Calculus

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• 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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• Chain and product rules
• Integration by substitution  

Web links

SOS Mathematics (calculus) - short explanations and examples