# Mathematical Sciences

COURSE SYNOPSIS
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MTS 501
Mathematical Methods II

Course Synopsis

This is an advance course in Mathematical Methods to prepare students for a higher level of mathematics. The topics to be covered in this course include Calculus of variation; Lagrangeâ€™s function and its associated density; Necessary condition for a weak relative extremum; Lagrangeâ€™s equation and geodesic problems; Du-Bios-Raymond equation and corner conditions; variable end points and related theorems; sufficient conditions for a minimum; isoperimetric problems; variational integral transforms â€“ Laplace, Fourier and Hankel transforms; convolution theorems.

MTS 511(E)
Fluid Dynamics II

Course Synopsis

This course focuses on the followings: Navier-Stokes and energy equations for viscous incompressible fluids. Dynamical similarity and Reynolds number. Steady one-dimensional flow of viscous fluid. Two-dimensional flow and small disturbance theory. Radial flow between plane walls, axi-symmetric jets. Boundary layer theory. Inviscid compressible flow, energy equation and compressibility effect. Unsteady one-dimensional flow. Equations of motion for some specific types of flow and ensuring solutions.

MTS 527
OPTIMIZATION THEORY

Course Synopsis

This course is compulsory for applied mathematicians who wish to spenalise in the areas of operations research, multi-stage system, simulation, modelling, discrete and continuous optimization, The course synopsis is as follows: Single variable optimization, multivariable techniques and gradient method; Linear programming models; The Simplex: formulation and theory; Integer programming; transportation problem; non-linear programming;Quadratic programming; Kuhn-Tucker methods; Optimality criteria; Two-person zero-sum games.

MTS 502(E)
GENERAL TOPOLOGY