A Course in Ordinary Differential Equations, Second Edition

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 dierential 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 dierential equations and linear algebra (such as Cal Poly Pomona Math 224), or a one-semester course in dierential equations that brings in linear algebra in a signicant way (such as ASU’s MAT 275 or MIT’s 18.03 without the PDEs). Most signicantly, 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 Dierential 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 Dierential 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