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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Discrete Hamiltonian Systems - Difference Equations, Continued Fractions, and Riccati Equations (Paperback, Softcover reprint of the original 1st ed. 1996)
Loot Price: R8,506
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Discrete Hamiltonian Systems - Difference Equations, Continued Fractions, and Riccati Equations (Paperback, Softcover reprint of the original 1st ed. 1996)
Series: Texts in the Mathematical Sciences, 16
Expected to ship within 10 - 15 working days
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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.
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