# Calculus

**Calculus**

A Wikibookian suggests that Calculus Course be merged into this book.Discuss whether or not this merger should happen on the discussion page. |

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!

2.5 Formal Definition of the Limit

### Basics of Differentiation

edit3.2 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

edit3.12 Extrema and Points of Inflection

3.17 Approximating Values of Functions

### Basics of Integration

edit4.2 Fundamental Theorem of Calculus

### Integration Techniques

edit4.6 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 Equations

edit5.1 Introduction to Parametric Equations

5.2 Differentiation and Parametric Equations

5.3 Integration and Parametric Equations

### Polar Equations

edit5.5 Introduction to Polar Equations

### Sequences

edit### Series and Tests

edit### Convergence

edit6.10 Absolute and Conditional Convergence

### Series and Calculus

edit### Exercises

edit

### Introduction to Multivariable Calculus

edit7.2 Curves and Surfaces in Space

7.4 Introduction to multivariable calculus

### Differentiation

edit7.7 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

edit7.15 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

### Advanced Integration Techniques

edit### Further Analysis

edit9.2 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.