620-123 Applied Mathematics (Advanced)

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

One of [00]620-111, 620-120 (MUPHAS Mathematics), 620-121 or a grade of H1 in either 620-140 or 620-141.

This subject introduces the classification and principles governing the solution of the basic first and second order differential equations. Students completing the subject develop the ability to classify and solve with accuracy and confidence the basic differential equations of first and second order and to translate that understanding into mathematical formulation of physical problems. This subject demonstrates the power of differential equation modelling in advancing an understanding of complex physical processes from a wide variety of real world phenomena.

Integration topics include systematic integration; approximate 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 (linear via integrating factors, separable and homogeneous) and applications; second order differential equations (reducible to first order, linearly independent solutions), second order linear differential equations with constant coefficients, particular integrals, complementary functions and applications. Systems of differential equations include systems of linear differential equations with constant coefficients, applications of matrix methods, stability; equilibrium and stability of conservative systems, small oscillations; and first-order autonomous nonlinear systems and the phase plane.

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