Calculus:-

Differential Calculus
Differentiation
  • Gradients

  • Limits

  • Derived Function

  • Notation


  • First Principles

    • First Principles - Examples
  • x^n

  • ax^n

  • Derivatives of sums

  • (x + a)^n

  • (ax + b)^n

  • The Chain Rule

  • The Product Rule

  • The Quotient Rule

  • Derived trig functions


    • Differentiation Refresher Examples
  • x^n

  • ax^n

  • Derivatives of sums

  • (x + a)^n

  • (ax + b)^n

  • The Chain Rule

  • The Product Rule

  • The Quotient Rule

  • Trig functions
  • Logs and exponentials
  • Table of Derived Functions

    • Sketching Functions
  • Tangents- gradients

  • Tangents- equations

  • Increasing / decreasing functions
  • Stationary points

  • Finding Stationary points

  • Maxima and Minima

  • Using 2nd Derivative (Ad Higher)

  • Closed Intervals

  • Critical points (Ad Higher)

  • Curve sketching

  • Graphing derived functions

  • Applications

  • Rectilinear Motion

  • Higher derivatives

  • First Order Differential Equations



    • Integration

  • Integral Calculus

  • Indefinite integrals

  • Basic rules of integration

  • Indefinite integral of (ax+b)^n

  • Indefinite integrals - Trig functions

  • Indefinite integrals - Exponentials & logarithmic functions

  • Integration by substitution


  • Areas of graphs

  • Newton's Equations of Motion

  • Areas under curves

  • Lower bound

  • Upper bound

  • Area Function



  • Integration and the area function

  • Definite integrals

  • Fundamental theorem of calculus

  • Areas enclosed by graph and x-axis

  • Area between two graphs

  • Formula for Area between two graphs