A First Course in Differential Equations

J. David Logan - Collection Undergraduate Texts in Mathematics

288 pages, parution le 01/12/2005

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Résumé

While the standard sophomore course on elementary differential equations is typically one semester in length, most of the texts currently being used for these courses have evolved into calculus-like presentations that include a large collection of methods and applications, packaged with state-of-the-art color graphics, student solution manuals, the latest fonts, marginal notes, and web-based supplements. All of this adds up to several hundred pages of text and can be very expensive. Many students do not have the time or desire to read voluminous texts and explore internet supplements. Thats what makes the format of this differential equations book unique. 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 textbook. The author writes 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 ODEs to problems in engineering, science, and applied mathematics. It will also give instructors, who want more concise coverage, an alternative to existing texts.

This text also encourages students to use a computer algebra system to solve problems numerically. It can be stated with certainty that the numerical solution of differential equations is a central activity in science and engineering, and it is absolutely necessary to teach students scientific computation as early as possible. Templates of MATLAB programs that solve differential equations are given in an appendix. Maple and Mathematica commands are given as well. The author taught this material on several occasions to students who have had a standard three-semester calculus sequence. It has been well received by many students who appreciated having a small, definitive parcel of material to learn. Moreover, this text gives students the opportunity to start reading mathematics at a slightly higher level than experienced in pre-calculus and calculus; not every small detail is included. Therefore the book can be a bridge in their progress to study more advanced material at the junior-senior level, where books leave a lot to the reader and are not packaged with elementary formats.

Written for:

Undergraduate math and engineering majors

L'auteur - J. David Logan

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).

Sommaire

Preface
To the Student
Differential Equations and Models
Analytic Solutions and Approximations
Second-Order Differential Equations
Laplace Transforms
Linear Systems
Nonlinear Systems
Appendix A: References
Appendix B: Computer Algebra Systems
Appendix C: Sample Examinations
Appendix D: Solutions to Selected Exercises
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	J. David Logan
Collection	Undergraduate Texts in Mathematics
Parution	01/12/2005
Nb. de pages	288
Format	18 x 24
Couverture	Relié
Poids	646g
Intérieur	Noir et Blanc
EAN13	9780387259635
ISBN13	978-0-387-25963-5