Courses Catalogue

Introduction To Mathematical Analysis

ACADEMIC PROGRAMME: Computer Science, B.Sc
COLLEGE/SCHOOL/FACULTY: School of Mathematics and Computing
PROGRAMME TYPE: Undergraduate

Course Content and Outline

Course Outline

·         Functions of one variable [6 hrs]

    • Using the derivative in Optimisation and modelling;
    • Using the definite integral in applications including probability
    • Approximating functions by simpler functions (Taylor and Fourier Series)
  • Limits [9 hrs]

o    Informal definition of limits of functions and continuity; 

o    One sided limits 

o    Removable discontinuity

o    Techniques and theorems of evaluating limits 

o    Formal definition of limits

o    Application to definition and properties of continuous functions 

o    Use of the definition in proofs and problem of limits and continuity

•  Differentiation and Integration [15 hrs]

·         Definition of a derivative, continuity and differentiability

·         Rules and theorems of determining derivatives

·         Inverse functions:   their derivatives and graphs 

·         Differentials: applications to approximation. Rolle’s theorem, Mean Value Theorem, L’Hospital’s Rule 

·         Anti- derivatives: Techniques and theorems for determining anti derivatives 

·         Integration: Define Intergral, Rieman sums, the definite intergral and area,

·         The fundamental theorem of calculus: application to evaluation of definite intergrals (by substitution) 

·         Functions defined by integration: f(t) dt as an anti - derivative of f(x), mean value theorem for integrals [ 6 hrs]

·         Functions of two (or more) variables [9 hrs]

o    Linear Functions in two variables

o    A Fundamental Tool: Vectors

o    Differentiating functions of two (or more) variables (partial derivatives, gradients, directional derivative, chain rule, linear approximations)

o    Using the derivative in optimisation and modelling

o    Integrating functions of two variables (with applications )

Mode of delivery

Lectures, Case studies, Peer discussions, Role plays, Demonstrations