STATISTICS AND PROBABILITY 1st SEMESTER 2019/2020 DISCRETE MATHEMATICS 2018/2019 SECOND SEMESTER DIFFERENTIAL CALCULUS

The course is designed to provide students with the basic notions and important concepts in Calculus. Basically, concepts of calculus and their applications would be focused on.  It is assumed that the students have a good background in the pre-calculus aspect or in algebra and trigonometry. This course covers the Calculus of functions of several variables. We will cover generalizations of results from fundamental Calculus to higher dimensions; generalizations of results such as the second derivatives test and the fundamental theorem of calculus. We will go over several physics applications throughout the class in order to illustrate the usefulness of the calculus of several variables. Prerequisites: A minimum grade of C-(Minus) in MATH 124 or Departmental Consent COMPLEX ANALYSIS

A three-hour, one semester course on the theory of the complex variable from elementary functions, differentiation and integration of the complex functions and their application to some areas in mathematics and in the physicial sciences.             Prerequisite:    A minimum grade of C – in MATH 248

The main topics for each are as follows:

Complex variables and regions, analytuic functions, Cauchy-Riemann conditions and harmonic functions, Elementary functions in  z ,  as exponential, trigonometric, hyperbolic    and  trigonometric and their corresponding inverses, Mapping by elementary functions, integration, Cauhy-Goursat Theorem, Residues andpoles and conformal mapping, Applications of conformal mapping and Schwarz-Christoffel transformation NUMERICAL ANALYSIS

Numerical Analysis I is designed to introduce to students  to the design and analysis techniques that use numerical approximations for problems of analysis and equip them with numerical literacy and methods of solving equations with minimal errors.

Objectives and rationale in the use of the different numerical methods in solving different problems which cannot be done by the ordinary and well-known methods   learned in the lower level mathematics such as the determination of roots by the Newston’s, bisection, secant, Newton-Raphson etc., and generally showing the analytical   background of each method  Solutions of simultaneous algebnraic equations by Gauss elimination method, matrix inversion method, Lagrange interpolation; Interpolation based on finite differences; Iterated interpolation Numerical integration and differentiation. The prerequisite of the course is MATH 248 Basic Mathematics & Analytic Geometry

This is a beginning course in plane analytic geometry emphasizing the correspondence between geometric curves and algebraic equations. This correspondence makes it possible to reformulate problems in geometry as equivalent problems in algebra, and vice versa. Curves studied include straight lines, circles, parabolas, ellipses, and hyperbolas. Coordinate transformations, polar coordinates, and parametric equations are also studied. The course assumes a sound background in algebra, geometry, and trigonometry. Prerequisites: A minimum grade of C+ in mathematics in KCSE or Departmental Consent.

Differential Calculus

The course is designed to provide students with the basic notions and important concepts in Calculus. Basically, concepts of calculus and their applications would be focused on.  It is assumed that the students have a good background in the pre-calculus aspect or in algebra and trigonometry. This course covers the Calculus of functions of several variables. We will cover generalizations of results from fundamental Calculus to higher dimensions; generalizations of results such as the second derivatives test and the fundamental theorem of calculus. We will go over several physics applications throughout the class in order to illustrate the usefulness of the calculus of several variables. Prerequisites: A minimum grade of C-(Minus) in MATH 124 or Departmental Consent.