MATH12222 - Advanced Mathematical Applications

General Information

Unit Synopsis

Techniques of advanced mathematics and applications are developed through a selection of various methods to solve linear and non-linear differential equations in science and engineering. You will study interpolation, curve fitting, and utilise the concepts of linear transformations and interpretation of eigenvalues to analyse a variety of scientific and engineering problems. Numerical methods for solving ordinary differential equations, the Fourier Analysis of periodic and non-periodic functions and partial differential equations with initial and boundary conditions are included. You will communicate results, concepts and ideas using mathematics as a language and be able to document the solution to problems in a way that demonstrates a clear, logical and precise approach.


Level Undergraduate
Unit Level 2
Credit Points 6
Student Contribution Band SCA Band 1
Fraction of Full-Time Student Load 0.125
Pre-requisites or Co-requisites
Pre-requisite: MATH11219

Important note: Students enrolled in a subsequent unit who failed their pre-requisite unit, should drop the subsequent unit before the census date or within 10 working days of Fail grade notification. Students who do not drop the unit in this timeframe cannot later drop the unit without academic and financial liability. See details in the Assessment Policy and Procedure (Higher Education Coursework).

Class Timetable View Unit Timetable
Residential School No Residential School

Unit Availabilities from Term 2 - 2023

There are no availabilities for this unit on or after Term 2 - 2023

Attendance Requirements

All on-campus students are expected to attend scheduled classes – in some units, these classes are identified as a mandatory (pass/fail) component and attendance is compulsory. International students, on a student visa, must maintain a full time study load and meet both attendance and academic progress requirements in each study period (satisfactory attendance for International students is defined as maintaining at least an 80% attendance record).

Assessment Overview

Recommended Student Time Commitment

Each 6-credit Undergraduate unit at CQUniversity requires an overall time commitment of an average of 12.5 hours of study per week, making a total of 150 hours for the unit.

Assessment Tasks

Assessment Task Weighting
1. Written Assessment 20%
2. Written Assessment 20%
3. Examination 60%

This is a graded unit: your overall grade will be calculated from the marks or grades for each assessment task, based on the relative weightings shown in the table above. You must obtain an overall mark for the unit of at least 50%, or an overall grade of ‘pass’ in order to pass the unit. If any ‘pass/fail’ tasks are shown in the table above they must also be completed successfully (‘pass’ grade). You must also meet any minimum mark requirements specified for a particular assessment task, as detailed in the ‘assessment task’ section (note that in some instances, the minimum mark for a task may be greater than 50%).

Consult the University’s Grades and Results Policy for more details of interim results and final grades

Past Exams

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Previous Feedback

Term 1 - 2022 : The overall satisfaction for students in the last offering of this course was 46.88% (`Agree` and `Strongly Agree` responses), based on a 44.44% response rate.

Feedback, Recommendations and Responses

Every unit is reviewed for enhancement each year. At the most recent review, the following staff and student feedback items were identified and recommendations were made.

Source: Student evaluation
Sufficient learning & teaching material provided.
Provide the same amount of learning resources.
Action Taken
Continued with the same amount of learning resources.
Source: Student evaluation
Good split of exams and assignments.
Continue to maintain a similar mix of assessment items.
Action Taken
Maintained a same mix of assessment items.
Source: In class
It would be better to have face-to-face tutorial support.
Look into providing face-to-face on-campus tutorial support.
Action Taken
Provided face to face on -campus support
Source: In-class
Students were appreciative for providing individual attention, keeping frequent engagement, providing the tutorial solutions with appropriate scaffolding.
Continue to provide individual support, and add guidelines to students on how to seek individual support so all students can take advantage of it.
Action Taken
Continued with the same amount of individual support and also provided support from ALC as well by conducting additional support sessions.
Source: Course review
Some content taught in this unit is not directly applicable to some disciplines.
This unit will be terminated from this year. Content in this unit will be embedded to discipline specific units.
Action Taken
Unit learning Outcomes

On successful completion of this unit, you will be able to:

  1. Model engineering application problems by applying interpolation and curve fitting techniques
  2. Analyse problems using the concepts of linear transformation and the interpretation of eigenvalues
  3. Use numerical methods to solve ordinary differential equations
  4. Apply Fourier Analysis to periodic and non-periodic functions in the solution of scientific and engineering problems
  5. Solve simple partial differential equations with initial and boundary conditions
  6. Communicate results, concepts and ideas in context using mathematics as a language.

The Learning Outcomes for this unit are linked with the Engineers Australia Stage 1 Competency Standards for Professional Engineers in the areas of 1. Knowledge and Skill Base, 2. Engineering Application Ability and 3. Professional and Personal Attributes at the following levels:

1.4 Discernment of knowledge development and research directions within the engineering discipline. (LO: 1N 3N)
2.3 Application of systematic engineering synthesis and design processes. (LO: 1N)
1.1 Comprehensive, theory-based understanding of the underpinning natural and physical sciences and the engineering fundamentals applicable to the engineering discipline. (LO: 1I 2I 3I 4I 5N)
1.5 Knowledge of engineering design practice and contextual factors impacting the engineering discipline. (LO: 1I 2I 3I 4I)
2.2 Fluent application of engineering techniques, tools and resources. (LO: 1I 2I 3I 4N 5N)
3.2 Effective oral and written communication in professional and lay domains. (LO: 6I)
3.4 Professional use and management of information. (LO: 6I)
1.2 Conceptual understanding of the mathematics, numerical analysis, statistics, and computer and information sciences which underpin the engineering discipline. (LO: 1A 2A 3A 4A 5I 6I)
1.3 In-depth understanding of specialist bodies of knowledge within the engineering discipline. (LO: 1I 3I 4A 5I)
1.6 Understanding of the scope, principles, norms, accountabilities and bounds of sustainable engineering practice in the specific discipline. (LO: 1A)
2.1 Application of established engineering methods to complex engineering problem solving. (LO: 1I 2A 3I 4I 5N)

Note: LO refers to the Learning Outcome number(s) which link to the competency and the levels: N – Introductory, I – Intermediate and A - Advanced.
Refer to the Engineering Undergraduate Course Moodle site for further information on the Engineers Australia's Stage 1 Competency Standard for Professional Engineers and course level mapping information

Alignment of Assessment Tasks to Learning Outcomes
Assessment Tasks Learning Outcomes
1 2 3 4 5 6
1 - Written Assessment
2 - Written Assessment
3 - Examination
Alignment of Graduate Attributes to Learning Outcomes
Introductory Level
Intermediate Level
Graduate Level
Graduate Attributes Learning Outcomes
1 2 3 4 5 6
1 - Communication
2 - Problem Solving
3 - Critical Thinking
4 - Information Literacy
6 - Information Technology Competence
Alignment of Assessment Tasks to Graduate Attributes
Introductory Level
Intermediate Level
Graduate Level
Assessment Tasks Graduate Attributes
1 2 3 4 5 6 7 8 9 10