A First Course in Differential Equations

ISBN-13: 9780387259642 / Angielski / Miękka / 2005 / 290 str.

J. David Logan

Opis

Therearemanyexcellenttextsonelementarydi?erentialequationsdesignedfor 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 di?erential equations book is di?erent; it is a one-semester, brief treatment of the basic ideas, models, and solution methods. Itslimitedcoverageplacesitsomewherebetweenanoutlineandadetailedte- 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 di?erential 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.

Recenzje

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)

Spis treści

Differential Equations and Models.- Analytic Solutions and Approximations.- Second-Order Differential Equations.- Laplace Transforms.- Linear Systems.- Nonlinear Systems.

O autorze

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).

Blurb

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.