# Calculus and Applications

MTH10012 12.5 Credit Points Hawthorn, Sarawak Available to incoming Study Abroad and Exchange students

### Duration

• One Semester or equivalent

### Contact hours

• 60 hours

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

## 2022 teaching periods

HawthornHigher Ed. Semester 1 HawthornHigher Ed. Semester 2 Dates: 28 Feb 22 - 29 May 22Results: 5 Jul 22Last self enrolment: 13 Mar 22Census: 31 Mar 22Last withdraw without fail: 15 Apr 22 Dates: 1 Aug 22 - 30 Oct 22Results: 6 Dec 22Last self enrolment: 14 Aug 22Census: 31 Aug 22Last withdraw without fail: 16 Sep 22

### Prerequisites

Assumed Knowledge
VCE Mathematical Methods or Equivalent

Anti-requisite

### Aims and objectives

Offered from 2017

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’Hopital’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).