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Difference Equations: Theory and Applications, by Ronald E. Mickens
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In recent years, the study of difference equations has acquired a new significance, due in large part to their use in the formulation and analysis of discrete-time systems, the numerical integration of differential equations by finite-difference schemes, and the study of deterministic chaos. The second edition of Difference Equations: Theory and Applications provides a thorough listing of all major theorems along with proofs. The text treats the case of first-order difference equations in detail, using both analytical and geometrical methods. Both ordinary and partial difference equations are considered, along with a variety of special nonlinear forms for which exact solutions can be determined. Numerous worked examples and problems allow readers to fully understand the material in the text. They also give possible generalization of the theorems and application models.
The text's expanded coverage of application helps readers appreciate the benefits of using difference equations in the modeling and analysis of "realistic" problems from a broad range of fields. The second edition presents, analyzes, and discusses a large number of applications from the mathematical, biological, physical, and social sciences. Discussions on perturbation methods and difference equation models of differential equation models of differential equations represent contributions by the author to the research literature. Reference to original literature show how the elementary models of the book can be extended to more realistic situations.
Difference Equations, Second Edition gives readers a background in discrete mathematics that many workers in science-oriented industries need as part of their general scientific knowledge. With its minimal mathematical background requirements of general algebra and calculus, this unique volume will be used extensively by students and professional in science and technology, in areas such as applied mathematics, control theory, population science, economics, and electronic circuits, especially discrete signal processing.
- Sales Rank: #3941499 in Books
- Published on: 1991-01-01
- Original language: English
- Number of items: 1
- Dimensions: 9.50" h x 6.25" w x 1.25" l, 1.94 pounds
- Binding: Hardcover
- 464 pages
Most helpful customer reviews
4 of 5 people found the following review helpful.
Fantastic preview of Discrete Calculus!
By Arthur Reever
I'm currently and undergraduate mathematics major who, like too few others, enjoy studying mathematics outside the classroom. I've recently purchased the 2nd edition of this book and find it to be quite fantastic. Having only 4 semesters of calculus, and half a semester of proof structures, under my belt I found this book to be very intuitive and easy to understand. Discrete Calculus (i.e. difference equations)is a very beautiful branch of mathematics, with diverse applications that are just gaining a foothold in mathematics, economics, biology, ecology, physics,...., the list goes on.
If you've ever wondered where the formula [n(n+1)]/2 = 1 + 2 + 3 + 4 + ... + n + ... came from, this book will teach you that within the first 40 pages! And the best is yet to come. Who knew that taking Calculus(the toolbox of the continuous) could be applied to the integers with such beautiful results!!
One extra bit of helpful information for those self studied mathematicians, like myself, who may have little confidence on the accuracy of your arithmetic, this book contains no answers to the questions (which Mickens left in the very back of the book). But fortunately, if you've ever studied some differential calculus, the concepts here are merely a logical extension of that topic applied to the integers, and the best resource one has in Mathematics is patience, reason, and lots of practice.
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