Calculus

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This wikibook aims to be a quality calculus textbook through which users may 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.

Introduction

• Introduction
• Contributing

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

• Extrema and Points of Inflection
• Newton's Method
• Related Rates
• Kinematics
• Optimization
• Euler's Method
• Exercises

Important Theorems

• 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 and Polar Equations

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

References

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

Acknowledgements and Further Reading