A First Course in Differential Equations / Edition 1

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"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." 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 provided, and an appendix contains templates of Maple and MATLAB commands and programs that are useful in differential equations.
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Editorial Reviews

From the Publisher
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 reviews of the second edition:

“Designed for standard second-year courses in differential equations, this text covers the basic ideas, models and solution methods in a format intended to be accessible to engineering, economics and mathematics students. Logan emphasises analytical, graphical and numerical techniques, and provides a strong connection to applications with motivations in mechanics and heat transfer, circuits, biology, economics and chemical reactors.” (Times Higher Education, May, 2011)

“The new edition covers essentially the same material as the first, with minor rearrangements, and it is about one-third longer. The coverage of linear systems in the plane is nicely detailed and illustrated. … Simple numerical methods are illustrated and the use of Maple and MATLAB is encouraged. There are over thirty pages of solutions and hints to selected exercises as well. … select Dave Logan’s new and improved text for my course.” (Robert E. O’Malley, Jr., SIAM Review, Vol. 53 (2), 2011)

“Aims to provide material for a one-semester course that emphasizes the basic ideas, solution methods, and an introduction to modeling. … The book that results offers a concise introduction to the subject for students of mathematics, science and engineering who have completed the introductory calculus sequence. … There are an adequate number of exercises … . Solutions are provided for … exercises in an appendix. This book is worth a careful look as a candidate text for the next differential equations course you teach.” (William J. Satzer, The Mathematical Association of America, January, 2011)

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Product Details

  • ISBN-13: 9780387259642
  • Publisher: Springer New York
  • Publication date: 12/28/2005
  • Series: Undergraduate Texts in Mathematics Series
  • Edition description: 2006
  • Edition number: 1
  • Pages: 290
  • Product dimensions: 6.90 (w) x 9.10 (h) x 0.60 (d)

Meet the Author

J. David Logan is Willa Cather Professor of Mathematics at the University of Nebraska Lincoln. His extensive research is in the areas of theoretical ecology, hydrogeology, combustion, mathematical physics, and partial differential equations. He is the author of six textbooks on applied mathematics and its applications, including Applied Partial Differential Equations, 2nd edition (Springer 2004) and Transport Modeling in Hydrogeochemical Systems (Springer 2001).

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Table of Contents

1 Differential equations and models 1
2 Analytic solutions and approximations 55
3 Second-order differential equations 83
4 Laplace transforms 133
5 Linear systems 159
6 Nonlinear systems 209
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