The Laplace transform
Properties of the transform
Solution of equations by transforms
Picard's Existence Theorem
Outline of the Picard method
Proof of existence and uniqueness
Approximations to solutions
Systems of Equations
Geometric interpretation of a system
Other interpretations of a system
A system equivalent to M(x,y)dx+N(x,y)dy=0
Existence and uniqueness theorems
Existence theorem for nth order equations
Polygonal approximations for systems
Linear systems
Operator methods
Laplace transform methods
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