Calculus

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Module C6-Differentiation - looking at change (PDF*790kb)

This document includes:

This document includes:
  • Rate of change – the problem of the curve
  • Instantaneous rate of change and the derivative function
  • Shortcuts for differentiation (including: polynomial and other power functions, exponential functions, logarithmic functions, trigonometric functions, and where the derivative cannot be found)
  • Some applications of differential calculus (including: displacement-velocity-acceleration: when derivatives are meaningful in their own right, twists and turns, and optimization)

A more detailed list of topics is also available: C6: Differentiation: looking at change – contents.

Module C7-Integration - looking at total change (PDF*550kb)

This document includes:

  • Area under the curve
  • The definite integral
  • The antiderivative
    Steps in integration (including: using standard rules of integration, integrals of functions with constant multiples, and integrals of sum and difference functions)
  • More areas
  • Applications of integral calculus

A more detailed list of topics is also available: C7: integration: looking at total change – contents.

Module D5-Differentiation (PDF*899kb)

This document includes:

  • Derivatives
  • Gradient functions
  • Differentiability
  • Derivatives of simple functions
  • Practical interpretations of the derivative
  • Simple applications of the derivative
  • The product rule
  • The quotient rule
  • The chain rule
  • Stationary points
  • Curve sketching
  • Maximum / minimum problems
  • Newton-Raphson method for finding roots
  • Solutions to exercise sets

A more detailed list of topics is also available: D5: Differentiation – contents.

Module D6-Integration (PDF*251kb)

This document includes:

  • Integration of basic functions
  • Integration by guess and check
  • Integration by substitution
  • Definite integration
  • Trapezoidal Rule
  • Simpson’s Rule

A more detailed list of topics is also available: D6: Integration – contents 

Animated activities (videos, Breeze presentations, online tutorials)
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Web links

SOS Mathematics (calculus) - short explanations and examples