Engineering Mathematics

This subject has the following teaching availabilities in 2010:

One of

• 620-155 Calculus 2
• 620-158 Accelerated Mathematics 2

Plus one of

• 620-156 Linear Algebra
• 620-157 Accelerated Mathematics 1
• 620-190 UMEP Maths for High Achieving Students

Or

• 431-201 Engineering Analysis A (prior to 2010)

Students may only gain credit for one of

• 620-293 Engineering Mathematics
• 620-232 Mathematical Methods (prior to 2010)
• 620-234 Mathematical Methods Advanced (prior to 2009)
• 431-202 Engineering Analysis B (prior to 2009)

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; first and second order partial differential equations, including characteristics, fans, shocks, D’Alembert’s solution 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 first order partial differential equations using the method of characteristics
• solve second order partial differential equations using separation of variables
• use Matlab to perform simple numerical and symbolic calculations

Four written assignments due at regular intervals during semester amounting to a total of up to 50 pages (20%), and a 3-hour written examination in the examination period (80%).

E Kreysig, Advanced Engineering Mathematics, Ninth Edition, Wiley, 2006.

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.