# DEPARTMENT OF MATHEMATICAL SCIENCES

PROF. B. T. OLABODE
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MTS 301
Vector and Tensor Analysis

Course Synopsis

This course is designed primarily for those students taking courses in mathematics, physics, mechanics, electromagnetic theory, aerodynamics, geophysics, metrology or any of the numerous other fields in which vector methods are applicable. Vector and tensor algebra have in recent years become basic part of fundamental mathematical background required of those in engineering, sciences and allied disciplines. It is said that vector and tensor analysis is a natural aid in forming mental pictures of physical and geometrical ideas. A most rewarding language and mode of thought for the physical sciences. The focus therefore, is to impart useful skills on the students in order to enhance their Mathematical ability in applying vector technique to solve problems in applied sciences and to equip them with necessary skill required to cope with higher levels courses in related subjects. Topics to be covered in this course include, basic vector algebra, coordinate bases, gradient, divergence, and curl, Greenâ€™s, Gaussâ€™ and Stokesâ€™ theorems. The metric tensor, Christoffel symbols and Riemann curvature tensor. Applications will be drawn from differential geometry, continuum mechanics, electromagnetism, general relativity theory.

MTS 303
Abstract algebra I

Course Synopsis

This course is an exploratory, first introduction to Abstract Algebra designed primarily for students in Computer Science and Mathematical Sciences. However, it also meets the need of students in other fields, as a course that provides hands-on training in abstractive thinking genuine step are taking to provide sufficient based examples to render them credible or natural. As a course treating abstract ideas, the focus is to impart useful skills on the students in order to enhance their deductive thinking ability and prepare them for the greater task of rigorous proofs and other specialised applications to be encountered at higher levels. Topics to be covered include language and concept of modern mathematics: basic set theory,mappings, relations, equivalence and other relations, Cartesian products. Binary logic, method of proof. Binary operations, algebraic structures, semi-groups, rings, integral domains, fields; homomorphism; number systems, properties of integers,rational,real and complex numbers.

MTS 305
Real Analysis II

Course Synopsis

MTS 305 is an abstract course; second course in Real Analysis for students in the Departments of Mathematical Sciences and Statistics. It is a continuation of MTS 206-Real Analysis I which is a pre-requisite for this course. Although the course is abstract in nature, we have simplified and included some practical examples and areas of applications so that students can find it very interesting. We have included some areas of application which include computation of areas between two curves, volumes of solids of revolution, calculation of arc length, work performed by a variable force, consumersâ€™ surplus, present value of future income, expected values and variance etc

MTS 307
Introduction to Mathematical Modelling

Course Synopsis

This course is an introductory course on Mathematical Modelling. It is designed for students studying mathematical sciences (i.e. Mathematics and Statistics). It may, however, be useful to students in sciences, engineering and other related fields. It introduces students to basic concepts in mathematical modelling. It also equips the students with mathematical modelling skills with emphasis on using mathematical models to solve real- life problems. Topics to be covered in this course includes: methodology of model building, problem identification and definition, model formulation and solution, consideration of varieties of models involving equations like algebraic, ordinary differential equation, partial differential equation, difference equation, integral and functional equations, consideration of some specific applications of mathematical models to biological, social, and behavioural sciences.

MTS 309
Elementary Differential Equations II

Course Synopsis

This course is a follow-up to MTS 209 â€“ Elementary Differential Equations I. It is designed for students in Mathematics to equip them with methods of solving differential equations and other special functions. The topics to be covered in this course include series solutions to second order linear equations â€“ Bessel, Legendre equations; hypergeometric functions/equations; Gamma and Beta functions; Sturm-Liouville problems; orthogonal polynomials and functions; Fourier series and transform; solution of Laplace, wave and heat equations by Fourier method.

MTS 311(E)
Analytical Dynamics

Course Synopsis

This course is designed primarily for students in Sciences and Engineering. However, it also meets the need of students in other fields; as a course that introduces students to theory of motions. The course focuses on Degree of freedom, Generalized coordinates, Lagrangeâ€™s equations for holonomic systems and impulsive forces.

MTS 315
Engineering Mathematics

Course Synopsis

This course is the first course in Mathematical sciences designed for students in School of Engineering only. The focus of the course is to teach students an application of mathematics in the real life problems in the area of Engineering.Topics to be covered include first order ordinary differential equations ,Existence and uniqueness theorem, second order ordinary differential equations, linear dependence, Wronskian, reduction of undetermined coefficient, variation of parameters, general theory of nth order linear equation, Series solution about ordinary and regular points, special functions, Bessel , Lengendre and Hypergeometric. Laplace transform and application to initial value problems.

MTS 302
Complex Analysis I

Course Synopsis

This course is an introductory course on Complex Analysis. It is designed for students in Mathematics and Physics disciplines. It may, however, be useful to students in engineering and other related fields. It introduces students to the complex numbers system and varieties of operations, analyses and problems that may arise within the context. It also equips the students with mathematical techniques and skills to handles such cases. Topics to be covered in this course includes: Introduction to complex number system, Limits and Continuity of Complex variable functions, Derivation of the Cauchy â€“Riemannâ€s Equation, Analytic functions. Harmonic functions, Bilinear transformation, Conformal mapping, Contour Integrals, Convergence of a sequences and series of function of Complex variable.

MTS 304
Metric Space Topology

Course Synopsis

This course is designed as a basic introductory course in the analysis of metric for undergraduate students. It is aimed at providing the abstract analysis components for the degree course of a student majoring in mathematics. It is assumed that such students will have completed a first course in real analysis or a course in calculus which has been carefully developed with attention given to the real analysis foundations. It is also assumed that the student will have some background in elementary linear algebra. This course affords students majoring in mathematics to gain some familiarity with the axiomatic method in analysis for it provides a logically tight investigation of a basically simple abstract structure which manifests itself in a number of diverse examples.

MTS 306
ABSTRACT ALGEBRA II

Course Synopsis

This course is compulsory for pure mathematicians who wish to specialise in the areas of real , complex analysis and functional analysis. The course synopsis is as follows: Normal subgroups and quotient groups. Homomorphism and isomorphism theorems. Cayleyâ€™s Theorem. Direct product. Groups of small orders. Group acting on sets. Sylowâ€™s Theorems. Ideals and quotient rings. Principal deal Domains; Unique Factorization Domains; Euclidean Rings; Irreducibility; Field Extensions; Degree of an Extension; Minimum Polynomial; Algebraic and Transcendental Extensions.

MTS 312(E)
Geometry

Course Synopsis

This course is an exploratory, first course in computer usage designed primarily for students in forestry and allied disciplines. However, it also meets the need of students in other fields, as a course that provides hands-on training in the use of computers for word processing.

MTS 316
Engineering Mathematics II