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

# Discrete calculus

*Discrete Calculus* by Peter Saveliev

Some of this material is now appearing as a part of a general purpose calculus book I am working on: *Calculus Illustrated*. The program is described here: From the discrete to the continuous. There is also an article “Discrete calculus” for Wikipedia.

**Chapter 0: Freshman's introduction to discrete calculus**

- Treat calculus discretely!
- Calculus I: functions of single variable
- Calculus II: parametric curves and ODEs
- Calculus III: functions of several variables and PDEs

**Chapter 1: Calculus in dimension $1$**

**Chapter 2: Chains**

**Chapter 3: Calculus on chain complexes**

**Chapter 4: Geometry and calculus**

- Metric tensor
- Metric complexes
- Diffusion equation and wave equation
- Convergence of the discrete to the continuous

- Link: Spreadsheets
- Link: Discrete calculus: contributors