# 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!

## 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

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.