# Engineering Mathematics 1

MTH10006 12.5 Credit Points Hawthorn, Sarawak

• One Semester

### Contact hours

• 60 hours

On-campus unit delivery combines face-to-face and digital learning.

### Prerequisites

Anti-Requisite:
Successfully completed a unit that is very similar in content or the content overlaps with another unit.

### Aims and objectives

From 2017 MTH10006 will be replaced by MTH10012 - Calculus and Applications

This unit of study aims to provide students with mathematical knowledge and skills needed to support their concurrent and subsequent engineering and science studies

Unit Learning Outcomes (ULO)
After successfully completing this unit, you should be able to:

1. Determine limits of functions (K2).
2. Determine inverse functions and the composition of two functions (K2).
3. 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).
4. Determine the partial fractions form of rational functions (K2).
5. 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).
6. Determine indefinite integrals of basic trigonometric, hyperbolic, rational and other functions, using substitutions and integration by parts (K2).
7. 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).
8. 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).
9. Determine sums and products of matrices, and determine the solution to systems of linear equations using augmented matrix form and the Gaussian algorithm (K2).