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.

This diagram shows an approximation to an area under a curve. Credit: Dubhe.

It includes the examination of changes in an expression by smaller and smaller differences.

Resources

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

MIT

Other Resources

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