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Part: Discrete Calculus and Difference Equations
This part is dedicated to the socalled discrete calculus, sometimes also called the calculus of finite differences. This is a subject providing methods for solving difference equations. As opposed to differential equations, difference equations are useful as a mathematical representation for certain physical problems.
The purpose of this part is to develop a calculus of "differences" and a "sums", in analogy to the calculus of
derivatives and Riemann integrals.
Table of Contents
Examples: 1
 Definition: Difference Operator
 Proposition: Basic Calculations Involving the Difference Operator
 Proposition: Nth Difference Operator
 Proposition: Difference Operator of Powers
 Definition: Factorial Polynomials
 Definition: Falling and Rising Factorial Powers of Functions
 Theorem: Taylor's Formula Using the Difference Operator
 Definition: Indefinite Sum, Antidifference
 Proposition: Basic Calculations Involving Indefinite Sums
 Proposition: Antidifferences of Some Functions
 Definition: Falling And Rising Factorial Powers
 Proposition: Difference Operator of Falling Factorial Powers
 Theorem: Fundamental Theorem of the Difference Calculus
Mentioned in:
Chapters: 1
Solutions: 2
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References
Bibliography
 Graham L. Ronald, Knuth E. Donald, Patashnik Oren: "Concrete Mathematics", AddisonWesley, 1994, 2nd Edition
 Miller, Kenneth S.: "An Introduction to the Calculus of Finite Differences And Difference Equations", Dover Publications, Inc, 1960
 Bool, George: "A Treatise on the Calculus of Finite Differences", Dover Publications, Inc., 1960