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Discrete Calculus and Difference Equations

This part is dedicated to the so-called 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.

| | | | created: 2020-03-23 20:38:13 | modified: 2020-03-25 19:23:22 | by: bookofproofs | references: [1112], [8404], [8405]

1.Definition: Difference Operator

2.Proposition: Basic Calculations Involving the Difference Operator

3.Proposition: Nth Difference Operator

4.Definition: Falling And Rising Factorial Powers

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)

[8405] Bool, George: “A Treatise on the Calculus of Finite Differences”, Dover Publications, Inc., 0

[1112] Graham L. Ronald, Knuth E. Donald, Patashnik Oren: “Concrete Mathematics”, Addison-Wesley, 1994, 2nd Edition

[8404] Miller, Kenneth S.: “An Introduction to the Calculus of Finite Differences And Difference Equations”, Dover Publications, Inc, 0