# Calculus

**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

## LimitsEdit

## DifferentiationEdit

### 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

### Applications of Derivatives Edit

3.11 Extrema and Points of Inflection

## IntegrationEdit

### Basics of IntegrationEdit

4.2 Fundamental Theorem of Calculus

### Integration TechniquesEdit

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 IntegrationEdit

## Parametric and Polar EquationsEdit

### Parametric EquationsEdit

- Introduction to Parametric Equations
- Differentiation and Parametric Equations
- Integration and Parametric Equations
- Exercises

### Polar EquationsEdit

## Sequences and SeriesEdit

### SequencesEdit

### SeriesEdit

- Definition of a Series
- Series
- Limit Test for Convergence
- Comparison Test for Convergence
- Integral Test for Convergence

### Series and calculusEdit

### ExercisesEdit

## Multivariable and Differential CalculusEdit

- Vectors
- Lines and Planes in Space
- Multivariable Calculus
- Derivatives of multivariate functions
- The chain rule and Clairaut's theorem
- Inverse function theorem, implicit function theorem
- Vector calculus
- Vector calculus identities
- Inverting vector calculus operators
- Points, paths, surfaces, and volumes
- Helmholtz Decomposition Theorem
- Discrete analog to Vector calculus
- Exercises

## Differential EquationsEdit

## ExtensionsEdit

## ReferencesEdit

- 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.