The construction of mathematical models to address real-world problems has been one of the most important aspects of each of the branches of science. It is often the case that these mathematical models are formulated in terms of equations involving functions as well as their derivatives. Such equations are called differential equations. If only one independent variable is involved, often time, the equations are called ordinary differential equations. The course will demonstrate the usefulness of ordinary differential equations for modelling physical and other phenomena. Complementary mathematical approaches for their solution will be presented. Topics covered include linear differential equation of order n with coefficients continuous on some interval J, existence-uniqueness theorem for linear equations of order n, determination of a particular solution of non-homogeneous equations by the method of variation of parameters, Wronskian matrix of n independent solutions of a homogeneous linear equation, ordinary and singular points for linear equations of the second order, solution near a singular point, method of Frobenius, singularities at infinity, simple examples of Boundary value problems for ordinary linear equation of the second order, Green’s functions, eigenvalues, eigenfunctions, Sturm-Liouville systems, properties of the gamma and beta functions, definition of the gamma function for negative values of the argument; Legendre, Bessel, Chebyshev, Hypergeometic functions and orthogonality properties.
This course provides an introduction to complex analysis which is the theory of complex functions of a complex variable. The topics to be covered in the course are: complex numbers, sequences and series of complex numbers, limits and continuity of functions of complex variables, elementary functions of a complex variable, Cauchy-Riemann criterion for differentiability, analytic functions, complex integrals, Taylor’s and Laurent’s series, calculus of residues, contour integration and conformal mapping.
This course is designed to offer a basic introduction to measure theory and Lebesgue’s integral. The topics to be covered are: countable and uncountable sets, countability of the rationals, uncountability of the reals, measurable sets and functions, the Lebesgue’s integral where E is a measurable subset of the real line and f is measurable on E, the spaces as metric spaces, Cauchy sequences in spaces, completeness of spaces, the Riesz-Fischer theorem and Mean convergence in the space .
This course is designed as a basic introductory course in the analysis of metric spaces. It is aimed at providing the abstract analysis components for the degree course of a student majoring in mathematics. This course affords students an opportunity to gain some familiarity with the axiomatic method in analysis. The topics to be covered are: metric spaces, open spheres, open sets, limit points, closed sets, interior, closure, boundary of a set, sequences in metric spaces, subsequences, upper and lower limits of real sequences, continuous functions on metric spaces, uniform continuity, isometry, homomorphism, complete metric spaces, compact sets in a metric space, Heine-Borel theorem, connected set, and the inter-mediate value theorem.
Laser sources, application formula, optical system design, He-Ne laser, spectroscopy, mode selections, stabilization methods, gas lasers, measuring techniques.
Physics of the ionosphere; Interaction of electromagnetic radiation with the constituents of the middle atmosphere; Rarefied aerodynamics – a study of perturbation; Mesosphere as a transition region; Transport and dynamics in the middle atmosphere; Hydro magnetic behavior near neutral point; The model of the interplanetary magnetic field.
This course will look at the definition of organometallic compounds, reactions of organometallic compounds and synthesis of some of them. The course will help students identify organometallic compounds from other organic compounds containing metals. The course will conclude with some catalytic processes and cycles.
This course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics. The topics to be covered are: axioms for groups with examples, subgroups, simple properties of groups, cyclic groups, homomorphism and isomorphism, axioms for rings, and fields, with examples, simple properties of rings, cosets and index of a subgroup, Lagrange’s theorem, normal subgroups and quotient groups, the residual class ring, homomorphism and isomorphism of rings, subrings.
This course introduces students to basic knowledge within natural product chemistry including the distribution of selected secondary metabolites, their biosynthesis and bioactivity. Furthermore, the objective of the course is to provide students with knowledge on biotechnology-based production of secondary metabolites in particular bioactive natural products as well as knowledge on and experience with isolation, and quantification of secondary metabolites using chromatographic and spectroscopic techniques as well as bioassay-guided chromatographic fractionation.
This course deals mainly with the fundamental principles of chromatography, liquid chromatography, gas chromatography, electrophoresis and other separation techniques. Instrumentation and fundamental concepts with broad relevance in many disciplines of Analytical Chemistry will be covered in the course.