Overview
- Authors:
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Calvin D. Ahlbrandt
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University of Missouri, USA
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Allan C. Peterson
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University of Nebraska, USA
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Table of contents (9 chapters)
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- Calvin D. Ahlbrandt, Allan C. Peterson
Pages 1-44
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- Calvin D. Ahlbrandt, Allan C. Peterson
Pages 45-69
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- Calvin D. Ahlbrandt, Allan C. Peterson
Pages 71-151
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- Calvin D. Ahlbrandt, Allan C. Peterson
Pages 153-197
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- Calvin D. Ahlbrandt, Allan C. Peterson
Pages 199-262
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- Calvin D. Ahlbrandt, Allan C. Peterson
Pages 263-294
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- Calvin D. Ahlbrandt, Allan C. Peterson
Pages 295-317
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- Calvin D. Ahlbrandt, Allan C. Peterson
Pages 319-330
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- Calvin D. Ahlbrandt, Allan C. Peterson
Pages 331-356
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Back Matter
Pages 357-375
About this book
This book should be accessible to students who have had a first course in matrix theory. The existence and uniqueness theorem of Chapter 4 requires the implicit function theorem, but we give a self-contained constructive proof ofthat theorem. The reader willing to accept the implicit function theorem can read the book without an advanced calculus background. Chapter 8 uses the Moore-Penrose pseudo-inverse, but is accessible to students who have facility with matrices. Exercises are placed at those points in the text where they are relevant. For U. S. universities, we intend for the book to be used at the senior undergraduate level or beginning graduate level. Chapter 2, which is on continued fractions, is not essential to the material of the remaining chapters, but is intimately related to the remaining material. Continued fractions provide closed form representations of the extreme solutions of some discrete matrix Riccati equations. Continued fractions solution methods for Riccati difference equations provide an approach analogous to series solution methods for linear differential equations. The book develops several topics which have not been available at this level. In particular, the material of the chapters on continued fractions (Chapter 2), symplectic systems (Chapter 3), and discrete variational theory (Chapter 4) summarize recent literature. Similarly, the material on transforming Riccati equations presented in Chapter 3 gives a self-contained unification of various forms of Riccati equations. Motivation for our approach to difference equations came from the work of Harris, Vaughan, Hartman, Reid, Patula, Hooker, Erbe & Van, and Bohner.
Reviews
`In short, the book is well written and includes all the recent results in this are. It will be very useful to undergraduate and postgraduate students in mathematics as well as to researchers in discrete integrable systems.'
Mathematical Reviews, 98m
Authors and Affiliations
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University of Missouri, USA
Calvin D. Ahlbrandt
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University of Nebraska, USA
Allan C. Peterson
