Calculus

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Mathematics is a universal study. It can be studied for its own sake as pure mathematics, or it can be applied to the natural world and to humanity as in the study of statistics. In the natural world, the nautilus shell presents one of the finest natural examples of a logarithmic spiral.

A printable version of Calculus is available. (edit it)

We at the Calculus wikibooks aim to write a quality textbook through which users may master the topics of differentiation, integration, infinite series, conics, and parametric and polar equations. Please contribute wherever you feel the need.

This book has ten sections:

See below for a detailed table of contents.

• Introduction

Precalculus

• Functions
• Exercises

Limits

• Introduction to Limits
• Finite Limits
• Infinite Limits
• Continuity
• Formal Definition of the Limit
• Exercises

Differentiation

Basics of Differentiation

• Differentiation - An Introduction
• More differentiation rules - More rules for differentiation
• Higher Order derivatives - An introduction to second power derivatives
• Implicit Differentiation
• Exercises

Applications of Derivatives

• Newton's Method
• Related Rates
• Kinematics
• Optimization
• Exercises

Important Theorems

• Extreme Value Theorem
• Extreme value theorem
• Rolle's Theorem
• Mean Value Theorem

Integration

Basics of Integration

• Integration

Integration techniques

• Integration techniques
• Improper integrals
• Exercises

Applications of Integration

• Area
• Volume
• Volume of solids of revolution
• Arc length
• Surface area
• Work
• Centre of mass
• Pressure and force
• Probability

Parametric Equations

• Introduction to Parametric Equations
• Differentiation and Parametric Equations
• Integration and Parametric Equations

Polar Equations

• Introduction to Polar Equations
• Differentiation and Polar Equations
• Integration and Polar Equations

Sequences and Series

Basics

• Sequences
• Series

Series and calculus

• Taylor series
• Power series
• Exercises

Vector Calculations

• Vectors
• Lines and Planes in Space

Multivariable & Differential Calculus

• Multivariable Calculus
• Ordinary Differential Equations
• Partial Differential Equations

Extensions

Further Analysis

• Systems of Ordinary Differential Equations

Formal Theory of Calculus

• Real numbers
• Complex numbers
• Theory of Sequences

References

• Table of Trigonometry
• Summation notation
• Tables of Derivatives
• Tables of Integrals

Acknowledgements and Further Reading