# Calculus and Applications

MTH10015 12.5 Credit Points Hawthorn, Sarawak Available to incoming Study Abroad and Exchange students

### Duration

• One Semester or equivalent

This unit will be delivered on-line in Semester 2 2020

### Contact hours

• 84

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

## 2023 teaching periods

HawthornHigher Ed. Semester 2 Dates: 31 Jul 23 - 29 Oct 23Results: 5 Dec 23Last self enrolment: 13 Aug 23Census: 31 Aug 23Last withdraw without fail: 15 Sep 23

### Prerequisites

MTH00005 Applied Engineering Mathematics

### 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.

Unit Learning Outcomes (ULO)

Students who successfully complete this unit will be able to:
1. Apply general concepts of functions and graphs to polynomial, rational, exponential, logarithmic, trigonometric, hyperbolic functions of one variable, their inverses and compositions (K2).
2. Apply the induction principle and basic inequalities to verify important relations (K2).
3. Determine the convergence or divergence of sequences. Determine limits of functions of one variable (K2).
4. Determine first and higher order derivatives of functions of one variable.  Determine the derivatives of inverse functions of one variable and apply implicit differentiation. Use differentiation for detailed graph drawing of relevant functions. Apply differentiation to determine rates of change, derivation of Taylor polynomials and correct use of de L’Hôpital’s rule (K2).
5. Determine indefinite and definite integrals of basic trigonometric, hyperbolic, rational and other functions of one variable, using partial fractions, substitutions and integration by parts. Apply these concepts to evaluate the area under and between curves, arc lengths, volumes of solids of revolution and other examples (K2, S1).
6. Determine the solution to first order separable differential equations and linear differential equations using an integrating factor. Determine the solution to second order homogeneous and non-homogeneous linear differential equations with constant coefficients. Apply these methods to simple, fundamental equations (K2, S1).
7. Determine partial derivatives of functions of more than one variable and stationary points (K2).

### Courses with unit

Associate Degree of Engineering