Movatterモバイル変換

[0]ホーム
URL:

Jump to content
WikibooksThe Free Textbook Project
Search

Calculus

75% developed
From Wikibooks, open books for an open world
Welcome to the Wikibook of
Calculus
A Wikibookian suggests thatCalculus Course bemerged into this book.
Discuss whether or not this merger should happen on thediscussion page.

Aprintable version of Calculus is available. (edit it)

APDF version is available. (info)

Wikiversity has learning materials aboutCalculus

This book requires that you first read Algebra.


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

Precalculus

[edit |edit source]

1.1Algebra75% developed  as of 24 October 2020

1.2Functions75% developed  as of 24 October 2020

1.3Trigonometric functions75% developed  as of 16 November 2020

1.4Graphing functions75% developed  as of 20 November 2020

1.5Rational functions

1.6Conic sections75% developed  as of 21 November 2020

1.7Exercises

1.8Hyperbolic logarithm and angles75% developed

Limits

[edit |edit source]

2.1An Introduction to Limits75% developed

2.2Finite Limits50% developed

2.3Infinite Limits50% developed

2.4Continuity25% developed

2.5Formal Definition of the Limit25% developed

2.6Proofs of Some Basic Limit Rules

2.7Exercises

Differentiation

[edit |edit source]

Basics of Differentiation75% developed

[edit |edit source]

3.1Differentiation Defined

3.2Product and Quotient Rules

3.3Derivatives of Trigonometric Functions

3.4Chain Rule

3.5Higher Order Derivatives: an introduction to second order derivatives

3.6Implicit Differentiation

3.7Derivatives of Exponential and Logarithm Functions

3.8Derivatives of Hyperbolic Functions

3.9Some Important Theorems

3.10Exercises

Applications of Derivatives50% developed

[edit |edit source]

3.11L'Hôpital's Rule75% developed

3.12Extrema and Points of Inflection

3.13Newton's Method

3.14Related Rates

3.15Optimization

3.16Euler's Method

3.17Approximating Values of Functions

3.18Exercises


Integration

[edit |edit source]
The definite integral of a functionf(x) fromx=0 tox=a is equal to the area under the curve from 0 toa.

Basics of Integration

[edit |edit source]

4.1Definite integral25% developed

4.2Fundamental Theorem of Calculus25% developed

4.3Indefinite integral25% developed

4.4Improper Integrals

Integration Techniques

[edit |edit source]
From bottom to top:
  • an acceleration functiona(t);
  • the integral of the acceleration is the velocity functionv(t);
  • and the integral of the velocity is the distance functions(t).

4.5Infinite Sums

4.6Derivative Rules and the Substitution Rule

4.7Integration by Parts

4.8Trigonometric Substitutions

4.9Trigonometric Integrals

4.10Rational Functions by Partial Fraction Decomposition

4.11Tangent Half Angle Substitution

4.12Reduction Formula

4.13Irrational Functions

4.14Numerical Approximations

4.15Exercises

Applications of Integration

[edit |edit source]

4.16Area

4.17Volume

4.18Volume of Solids of Revolution

4.19Arc Length

4.20Surface Area

4.21Work

4.22Center of Mass

4.23Pressure and Force

4.24Probability

Parametric and Polar Equations

[edit |edit source]

Parametric Equations

[edit |edit source]

5.1Introduction to Parametric Equations

5.2Differentiation and Parametric Equations

5.3Integration and Parametric Equations

Polar Equations

[edit |edit source]

5.5Introduction to Polar Equations

5.6Differentiation and Polar Equations

5.7Integration and Polar Equations

Sequences and Series

[edit |edit source]

Sequences

[edit |edit source]

6.1Definition of a Sequence

6.2Sequences

Series and Tests

[edit |edit source]

6.3Definition of a Series

6.4Series

6.5Divergence Test

6.6Ratio Test

6.7Limit Comparison Test

6.8Direct Comparison Test

6.9Integral Test

Convergence

[edit |edit source]

6.10Absolute and Conditional Convergence

Series and Calculus

[edit |edit source]

6.11Taylor series

6.12Power series

6.13Leibniz' formula for pi

Exercises

[edit |edit source]

6.14Exercises


Multivariable Calculus

[edit |edit source]
This is an example of using spherical coordinates in 3 dimensions to calculate the volume of a given shape

Introduction to Multivariable Calculus

[edit |edit source]

7.1Vectors75% developed

7.2Curves and Surfaces in Space75% developed  as of 9 Feb 2021

7.3Vector Functions75% developed  as of 11 Mar 2021

7.4Introduction to multivariable calculus50% developed

Differentiation

[edit |edit source]

7.5Limits and Continuity

7.6Partial Derivatives

7.7The chain rule and Clairaut's theorem50% developed

7.8Chain Rule

7.9Directional derivatives and the gradient vector

7.10Derivatives of Multivariate Functions50% developed

7.11Inverse Function Theorem, Implicit Function Theorem (optional)100% developed

Integration

[edit |edit source]

7.12Multiple integration

7.13Change of variables

Vector calculus

[edit |edit source]

7.14Vector Calculus100% developed

7.15Vector Calculus Identities100% developed

7.16Inverting Vector Calculus Operators100% developed

7.17Points, Paths, Surfaces, and Volumes75% developed

7.18Helmholtz Decomposition Theorem75% developed

7.19Discrete Analog to Vector Calculus100% developed

7.20Exercises


Differential Equations

[edit |edit source]

8.1Ordinary Differential Equations25% developed

8.2Partial Differential Equations50% developed

Extensions

[edit |edit source]

Advanced Integration Techniques

[edit |edit source]

9.1Complexifying

Further Analysis

[edit |edit source]

9.2Systems of Ordinary Differential Equations0% developed

Formal Theory of Calculus

[edit |edit source]

9.3Real Numbers25% developed

9.4Complex Numbers50% developed

9.5Hyperbolic Angle100% developed

References

[edit |edit source]

Acknowledgements and Further Reading

[edit |edit source]

Navigation:Main Page ·Precalculus ·Limits ·Differentiation ·Integration ·Parametric and Polar Equations ·Sequences and Series ·Multivariable Calculus ·Extensions ·References

Retrieved from "https://en.wikibooks.org/w/index.php?title=Calculus&oldid=4443818"
Categories:
Hidden categories:
[8]ページ先頭
©2009-2025 Movatter.jp