Vector analysis: gradient, divergence, curl, Orthogonal curvilinear coordinates: Cartesian, Cylindrical and spherical. Line, surface, volume integrals, Introduction to tensors, kinematics and equations of motion for inviscid fluids, simple inviscid fluids, viscous flows

Linear programming and duality; mathematical modelling, mathematical structure of the primalprogramme; the simplex tableau and simplex techniques, dual linear programmes; complimentary slackness,  the duality theorem; networks; computations involving computers and software; sensitivity analysis.
       

Types of error, finite differences and interpolation, numerical solution of differential equations; roots of equations; linear systems and matrices; construction of algorithms for computation.

Study is continued on the applied aspects of MATH2150/M25B such as  analysis of variance, regression analysis, design of experiments and categorical data analysis, time series analysis, stochastic processes and decision theory.

Syllabus:   Projections in R^n and C^n; the adjoint of a matrix; special classes of matrices (Hermitian, positive definite, normal and unitary); polynomials of matrices; the Jordan canonical form; the singular value decomposition.

Finite fields, shift registers, algebraic coding theory.

Survival distributions and life tables, utility theory, life insurance, life annuities, commutation functions, net premiums and premium reserves, introduction to multiple life functions.

Fourier series; Vector calculus; Laplace transforms; Fourier transforms;  Special functions.

Differential equations and classifications - first order differential equations; the existence and uniqueness theorem; second and higher order linear differential equations; power series solutions; Legendre

 polynomials, Bessel functions; numerical methods.

Introduction to actuarial science; measurement of interest; solutions of  problems in interest, basic annuities; more general annuities, yield rates, amortization schedules and sinking funds, bonds and other securities, practical applications.