Differentiablity, analyticity; contour integrals, Cauchy's theorem and its consequences; Taylor series, Laurent series; residue calculus.

Prime numbers; unique Factorization in Z and k[x]; arithmetic functions, m, d, w and lattice points; congruence; Chinese remainder theorem; quadratic reciprocity law; algebraic numbers and algebraic integers;  transcendental numbers; finite fields; diophantine equations; distribution of prime numbers; Chybeshev theorem; the Riemann-Zeta Function.

First order differential equations, separable and homogeneous types; Pfaffian forms in two variables, Bernoulli and Riccati types; existence anduniqueness theorem for the initial-value problem.



 Higher order equations, theory of the Wronskian and linear independence  of solutions of higher order linear equations, the Euler equation.

 First order linear systems, matrix formulation of first order systems for  both normal and defective matrices, funamental matrices, matrix-valued  functions and computation of the exponential of a matrix.

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.