Welcome to the Wikibook of
Calculus

This wikibook aims to be a high quality calculus textbook through which users can master the discipline. Standard topics such as limits, differentiation and integration are covered, as well as several others. Please contribute wherever you feel the need. You can simply help by rating individual sections of the book that you feel were inappropriately rated!

Precalculus

1.1 Algebra 1.2 Trigonometric functions 1.3 Functions 1.4 Graphing linear functions 1.5 Exercises

Limits

2.1 An Introduction to Limits 2.2 Finite Limits 2.3 Infinite Limits 2.4 Continuity 2.5 Formal Definition of the Limit 2.6 Proofs of Some Basic Limit Rules 2.7 Exercises

Differentiation

Basics of Differentiation

3.1 Differentiation Defined 3.2 Product and Quotient Rules 3.3 Derivatives of Trigonometric Functions 3.4 Chain Rule 3.5 Higher Order Derivatives: an introduction to second order derivatives 3.6 Implicit Differentiation 3.7 Derivatives of Exponential and Logarithm Functions 3.8 Some Important Theorems 3.9 Exercises

Applications of Derivatives

3.10 L'Hôpital's Rule 3.11 Extrema and Points of Inflection 3.12 Newton's Method 3.13 Related Rates 3.14 Optimization 3.15 Euler's Method 3.16 Exercises

Integration

The definite integral of a function f(x) from x=0 to x=a is equal to the area under the curve from 0 to a.

Basics of Integration

4.1 Definite integral 4.2 Fundamental Theorem of Calculus 4.3 Indefinite integral 4.4 Improper Integrals

Integration Techniques

From bottom to top:
  • an acceleration function a(t);
  • the integral of the acceleration is the velocity function v(t);
  • and the integral of the velocity is the distance function s(t).

4.5 Infinite Sums 4.6 Derivative Rules and the Substitution Rule 4.7 Integration by Parts 4.8 Trigonometric Substitutions 4.9 Trigonometric Integrals 4.10 Rational Functions by Partial Fraction Decomposition 4.11 Tangent Half Angle Substitution 4.12 Reduction Formula 4.13 Irrational Functions 4.14 Numerical Approximations 4.15 Exercises

Applications of Integration

4.16 Area 4.17 Volume 4.18 Volume of solids of revolution 4.19 Arc length

Parametric and Polar Equations

Parametric Equations

Polar Equations

Sequences and Series

Sequences

Series

Series and calculus

Exercises

Multivariable and Differential Calculus


Differential Equations

Extensions

Advanced Integration Techniques

Further Analysis

Formal Theory of Calculus

References

Acknowledgements and Further Reading

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