620-143 Applied Mathematics

Students may only gain credit for one of 620-113, 620-123, 620-143 or [05]620-193.

Normally one of 620-140 or 620-141, or any one of [00]620-111, 620-120 (MUPHAS Mathematics), 620-121.

This subject introduces the terminology of ordinary differential equations (ODEs), the principles of first and second order ODEs, and their applications. This subject also introduces the basic properties of sequences and series, including Taylor series for functions. Students completing the subject develop the ability to solve analytically first order ODEs, second order linear ODEs; and learn how to apply the above techniques to simple problems. Students should develop the ability to understand the convergence of series and sequences. The subject demonstrates the role of differential equations and sequences and series in applied mathematics.

Integration topics include antiderivatives and the definite integral; systematic integration; applications of integration, areas, arc length, surface areas and volumes of solids of revolution in cartesian, parametric and polar coordinates; double integrals. Differential equations topics include first order ODEs (separable, linear via integrating factor, homogeneous) and applications; second-order ODEs (reducible to first order, linearly independent solutions); second-order linear ODEs (particular integrals, complementary functions) and applications. Sequences and series topics include convergence and divergence of sequences and series; tests for convergence; Taylor's theorem and series representation of elementary functions; generation of series solutions of first order ODEs, including non-linear types not solvable by elementary methods.

Up to 25 pages of written assignments during semester (10%), a 45 minute written mid-semester test (15%), and a 3-hour end-of-semester written examination (75%).