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A Course in Ordinary Differential Equations, Second Edition



A Course in Ordinary Differential Equations, Second Edition

Author: Stephen A. Wirkus

Publisher: Chapman and Hall

Genres:

Publish Date: December 15, 2014

ISBN-10: 1466509082

Pages: 807

File Type: PDF

Language: English

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Book Preface

This book is based on lectures given by the rst author at Cal Poly Pomona, Arizona State University (ASU), and the Massachusetts Institute of Technology (MIT), and by the second author atWestern Kentucky University (WKU) and California State Polytechnic University{Pomona (Cal Poly Pomona). The text can be used for a traditional one-semester sophomore-level course in ordinary di erential equations (such as WKU’s MATH 331). However, there is ample material for a two-quarter sequence (such as Cal Poly Pomona’s MAT 216-431), as well as sucient linear algebra in the text so that it can be used for a one-quarter course that combines di erential equations and linear algebra (such as Cal Poly Pomona Math 224), or a one-semester course in di erential equations that brings in linear algebra in a signi cant way (such as ASU’s MAT 275 or MIT’s 18.03 without the PDEs). Most signi cantly, computer labs are given in MATLABR ,1 MapleTM, and Mathematica at the end of each chapter so the book may be used for a course to introduce and equip the student with a knowledge of the given software (such as ASU’s MAT 275). Near the end of this Preface, we give some sample course outlines that will help show the independence of various sections and chapters. The focus of the text is on applications and methods of solution, both analytical and numerical, with emphasis on methods used in the typical engineering, physics, or mathematics student’s eld of study. We have tried to provide sucient problems of a mathematical nature at the end of each section so that even the pure math major will be suciently challenged.

Contents

  • 1 Traditional First-Order Di erential Equations
  • 2 Geometrical and Numerical Methods for First-Order Equations
  • 3 Elements of Higher-Order Linear Equations
  • 4 Techniques of Nonhomogeneous Higher-Order Linear Equations
  • 5 Fundamentals of Systems of Di erential Equations
  • 6 Geometric Approaches and Applications of Systems of Differential Equations
  • 7 Laplace Transforms
  • 8 Series Methods
  • A An Introduction to MATLAB, Maple, and Mathematica
  • B Selected Topics from Linear Algebra

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