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!

PrecalculusEdit

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

LimitsEdit

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

DifferentiationEdit

Basics of Differentiation  Edit

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  Edit

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


IntegrationEdit

 
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 IntegrationEdit

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

Integration TechniquesEdit

 
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 IntegrationEdit

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

Parametric and Polar EquationsEdit

Parametric EquationsEdit

Polar EquationsEdit

Sequences and SeriesEdit

SequencesEdit

SeriesEdit

Series and calculusEdit

ExercisesEdit

Multivariable and Differential CalculusEdit


Differential EquationsEdit

ExtensionsEdit

Advanced Integration TechniquesEdit

Further AnalysisEdit

Formal Theory of CalculusEdit

ReferencesEdit

Acknowledgements and Further ReadingEdit