# Calculus

 Educational level: this is a tertiary (university) resource.
 Wikibooks has a book on the topic of 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.

## 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 ${\displaystyle {}\pi }$ • 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

Lamar

MIT

## Other Resources

### 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