Calculus and Applications

Overview

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

Requisites

Prerequisites

MTH00005 Applied Engineering Mathematics

Teaching Periods

Location

Start and end dates

Last self-enrolment date

Census date

Last withdraw without fail date

Results released date

Semester 2

Hawthorn

29-July-2024
27-October-2024

11-August-2024

31-August-2024

13-September-2024

03-December-2024

Learning outcomes

Students who successfully complete this unit will be able to:

Apply general concepts of functions and graphs to polynomial, rational, exponential, logarithmic, trigonometric, hyperbolic functions of one variable, their inverses and compositions (K2)
Apply the induction principle and basic inequalities to verify important relations (K2)
Determine the convergence or divergence of sequences. Determine limits of functions of one variable (K2)
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)
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)
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)
Determine partial derivatives of functions of more than one variable and stationary points (K2)

Teaching methods

Hawthorn

Type	Hours per week	Number of weeks	Total (number of hours)
Live Online Lecture	2.00	12 weeks	24
On-campus Class	2.00	12 weeks	24
On-campus Class	2.00	12 weeks	24
Online Directed Online Learning and Independent Learning	1.00	12 weeks	12
Unspecified Activities Independent Learning	5.50	12 weeks	66
TOTAL			150

Assessment

Type	Task	Weighting	ULO's
Examination	Individual	40 - 50%	1,2,3,4,5,6,7
Online Assignment	Individual	20 - 30%	1,2,3,4,5,6,7
Test	Individual	10 - 20%	1,2,3,4
Tutorial Exercises	Individual	10 - 20%	1,2,3,4,5,6,7

Hurdle

As the minimum requirements of assessment to pass a unit and meet all ULOs to a minimum standard, an undergraduate student must have achieved:

(i) an aggregate mark of 50% or more, and(ii) at least 40% in the final exam.Students who do not successfully achieve hurdle requirement (ii) will receive a maximum of 45% as the total mark for the unit.

Content

Prerequisites & Fundamental properties of functions. Induction principle and inequalities. Domain, image, composition, inversion and graphs
Introduction to sequences, convergence and divergence. Limits of sequences and functions. Fundamental limits and indeterminate forms
Continuity: definition, properties, graphing and examples
Differentiation of functions of one variable. Rules, properties, applications to derivatives
Integration of functions of one variable. Anti-differentiation, substitutions, integration by parts, partial fractions and applications
Differential equations. First order separable & linear differential equations, second order linear differential equations with homogenous /particular solutions
Functions of two and more variables. Partial and directional derivatives. Properties and stationary points of simple, important surfaces

Study resources

Reading materials

A list of reading materials and/or required textbooks will be available in the Unit Outline on Canvas.