A Textbook on Ordinary Differential Equations

✍ Scribed by Shair Ahmad, Antonio Ambrosetti (auth.)

Publisher: Springer International Publishing
Year: 2014
Tongue: English
Leaves: 323
Series: Unitext - La Matematica per il 3+2
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

The book is a primer of the theory of Ordinary Differential Equations. Each chapter is completed by a broad set of exercises; the reader will also find a set of solutions of selected exercises. The book contains many interesting examples as well (like the equations for the electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, and many other) which introduce the reader to some interesting aspects of the theory and its applications. The work is mainly addressed to students of Mathematics, Physics, Engineering, Statistics, Computer Sciences, with knowledge of Calculus and Linear Algebra, and contains more advanced topics for further developments, such as Laplace transform; Stability theory and existence of solutions to Boundary Value problems.

A complete Solutions Manual, containing solutions to all the exercises published in the book, is available. Instructors who wish to adopt the book may request the manual by writing directly to one of the authors.

✦ Table of Contents

Front Matter....Pages i-xiv
First order linear differential equations....Pages 1-14
Theory of first order differential equations....Pages 15-34
First order nonlinear differential equations....Pages 35-64
Existence and uniqueness for systems and higher order equations....Pages 65-70
Second order equations....Pages 71-112
Higher order linear equations....Pages 113-122
Systems of first order equations....Pages 123-154
Qualitative analysis of 2 x 2 systems and nonlinear second order equations....Pages 155-172
Sturm Liouville eigenvalue theory....Pages 173-182
Solutions by infinite series and Bessel functions....Pages 183-205
Laplace transform....Pages 207-232
Stability theory....Pages 233-257
Boundary value problems....Pages 259-276
Errata....Pages E1-E5
Back Matter....Pages 277-312

✦ Subjects

Ordinary Differential Equations; Analysis; Numerical Analysis; Applications of Mathematics

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