Authorised by Academic Registrar, April 1996
Objectives On the completion of this subject students will achieve an understanding of some advanced mathematical methods for applications in science and applied mathematics; extend the basic concepts of ordinary differential equations to higher order and some nonlinear types of differential equations; develop skills for solving differential equations; distinguish between scalar and vector fields; comprehend the concepts of gradient, divergence and curl; use the Divergence theorem and Stokes' theorem; know and use some results for functions of a complex variable.
Synopsis Ordinary differential equations: first and second order equations soluble by analytic techniques. Variation of parameters for linear non-homogeneous differential equations. Power series solutions. Vector differential calculus: grad, div, curl. The integral theorems of Gauss and Stokes using multiple integrals. Functions of a complex variable.
Assessment Examinations (1.5 hours): 85% + Tests and assignments during the semester: 15%