# Calculus

Calculus uses methods originally based on the summation of infinitesimal differences.
It includes the examination of changes in an expression by smaller and smaller differences.

## Resources

* Calculus/Introduction
* Definitions
* Calculus I
* Calculus II
* Fundamental Calculus
* Quick Reference

## Osnabrück Calculus

Mathematics for Applied Sciences (Osnabrück 2023-2024)/Part I is a course for beginners at the University of Osnabrück. It covers logical foundation, sets, mappings, algebraic structures like fields and polynomials, the basics of analysis like sequences, continuity, differentiability, primitive functions and the basics of linear algebra like vector spaces, bases, linear maps, eigenvalues. While course has been taught many times, this is a textbook -- not an online course. The lectures dealing with calculus are as follows.
       Contents • Logic and argumentation• Quantifiers and induction• Sets and mappings• Fields• Complex numbers• Polynomials• Approximation and convergence• Completeness• Series• Continuity• Intermediate value theorem• Exponential function• Trigonometry• Differentiability• Mean value theorem• The number $\pi$• Taylor series• Integration• Fundamental theorem of calculus• Rules for integration

## Lessons

Wikibooks has a well developed Calculus Book in 10 sections which this Wikiversity web course should mirror to maximize resources.
| Chapter | Wikibook Chapter | Wikiversity Topics | Wikiversity for Review & Development |
| 1. | Precalculus | *The Real Numbers and Their Development | *Foundations of calculus |
| | | *Precalculus | |
| | | *Introduction to Calculus Overview Page | |
| | | **Any questions? | |
| | | **Introduction to Calculus/Introduction | |
| | | Calculus Pre-Test | |
| 2. | Limits | **Introduction to Calculus/Limits | |
| 3. | Differentiation | **Introduction to Calculus/Differentiation | |
| 4. | Integration | **Integration by parts | |
| | | **Integration by Substitution | |
| | | **Monte Carlo Integration | **Trigonometric Substitutions |
| 5. | Parametric equations | Parametric equations | |
| 6. | Polar equations | Polar equations | |
| 7. | Sequences and series | Sequences and series | |
| 8. | Vector Calculations | Vectors | |
| 9. | Multivariable and Differential Calculus | Multivariable Calculus | |
| 10. | Extensions | Complex Numbers | |
| 11. | | | *Calculus |
| | | | *Calculus II |

## Offsite Courses
### Lamar

* Calculus I
* Calculus II
MIT
* Single Variable calculus, Fall 2006, Prof. David Jerison(Video Lectures)
* Single Variable calculus, Fall 2005, Prof. Jason Starr
* Calculus II

## Other Resources

* Calculus
* Various Calculus Problems
* Calculus of generating functions

### Online Textbooks

* Wikibooks Calculus
* Prof Dale Hoffman. (2007). Contemporary Calculus: Part 1
* R.Courant. Differential and Integral Calculus, Vol. I by Richard Courant
* R.Courant. Differential and Integral Calculus, Vol. II by Richard Courant
* Gilbert Strang. (1991). Calculus
* Ray Mayer. (2007) Calculus I - Theoretical focus.

### Hard-copy Textbooks

* Spivak, Michael. (1994). Calculus ISBN 0914098896
* Spivak, Michael. (1965). Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus ISBN 0805390219
* Gilbert Strang. (1991). Calculus ISBN 0961408820

### Textbook Supplements

* Elliott Mendelson. (1988). 3,000 Solved Problems in Calculus ISBN 0070415234
* Frank Ayes, Elliott Mendelson. (1999). Schaum's Outline of Calculus (Fourth Edition) ISBN 0070419736
* Solutions to selected exercises from Apostol's Calculus Vol. 1
* Solutions to selected exercises from Calculus by Larson, Hostetler, Edwards

### Wikipedia

* Calculus
* List of basic calculus topics
* List of calculus topics
* Stochastic calculus