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 modeling physical and other phenomena. Complementary mathematical approaches for their solution will be presented. The topics to be covered are vector algebra with applications to three-dimensional geometry. First order differential equations; applications to integral curves and orthogonal trajectories. Ordinary linear differential equations with constant coefficients and equation reducible to this type. Simultaneous linear differential equations. Introduction to partial differential equations.
This course aims to provide a first approach to the subject of algebra, which is one of the basic pillars of modern mathematics. The focus of the course will be the study of certain structures called groups, rings, fields and some related structures. Abstract algebra gives to student a good mathematical maturity and enable learners to build mathematical thinking and skill. The topics to be covered are injective, subjective and objective mappings. Product of mappings, inverse of a mapping. Binary operations on a set. Properties of binary operations (commutative, associative and distributive properties). Identity element of a set and inverse of an element with respect to a binary operation. Relations on a set. Equivalence relations, equivalence classes. Partition of set induced by an equivalence relation on the set. Partial and total order relations on a set. Well-ordered sets. Natural numbers; mathematical induction. Sum of the powers of natural numbers and allied series. Integers; divisors, primes, greatest common divisor, relatively prime integers, the division algorithm, congruencies, the algebra of residue classes. Rational and irrational numbers. Least upper bound and greatest lower bound of a bounded set of real numbers. Algebraic structures with one or two binary operations. Definition, examples and simple properties of groups, rings, integral domains and fields.
The course is designed to familiarize learners with fundamental mathematical concepts such as basic set theory, mappings, linear and quadratic functions and their graphs. Other topics to be considered in the course are: matrices and determinants with applications to simultaneous linear equations. Permutations and combinations, binomial theorem. Radian measure, trigonometric functions, identities. Elementary calculus and co-ordinate geometry.
This course is designed to develop the topics of analytic geometry, differential and integral calculus. Emphasis is placed on limits, continuity, derivatives and integrals of algebraic and transcendental functions of one variable. The topics to be covered are: Rectangular Cartesian co-ordinate systems. Distance between two points, gradient of a line, co-ordinates of a point dividing a line segment in a given ratio. Equations of a circle in the form. Points of intersection of lines and circles. Limit of a function of one variable at a point. Continuous functions. Derivatives of a function and its interpretation as the rate of change. Higher order derivatives. Differentiation of algebraic, circular, exponential functions. Sum, product and quotient rules. Differentiation of composite, absolute value and implicit function. Small increments and calculation of approximate values. Application of derivative to increasing and decreasing of functions, maxima and minima. Curve sketching. Integration as the inverse of differentiation. Integration of simple continuous functions and rational functions by substitution. Parametric representation of loci. The parabola, ellipse and rectangular hyperbola. Chords, tangents and normal.
This course seeks to prepare students for advanced courses in Mathematics. Students will have a better appreciation of how to perform basic operations on sets, real numbers and matrices and to prove and apply trigonometric identities. The specific topics that will be covered are: commutative, associative and distributive properties of union and intersection of sets. DeMorgan’s laws. Cartesian product of sets. The real number system; natural numbers, integers, rational and irrational numbers. Properties of addition and multiplication on the set of real numbers. Relation of order in the system of real numbers. Linear, quadratic and other polynomial functions, rational algebraic functions, absolute value functions, functions containing radicals and their graphical representation. Inequalities in one and two variables. Application to linear programming. Indices and logarithms, their laws and applications. Binomial theorem for integral and rational indices and their application. Linear and exponential series. Circular functions of angles of any magnitude and their graphs. Trigonometric formula including multiple angles, half angles and identities. Solution to trigonometric equations.
Principles; Properties; Pumping Process; Process; Optics Resources; Types of Lasers; Output Characteristics; Theory of Laser Oscillation. Laser modulation; demodulation, detection, Laser Applications in metrology, holography medicine etc.
Basic field concepts; Review of equations in electrostatics; Magnetostatics and electromagnetic induction; Maxwell’s equations; Electromagnetic wave equation; Poynting theorem; Reflection and refraction; Propagation in conducting and in ionized media; The ionosphere.
The course will focus on the treatment of electroanlytical methods (potentiometric, voltametric and polarographic methods) and the application of electromotive force measurement and activities in cell potential determination. Electrodes types and their fabrication, assessment of their performance characteristics related to sensitivity, selectivity coefficient, etc. will be reviewed.
This course seeks to promote understanding of the significance of natural products in terms of their biosynthesis, biological activity and chemical synthesis, combining organic chemistry and biological chemistry. It will focus on the diversity of natural products and their roles in biological systems, the chemistry and biosynthesis of the major natural products classes and the synthesis of important natural products. A special emphasis will be placed on how chemical structure affects the physiological function of various natural products.
Communicating biosafety information: Communication skills, Communicating with target groups (e.g. farmers, legislators, media, regulators etc.), Other methods of disseminating information (e.g. fliers, brochures, workshops etc.), Socio-economics of Biosafety and biotechnology; Assessing the costs of Biosafety Regulations: conceptual issues; Economics of Biotechnology, Economics of Biosafety (Cost of biosafety regulations and Strategic approaches to biosafety regulations (Trade, Labour, Socio-cultural issues); Non-biosafety issues (Bioethics).