### 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

Teaching periods
Location
Start and end dates
Last self-enrolment date
Census date
Last withdraw without fail date
Results released date
Semester 2
Location
Hawthorn
Start and end dates
29-July-2024
27-October-2024
Last self-enrolment date
11-August-2024
Census date
31-August-2024
Last withdraw without fail date
13-September-2024
Results released date
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
TOTAL150

### Assessment

ExaminationIndividual 40 - 50% 1,2,3,4,5,6,7
Online AssignmentIndividual 20 - 30% 1,2,3,4,5,6,7
TestIndividual 10 - 20% 1,2,3,4
Tutorial ExercisesIndividual 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