A First Course in Differential Equations

by J. David Logan

Overview

There are many excellent texts on elementary differential equations designed for the standard sophomore course. However, in spite of the fact that most courses are one semester in length, the texts have evolved into calculus-like pres- tations that include a large collection of methods and applications, packaged with student manuals, and Web-based notes, projects, and supplements. All of this comes in several hundred pages of text with busy formats. Most students do not have the time or desire to read voluminous texts and explore internet supplements. The format of this differential equations book is different; it is a one-semester, brief treatment of the basic ideas, models, and solution methods. Its limited coverage places it somewhere between an outline and a detailed te- book. I have tried to write concisely, to the point, and in plain language. Many worked examples and exercises are included. A student who works through this primer will have the tools to go to the next level in applying differential eq- tions to problems in engineering, science, and applied mathematics. It can give some instructors, who want more concise coverage, an alternative to existing texts.

Product Details

ISBN-13:	9780387259642
Publisher:	Springer New York
Publication date:	08/13/2005
Series:	Undergraduate Texts in Mathematics
Edition description:	2006
Pages:	290
Product dimensions:	8.50(w) x 10.98(h) x (d)

About the Author

J. David Logan is Professor of Mathematics at the University of Nebraska, Lincoln. He is the author of another recent undergraduate textbook, Applied Partial Differential Equations, 2nd Edition (Springer 2004).

Table of Contents

Preface.- Differential Equations and Models.- Analytic Solutions and Approximations.-Second-Order Differential Equations.- Laplace Transforms.- Linear Systems.- Nonlinear Systems.- Appendix A: References.- Appendix B: A Brief on MATLAB.- Appendix C: Maple Commands.- Appendix D: Sample Examinations.- Appendix E: Solutions to Selected Exercises.

Editorial Reviews

From the reviews:

"Logan has produced a well-crafted text, densely packed with interesting applications from diverse fields. The chapters cover (ordinary) differential equations, analytical solutions and approximations, second-order differential equations, Laplace transforms, linear and nonlinear systems. The material is well presented and introduces new concepts … . The text will certainly provide a good mental workout." (Christopher Howls, The Times Higher Education Supplement, November, 2006)

"This is a textbook for those who … want to learn some methods and techniques to handle mathematical models described by ordinary differential equations. … the book contains topics which are not included in other similar texts. … In addition, four appendices are added to complete the presentation … . The book is written in a pleasant and friendly style. It provides the reader with enough knowledge to engage with more advanced topics of differential equations … ." (Gheorghe Morosanu, Zentralblatt MATH, Vol. 1088 (14), 2006)

“This text book provides an introduction into ordinary differential equations on a post-calculus level. Its primary goal is a brief and concise … treatment of the basic ideas, models and solution methods. This goal is reached by a clever selection of the core material. The main text is written in an colloquial and friendly style and supplemented with many exercises and some appendices which among other things cover the use of computer algebra systems as well as solutions to selected exercises.” (R. Steinbauer, Monatshefte für Mathematik, Vol. 154 (1), May, 2008)

From the Publisher