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.

Difference Equations: An Introduction with Applications

Science & Math

Kelley, Walter G.

Peterson, Allan C.

Mathematics

Academic Press

This book introduces many of the important topics associated with modern and classical approaches to ordinary differential equations. Provides “refresher course” in differential equations. For mathematicians.

The Theory of Differential Equations: Classical and Qualitative

PRENTICE/HALL

The updated 2nd edition of this book offers an introduction to ordinary differential equations, including nonstandard topics such as a chapter on perturbation methods and a section showing how to solve differential equations using Mathematica codes.

The Theory of Differential Equations: Classical and Qualitative (Universitext)

Kelley, Walter G. G.

Reference

Springer

This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book.
The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the subject. Most chapters may be covered or omitted, depending upon the background of the student. For example, the text may be used as a primary reference in an introductory course for difference equations which also includes discrete fractional calculus. Chapters 1―2 provide a basic introduction to the delta calculus including fractional calculus on the set of integers. For courses where students already have background in elementary real analysis, Chapters 1―2 may be covered quickly and readers may then skip to Chapters 6―7 which present some basic results in fractional boundary value problems (FBVPs). Chapters 6―7 in conjunction with some of the current literature listed in the Bibliography can provide a basis for a seminar in the current theory of FBVPs. For a two-semester course, Chapters 1―5 may be covered in depth, providing a very thorough introduction to both the discrete fractional calculus as well as the integer-order calculus.

Discrete Fractional Calculus

Goodrich, Christopher

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