Discrete Calculus. An Introduction
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?
- Cubical complexes
- One-dimensional calculus in multi-dimensional spaces
- Continuous differential forms
- Cubical differential forms
- Integration of differential forms
- More algebra
- Vector calculus and differential forms
- Differential geometry
- Manifolds and differential forms
- Partial Differential equations
- Tensor fields
- Appendix A: Discrete calculus with Excel
- Appendix B: History of discrete calculus
- Appendix H:
- Cubical homology