# 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 | edit source]

1.8 Hyperbolic logarithm and angles

## Limits[edit | edit source]

2.5 Formal Definition of the Limit

2.6 Proofs of Some Basic Limit Rules

## Differentiation[edit | edit source]

### Basics of Differentiation [edit | edit source]

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 | edit source]

3.12 Extrema and Points of Inflection

3.17 Approximating Values of Functions

## Integration[edit | edit source]

### Basics of Integration[edit | edit source]

4.2 Fundamental Theorem of Calculus

### Integration Techniques[edit | edit source]

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 | edit source]

4.18 Volume of Solids of Revolution

## Parametric and Polar Equations[edit | edit source]

### Parametric Equations[edit | edit source]

5.1 Introduction to Parametric Equations

5.2 Differentiation and Parametric Equations

5.3 Integration and Parametric Equations

### Polar Equations[edit | edit source]

5.5 Introduction to Polar Equations

5.6 Differentiation and Polar Equations

5.7 Integration and Polar Equations

## Sequences and Series[edit | edit source]

### Sequences[edit | edit source]

### Series[edit | edit source]

6.5 Limit Test for Convergence

6.6 Comparison Test for Convergence

6.7 Integral Test for Convergence

### Series and calculus[edit | edit source]

### Exercises[edit | edit source]

## Multivariable Calculus[edit | edit source]

### Introduction to Multivariable Calculus[edit | edit source]

7.2 Curves and Surfaces in Space

7.4 Introduction to multivariable calculus

### Differentiation[edit | edit source]

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 | edit source]

- Old: Double Integrals

### Vector calculus[edit | edit source]

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 | edit source]

8.1 Ordinary Differential Equations

8.2 Partial Differential Equations

## Extensions[edit | edit source]

### Advanced Integration Techniques[edit | edit source]

### Further Analysis[edit | edit source]

9.2 Systems of Ordinary Differential Equations

### Formal Theory of Calculus[edit | edit source]

## References[edit | edit source]

- 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.