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This revised introduction to the basic methods, theory and applications of elementary differential equations employs a two part organization. Part I includes all the basic material found in a one semester introductory course in ordinary differential equations. Part II introduces students to certain specialized and more advanced methods, as well as providing a systematic introduction to fundamental theory.
Partial table of contents:
FUNDAMENTAL METHODS AND APPLICATIONS.
First-Order Equations for Which Exact Solutions Are Obtainable.
Explicit Methods of Solving Higher-Order Linear Differential Equations.
Series Solutions of Linear Differential Equations.
Approximate Methods of Solving First-Order Equations.
FUNDAMENTAL THEORY AND FURTHER METHODS.
Existence and Uniqueness Theory.
Sturm-Liouville Boundary-Value Problems and Fourier Series.
Partial Differential Equations.
Posted March 26, 2000
I would challenge anyone to find explanations which are as thorough and as understandable as may be found herein. Take a look at the section on the method of undetermined coefficients and you will see a salient example of its best features.
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