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

# Difference between revisions of "Discrete calculus"

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''Discrete Calculus'' by [[Peter Saveliev]] | ''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: [[Calculus_Illustrated_--_preface#From_the_discrete_to_the_continuous|From the discrete to the continuous]]. | + | 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: [[Calculus_Illustrated_--_preface#From_the_discrete_to_the_continuous|From the discrete to the continuous]]. There is also a draft article [https://en.wikipedia.org/wiki/Draft:Discrete_calculus “Discrete calculus” for Wikipedia]. |

## Revision as of 20:54, 8 September 2019

*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 a draft 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