620-143 Applied Mathematics

Students may only gain credit for one of 620-113, 620-123, 620-143.

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; the principles of first and second order ordinary differential equations; and linear systems of first and second order ordinary differential equations and their applications. Students completing the subject develop the ability to solve analytically first order ordinary differential equations (ODEs), second order linear ODEs, and systems of two or three linear first order ODEs using eigenvalue/eigenvector techniques; and to apply the above techniques to simple problems. The subject demonstrates the role of differential equations 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 and polar coordinates. Differential equations topics include first order differential equations (separable, linear via integrating factor, homogeneous) and applications; second-order differential equations (reducible to first order, linearly independent solutions), second-order linear differential equations (particular integrals, complementary functions) and applications. Systems of differential equations topics include eigenvalues and eigenvectors; systems of first order differential equations and applications; and systems of second order linear differential equations and applications.

Up to 24 pages of written assignments, a 3-hour end-of-semester written examination and class tests totalling not more than 1.5 hours.