Department of Statistics

This course is the second course in calculus, designed primarily for students in mathematics, pure and applied sciences. However, it also meets the need of students in other fields. The course’s focus is to impart useful skills on the students in order to enhance their knowledge in methods of solving mathematical problems and prepare them for other specialised applications to be encountered at higher levels. Topics to be covered include real-valued function of a real variable, review of differentiation and integration and their applications, mean value theorem, Taylor series, real-value functions of two or three variable, partial derivatives, chain rule, extrema, Lagrange’s multiplier, increment, differentials and linear approximations, evaluation of linear integral.

This course is intended as a first elementary introduction to Linear algebra designed primarily for students in mathematical sciences, statistics and computer sciences department. However, it also meets the need of students in other fields, such as engineering and social sciences. This course’s focus is to impart useful skills on the students in order to introduce them to Linear algebra, to enhance their knowledge and prepare them for other courses to be encountered at higher levels. Topics to be covered include vector space over real field, subspaces, linear independence, basis and dimension, linear transformation and their representation by matrices-range, null space, rank. Singular and non-singular transformation of matrices. Algebra of matrices.

This course is a first course in Differential Equations 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 ordinary differential equations. The course focuses on First and second order ordinary differential equations and general theory of nth order linear ordinary differential equations.

This course is the first course in numerical analysis designed for students in mathematics, physical sciences, engineering, mineral and earth sciences. The focus of the course is to equip students with basic useful skills to solve numerically both theoretical and empirical problems leading to linear and nonlinear equations. Topics to be covered include numerical solution of algebraic and transcendental equations; curve fitting; error analysis; interpolation and approximation; zeros of non linear equations in one variable; system of linear equations; numerical differentiation and integration.

This course is the first course in numerical analysis designed for students in mathematics, physical sciences, engineering, mineral and earth sciences. The focus of the course is to equip students with basic useful skills to solve numerically both theoretical and empirical problems leading to linear and nonlinear equations. Topics to be covered include system of linear equations; change of bases, equivalent and similarity; eigenvalues and eigenvectors problems; minimum and characteristic polynomials of a linear transformation (matrix); Cayley-Hamilton’s theorem; bilinear and quadratic forms; orthogonal diagonalization, canonical forms.

This course is an exploratory, first course in Real Analysis designed primarily for students in pure and applied mathematics. However, it also has great value for any undergraduate student in physical sciences, engineering and computer science who wishes to go beyond the routine manipulations of formulas to solve standard problems. Real analysis develops the ability to think deductively, analyze mathematical situations and extend ideas to a new context. The goal of the course is to equip the students with the fundamental concepts and techniques of real analysis. Topics to be covered include bounds of real numbers; monotone sequences, the theorem of nested intervals, Cauchy sequences, the tests for convergence of series and rearrangements, completeness of reals and incompleteness of rationals, continuity and differentiability of functions of real numbers, Rolle’s and mean value theorems for differentiable functions, Taylor series.

Vectors in Euclidean Spaces. Dot and vector products. Element of vector calculus. Gradient of scalar functions, curl and divergence of vector fields. General kinematics, momentum, angular momentum, fundamental equations of motion. Energy and conservation laws. Particle and rigid body dynamics. Simple harmonic oscillators and simple pendulum.