A First Course in Differential Equations

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. This is what makes the format of this differential equations book so unique. It is a one-semester, brief treatment of the basic ideas, models, and solution methods. The author writes concisely and to the point. 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.

Concise treatment of elementary differential equations, based on a course taught by the author at University of Nebraska, Lincoln Encourages the use of computer algebra systems - includes Maple, Mathematica, and Matlab codes Includes numerous examples and exercises, along with solutions to selected exercises Includes supplementary material: sn.pub/extras

Auteur

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).

Texte du rabat

This text is designed for the standard post-calculus course in elementary differential equations. It is a brief, one-semester treatment of the basic ideas, models, and solution methods. The book, which serves as an alternative to existing texts for instructors who want more concise coverage, emphasizes graphical, analytical, and numerical approaches, and is written with clear language in a user-friendly format. It provides students with the tools to continue on to the next level in applying differential equations to problems in engineering, science, and applied mathematics.

The topics include:

• separable and linear first-order equations;

• autonomous equations;

• second order linear homogeneous and nonhomogeneous equations;

• Laplace transforms;

• linear and nonlinear systems in the phase plane.

Many exercises are provided, in addition to examples from engineering, ecology, physics, economics, and other areas. An expanded section on the required linear algebra is presented, and an appendix contains templates of Maple and MATLAB commands and programs which are useful in differential equations.

Contenu
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.