Kelley W.G., Peterson A.C. Difference Equations: An Introduction with Applications

Academic Press, 2000. — 403 с. Second Edition ISBN: 012403330X.
Difference Equations, Second Edition, presents a practical introduction to this important field of solutions for engineering and the physical sciences. Topic coverage includes numerical analysis, numerical methods, differential equations, combinatorics and discrete modeling. A hallmark of this revision is the diverse application to many subfields of mathematics.
Phase plane analysis for systems of two linear equations.
Use of equations of variation to approximate solutions.
Fundamental matrices and Floquet theory for periodic systems.
LaSalle invariance theorem.
Additional applications: secant line method, Bison problem, juvenile-adult population model, probability theory.
Appendix on the use of Mathematica for analyzing difference equaitons.
Exponential generating functions.
Many new examples and exercises.