Engineering Mathematics

This subject has the following teaching availabilities in 2016:

Estimated total time commitment of 170 hours

One of

Plus one of

• MAST10013 UMEP Maths for High Achieving Students

Or

Enrolment in the Master of Engineering.

Students may only gain credit for one of

• MAST20030 Differential Equations
• MAST30023 Differential Equations for Engineers (prior to 2012)

Students who have completed MAST20009 Vector Calculus may not enrol in MAST20029 Engineering Mathematics for credit.

Concurrent enrolment in both MAST20029 Engineering Mathematics and MAST20009 Vector Calculus is not permitted.

For the purposes of considering request for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Student Support and Engagement Policy, academic requirements for this subject are articulated in the Subject Overview, Learning Outcomes, Assessment and Generic Skills sections of this entry.

It is University policy to take all reasonable steps to minimise the impact of disability upon academic study, and reasonable adjustments will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact on meeting the requirements of this subject are encouraged to discuss this matter with a Faculty Student Adviser and Student Equity and Disability Support: http://services.unimelb.edu.au/disability

This subject introduces important mathematical methods required in engineering such as manipulating vector differential operators, computing multiple integrals and using integral theorems. A range of ordinary and partial differential equations are solved by a variety of methods and their solution behaviour is interpreted. The subject also introduces sequences and series including the concepts of convergence and divergence.

Topics include: Vector calculus, including Gauss’ and Stokes’ Theorems; sequences and series; Fourier series, Laplace transforms; systems of homogeneous ordinary differential equations, including phase plane and linearization for nonlinear systems; second order partial differential equations and separation of variables.

At the completion of this subject, students should be able to

• manipulate vector differential operators
• determine convergence and divergence of sequences and series
• solve ordinary differential equations using Laplace transforms
• sketch phase plane portraits for linear and nonlinear systems of ordinary differential equations
• represent suitable functions using Fourier series
• solve second order partial differential equations using separation of variables
• use MATLAB to perform simple numerical and symbolic calculations

Semester 1 and 2: Three written assignments due at regular intervals during semester amounting to a total of up to 40 pages (15%), a 45 minute written test held mid-semester (15%), and a 3-hour written examination in the examination period (70%).

Summer semester: Two written assignments due at regular intervals during semester amounting to a total of up to 40 pages (15%), a 45 minute written test held mid-semester (15%), and a 3-hour written examination in the examination period (70%).

Students must pass the assessment during semester to pass the subject. That is, students must obtain a mark of at least 15% out of 30% for the combined assignment and mid semester test mark to pass the subject.

E Kreysig, Advanced Engineering Mathematics, 10th Edition, Wiley, USA 2011.

This subject potentially can be taken as a breadth subject component for the following courses:

• Bachelor of Arts
• Bachelor of Commerce
• Bachelor of Environments
• Bachelor of Music

You should visit learn more about breadth subjects and read the breadth requirements for your degree, and should discuss your choice with your student adviser, before deciding on your subjects.

In addition to learning specific mathematical skills, students will have the opportunity to develop generic skills that will assist them in any career path. These include:

• problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
• analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
• collaborative skills: the ability to work in a team;
• time-management skills: the ability to meet regular deadlines while balancing competing tasks;
• computer skills: the ability to use mathematical computing packages.

Students enrolled in the BSc (new degree only) will receive science credit for the completion of this subject.

Note for BSc (new degree) students: This subject is intended only for students pursuing an Engineering Systems major, who do not wish to take any further study in Mathematics and Statistics or Physics. Other students, including those wanting to supplement their Engineering Systems major with further study in Mathematics and Statistics or Physics, should seek advice.

Students undertaking this subject are required to regularly use computers with MATLAB installed.