Mathematics Skills

Mathematics Skills

Maths Topics

Calculus

Print based materials

Print Materials to assist with any pre-requisite mathematics required in USQ courses. These materials are based on USQ's Tertiary Preparation Program. Mathematics modules are presented in increasing level of difficulty and complexity from Level A through to Level D.

Differentiation – looking at change (Level C)

  • 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)

c6-differentiation

Integration – looking at change (Level C)

  • 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

C7-integration

Differentiation

  • 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

D5-differentiation

Integration

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

D6-integration

Videos:

Chain and Product rules:

This video shows worked examples for how to use the chain and product rules for differentiating functions.

chain-product-rules

Integration by Substitution:

This video shows worked examples of how to use the integration by substitution technique.

int-sub

You can also get help Mastering your calculator – free, easy to follow online booklets on a range of scientific calculators.