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