620-123 Applied Mathematics (Advanced)

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

One of 620-120 (UMEP Maths for High Achieving Students), 620-121 or a grade of H1 in either 620-140 or 620-141.

This subject introduces the principles governing the solution of the basic first and second order ordinary differential equations (ODEs). This subject also introduces the basic properties of sequences and series, including Taylor series for functions. Students completing the subject develop the ability to classify and solve with accuracy 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 techniques of integration; approximate integration; applications of integration to areas and arc length; improper integrals. Differential equations topics include first order ODEs (linear via integrating factors, separable and homogeneous) and applications; second order ODEs (reducible to first order, linearly independent solutions), and second order linear ODEs with constant coefficients, 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. Difference equations.

Up to 24 pages of written assignments due during the semester (10%); a 50-minute written test held mid semester (15%); a 3-hour written examination in the examination period (75%).