This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Discrete Calculus. An Introduction

### From Mathematics Is A Science

*Discrete Calculus. An Introduction* by Peter Saveliev

**Foreword:** The stated goal of the text is *discrete* calculus. In particular, this is about the calculus of differential forms. The *continuous* counterpart is developed first because, typically, it is not a part of a calculus course. Meanwhile, we want the discrete

- at least, to
*mimic*the continuous, and, - ideally, to
*converge to*the continuous.

There are still many gaps in the exposition...

Introduction: Why do we need differential forms?

- Algebra
- Cubical complexes
- One-dimensional calculus in multi-dimensional spaces
- Algebra
- Continuous differential forms
- Cubical differential forms
- Integration of differential forms
- More algebra
- Vector calculus and differential forms
- Differential geometry
- Manifolds and differential forms
- Maps
- Partial Differential equations
- Tensor fields

- Appendix A: Discrete calculus with Excel
- Appendix B: History of discrete calculus
- Appendix H:

Addendum

- Cubical homology
- Cohomology