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# Discrete calculus

*Elementary Discrete Calculus* by Peter Saveliev

How far we can go without limits?

Some of this material has appeared as a part of a "general purpose" calculus book of mine: *Calculus Illustrated*.

For now, I just picked 3 chapters from the first 3 volumes of Calculus Illustrated. Here is a PDF.

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