- 1 Semester
- 60 hours
Aims and objectives
This unit of study aims to provide students with mathematical knowledge and skills needed to support their concurrent and subsequent engineering and science studies
After successfully completing this unit, you should be able to:
1. Determine limits of functions (K2).
- Determine inverse functions and the composition of two functions (K2).
- Apply general concepts of functions and graphs to linear, quadratic, cubic and higher degree polynomials, straight lines, circles, ellipses, hyperbolae, parabolae; rational, exponential, logarithmic, trigonometric and hyperbolic functions (K2).
- Determine the partial fractions form of rational functions (K2).
- Determine first and higher order derivatives using the product, quotient and chain rules. Determine the derivatives of inverse functions and apply implicit and logarithmic differentiation. Use differentiation for detailed graph drawing (including maxima, minima and points of inflection), determining rates of change, stationary points, optimisation, simple error analysis, derivation of Taylor polynomials and series, applying L’Hopital’s rule and the Newton-Raphson method (K2,S1).
- Determine indefinite integrals of basic trigonometric, hyperbolic, rational and other functions, using substitutions and integration by parts (K2).
- Determine definite integrals exactly (and approximately, using Trapezoidal and Simpson’s rules), apply to regions under and between curves, centroids, arc length, volumes of solids of revolution (K2).
- Use vectors in two and three dimensions to determine the results of simple calculations such as dot product, projection of vectors and angles between vectors (K2).
- Determine sums and products of matrices, and determine the solution to systems of linear equations using augmented matrix form and the Gaussian algorithm (K2).
Courses with unit
Please note that unit codes have changed from 2014. Please ensure that you check the unit entry for the correct 2014 unit code.