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