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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]]. There is also a draft article [https://en.wikipedia.org/wiki/Draft:Discrete_calculus “Discrete calculus” for Wikipedia].  
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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 an article [https://en.wikipedia.org/wiki/Discrete_calculus “Discrete calculus” for Wikipedia].  
  
  

Latest revision as of 13:12, 11 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 an article “Discrete calculus” for Wikipedia.


Preface


Chapter 0: Freshman's introduction to discrete calculus

  1. Treat calculus discretely!
  2. Calculus I: functions of single variable
  3. Calculus II: parametric curves and ODEs
  4. Calculus III: functions of several variables and PDEs

Chapter 1: Calculus in dimension $1$

  1. Discrete functions
  2. Chains and cochains
  3. Elementary ODEs
  4. Elementary PDEs
  5. Chain maps

Chapter 2: Chains

  1. The cubical domain
  2. Simplicial complexes
  3. Chain complexes
  4. Chain maps

Chapter 3: Calculus on chain complexes

  1. Duality and cochains
  2. Cubical calculus
  3. ODEs of cochains and ODEs of chain maps

Chapter 4: Geometry and calculus

  1. Metric tensor
  2. Metric complexes
  3. Diffusion equation and wave equation
  4. Convergence of the discrete to the continuous