Calculus
Print modules
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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
Web links
SOS Mathematics (calculus) - short explanations and examples