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!
Precalculus Edit
Limits Edit
2.5 Formal Definition of the Limit
Differentiation Edit
Basics of Differentiation Edit
3.2 Product and Quotient Rules
3.3 Derivatives of Trigonometric Functions
3.5 Higher Order Derivatives: an introduction to second order derivatives
3.7 Derivatives of Exponential and Logarithm Functions
3.8 Derivatives of Hyperbolic Functions
Applications of Derivatives Edit
3.12 Extrema and Points of Inflection
3.17 Approximating Values of Functions
Integration Edit
Basics of Integration Edit
4.2 Fundamental Theorem of Calculus
Integration Techniques Edit
- 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).
4.6 Derivative Rules and the Substitution Rule
4.8 Trigonometric Substitutions
4.10 Rational Functions by Partial Fraction Decomposition
4.11 Tangent Half Angle Substitution
Applications of Integration Edit
Parametric and Polar Equations Edit
Parametric Equations Edit
5.1 Introduction to Parametric Equations
5.2 Differentiation and Parametric Equations
5.3 Integration and Parametric Equations
Polar Equations Edit
5.5 Introduction to Polar Equations
Sequences and Series Edit
Sequences Edit
Series Edit
6.5 Limit Test for Convergence
6.6 Comparison Test for Convergence
6.7 Integral Test for Convergence
Series and calculus Edit
Exercises Edit
Multivariable Calculus Edit
Introduction to Multivariable Calculus Edit
7.2 Curves and Surfaces in Space
7.4 Introduction to multivariable calculus
Differentiation Edit
7.7 The chain rule and Clairaut's theorem
7.9 Directional derivatives and the gradient vector
7.10 Derivatives of Multivariate Functions
7.11 Inverse Function Theorem, Implicit Function Theorem (optional)
Integration Edit
- Old: Double Integrals
Vector calculus Edit
7.15 Vector Calculus Identities
7.16 Inverting Vector Calculus Operators
7.17 Points, Paths, Surfaces, and Volumes
7.18 Helmholtz Decomposition Theorem
7.19 Discrete Analog to Vector Calculus
Differential Equations Edit
Extensions Edit
Advanced Integration Techniques Edit
Further Analysis Edit
9.2 Systems of Ordinary Differential Equations
Formal Theory of Calculus Edit
References Edit
- Lester R. Ford, Sr. & Jr. (1963) Calculus, McGraw-Hill via HathiTrust
- w:Mellen W. Haskell (1895) On the introduction of the notion of hyperbolic functions Bulletin of the American Mathematical Society 1(6):155–9.