Calculus Index

As a student enrolling in first year Calculus papers, you may have been introduced to some of the material on this web site in school. Depending on your mathematics background, a review of some or all of the topics covered may be useful.

Material on this site is divided into small sections covering topics needed for the first year Calculus paper 160.101.

Differentiation

• Tangents, Derivatives and Differentiation

  • The Slope of a Line
  • The Slope of a Tangent Line
  • The Derivative
  • The Basic Derivative Rules
  • The Rise and Fall of a Graph

• Sign of the Derivative

  • Increasing, Decreasing, Stationary
  • Maximum and Minimum
  • Points of Inflection

• Sign of the Second Derivative

  • The Second Derivative
  • Concave Up, Concave Down, Points of Inflection
  • Maxima and Minima
  • Summary

• The Basic Rules

  • Basic Formulae (Building Blocks)
  • The Multiple Rule
  • The Sum & Difference Rules

• Products and Quotients

  • The Product Rule
  • The Quotient Rule

• Chain Rule

  • Composite Functions
  • Inner and Outer Functions
  • Chain Rule by decomposition
  • Chain Rule by a concise method

• Logarithmic Differentiation

• also known as Variable Power Function Differentiation

• Mixed Differentiation Problems

  • Strategy
  • Mixed Problems 1
  • Mixed Problems 2

Integration

• Basics

  • Definition
  • Basic Integrals
  • Multiple, Sum and Difference Rules
  • Linear Substitution

• Substitution

• Simpler Algebraic Substitution
• Harder Algebraic Substitution
• Integration by Trigonometric Substitution 1
• Integration by Trigonometric Substitution 2

• Parts

  • Integration by Parts