A First Course in Differential Equations (Undergraduate Texts in Mathematics) - Hardcover

Logan, J. David

Hardcover

ISBN 10: 0387259635 ISBN 13: 9780387259635

Publisher: Springer-Verlag New York Inc., 2005

Synopsis

This book is intended as an alternative to the standard differential equations text, which typically includes 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. These texts adds up to several hundred pages of text and can be very expensive for students to buy. Many students do not have the time or desire to read voluminous texts and explore internet supplements. Here, however, the author writes concisely, to the point, and in plain language. Many examples and exercises are included. In addition, this text also encourages students to use a computer algebra system to solve problems numerically, and as such, templates of MATLAB programs that solve differential equations are given in an appendix, as well as basic Maple and Mathematica commands.

About this title

Review

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)

From the Back Cover

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.

Edition details

• Publisher: Springer-Verlag New York Inc.
• Publication date: 2005
• ISBN 10: 0387259635
• ISBN 13: 9780387259635
• Binding: Hardcover
• Language: English
• Number of pages: 308