Differential Equations for Engineers

This subject has the following teaching availabilities in 2010:

• 620-231 Vector Calculus
• 620-296 Multivariable and Vector Calculus (prior to 2010)

Students may only gain credit for one of

• 620-326 Differential Equations for Engineers
• 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).

Students who have completed 620-331 Applied Partial Differential Equations may not enrol in this subject for credit.

Students may only gain credit for one of

• 620-326 Differential Equations for Engineers
• 620-334 Partial Differential Equations

This subject introduces important mathematical methods required in engineering. Systems of ordinary differential equations and first order (linear and nonlinear) and second order linear partial differential equations are solved by a variety of methods and their solution behaviour is interpreted. The subject introduces the ideas of Laplace transforms, phase plane and stability, method of characteristics, Fourier series, eigenfunctions and eigenvalues and separation of variables.

Topics include: Laplace transforms; systems of linear and nonlinear first order ordinary differential equations including phase plane; first order linear and quasilinear partial differential equations including the method of characteristics, fans and shocks; classification of second order partial differential equations; method of characteristics for hyperbolic partial differential equations, method of separation of variables and eigenfunction expansion.

On completion of this subject students should be able to:

• solve ordinary differential equations using Laplace transforms
• determine phase plane portraits for linear and nonlinear systems of ordinary differential equations
• determine convergence and divergence of sequences and series
• represent suitable functions using Fourier series
• solve first order partial differential equations using the method of characteristics
• solve second order hyperbolic partial differential equations using the method of characteristics
• solve second order partial differential equations using separation of variables and Laplace transforms

Three or 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, 9th Ed. Wiley, 2006.

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

• 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 future 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 the 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.