Last modified on 14 October 2013, at 14:00

Calculus

Welcome to the Wikibook of
Calculus

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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 25% developed

1.2 Functions 50% developed

1.3 Graphing linear functions 25% developed

1.4 Exercises

LimitsEdit

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2.1 An Introduction to Limits 75% developed

2.2 Finite Limits 50% developed

2.3 Infinite Limits 50% developed

2.4 Continuity 25% developed

2.5 Formal Definition of the Limit 25% developed

2.6 Proofs of Some Basic Limit Rules

2.7 Exercises

DifferentiationEdit

Basics of Differentiation 75% developedEdit

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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 50% developedEdit

3.10 L'Hôpital's Rule 75% developed

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 25% developed

4.2 Fundamental Theorem of Calculus 25% developed

4.3 Indefinite integral 25% developed

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

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Parametric EquationsEdit

Polar EquationsEdit

Sequences and SeriesEdit

BasicsEdit

Series and calculusEdit

Multivariable and Differential CalculusEdit

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Differential EquationsEdit

ExtensionsEdit

Advanced Integration TechniquesEdit

Further AnalysisEdit

Formal Theory of CalculusEdit

ReferencesEdit

Acknowledgements and Further ReadingEdit