## Main Content

## 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)

**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

**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

### Videos:

**Chain and Product rules:**

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

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