# 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!

## Precalculus[edit]

1.7 Hyperbolic logarithm and angles

## Limits[edit]

2.5 Formal Definition of the Limit

2.6 Proofs of Some Basic Limit Rules

## 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

### Applications of Derivatives [edit]

3.11 Extrema and Points of Inflection

## 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]

4.18 Volume of Solids of Revolution

## 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

5.6 Differentiation and Polar Equations

5.7 Integration and 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 and Differential Calculus[edit]

7.4 Derivatives of Multivariate Functions

7.5 The Chain Rule and Clairaut's Theorem

7.6 Inverse Function Theorem, Implicit Function Theorem

7.8 Vector Calculus Identities

7.9 Inverting Vector Calculus Operators

7.10 Points, Paths, Surfaces, and Volumes

7.11 Helmholtz Decomposition Theorem

7.12 Discrete Analog to Vector Calculus

## Differential Equations[edit]

8.1 Ordinary Differential Equations

8.2 Partial Differential Equations

## 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.