# Calculus

**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

## LimitsEdit

2.5 Formal Definition of the Limit

## 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

3.8 Derivatives of Hyperbolic Functions

### Applications of Derivatives Edit

3.12 Extrema and Points of Inflection

3.17 Approximating Values of Functions

## 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

5.1 Introduction to Parametric Equations

5.2 Differentiation and Parametric Equations

5.3 Integration and Parametric Equations

### Polar EquationsEdit

5.5 Introduction to Polar Equations

## Sequences and SeriesEdit

### SequencesEdit

### SeriesEdit

6.5 Limit Test for Convergence

6.6 Comparison Test for Convergence

6.7 Integral Test for Convergence

### Series and calculusEdit

### ExercisesEdit

## Multivariable CalculusEdit

### Introduction to Multivariable CalculusEdit

7.2 Curves and Surfaces in Space

7.4 Introduction to multivariable calculus

### DifferentiationEdit

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)

### IntegrationEdit

- Old: Double Integrals

### Vector calculusEdit

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 EquationsEdit

## ExtensionsEdit

### Advanced Integration TechniquesEdit

### Further AnalysisEdit

9.2 Systems of Ordinary Differential Equations

### Formal Theory of CalculusEdit

## 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.