Mathematics AA HL

Topic 5 – Calculus

Introduction to Differentiation

  • First Principles
  • Simple Differentiation
  • Tangents and Normal
First Principles
Simple Differentiation
Tangents and Normal

Differentiation Techniques

  • Chain Rule
  • Product Rule
  • Quotient Rule
  • Functions
Chain Rule
Product Rule
Quotient Rule
Functions

Stationary Points

  • Local Maximum and Minimum
  • Optimization
  • Inflexion and Concavity
Local Maximum and Minimum
Optimization
Inflexion and Concavity

Implicit Differentiation

  • Implicit Differentiation
Implicit Differentiation

L'Hoptials

  • L’Hopital’s
L'Hopital's

Integration and Area

  • Anti Differentiation
  • Definite Integration
  • Bounded Area
Anti Differentiation
Definite Integration
Bounded Area

Integration Techniques

  • Substitution
  • By Parts
  • Partial Fractions
Substitution
By Parts
Partial Fractions

Volumes

  • The x-axis
  • The y-axis
  • Bounded Volume
The x-axis
The y-axis
Bounded Volume

Kinetics

  • Kinetics
Kinetics

Differential Equations

  • Separating Variables
  • Rates of Change
  • Euler’s Method
  • Homogeneous Equations
  • Integrating Factor
Separating Variables
Rates of Change
Euler's Method
Homogeneous Equations
Integrating Factor

Maclaurin's Series

  • Expansions
  • Calculus
  • Differential Equations
Expansions
Calculus
Differential Equations