Differential Equations

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Description

Most "real life" systems that are described mathematically, be they physical, financial, economic or some other kind, are described by means of differential equations. Our ability to predict the way in which these systems evolve or behave is determined by our ability to find solutions of these equations explicitly or to be able to approximate solutions as accurately as we need. Every differential equation presents its own challenges, but there are various classes of differential equations, and for some of these there are established approaches and methods for solving them. This course presents some of the most important such methods.

Objective

To introduce students to the basic concepts, methods, results and applications in mathematics for ordinary differential equations, partial differential equations, Laplace transforms and Fourier analysis. The objective of this course is to equip students with the analytical techniques required to solve a broad range of ordinary differential equations and classical linear partial differential equations of second order.

Content

Topics covered are: first order ordinary differential equations (ODEs), higher order ODEs, numerical techniques for solving ODEs, systems of ODEs, series solutions of ODEs, Laplace transforms, Fourier analysis, solution of linear partial differential equations using the method of separation of variables, and D'Alembert's solution of the wave equation.

Yvonne Stokes Lecturer for this course

Delivery

42 hours of lectures and tutorials

Assessment

Ongoing assessment 30%, exam 70%.

Graduate attributes

• Applying mathematical knowledge (1)
• Interpreting data and drawing conclusions (2)
• Formulating mathematical problems (3)
• Problem solving skills (4)
• Flexibility in working environment (5)
• Team participation and leadership (7)

Linkage past

Pre-requisite course is MTH 1012 or MTH 2004.

Linkage present

No present linkages have been noted.

Linkage future

This course is a pre-requisite course for MTH 3013, MTH 3002, MTH 3006. It is also a recommended course for students intending to take Honours Applied Mathematics.

Restrictions

Incompatible with the courses APP MTH 2007, APP MTH 2000, APP MTH2010, MTH 2201.

Recommended text

Advanced engineering mathematics, Kreyszig, Wiley. Any edition will suffice.