This module introduces the learner to differentiation and integration. It also covers the areas of curve sketching and series and sequences. It provides the student with the solid foundation in calculus, sequences and series, and vectors required for the development of later aspects of the programme.
Differential Calculus
Functions, limits, continuity. Differentiation from first principles. Rules and techniques of differentiation. Mean Value Theorem. Curve sketching. Inverse functions including trigonometric functions. Implicit differentiation.
Integral Calculus
Concept of the Riemann integral including upper and lower sums. Mean Value Theorem for integrals. Fundamental Theorem of Integral Calculus. Methods of integration – substitution, parts and partial fractions. Areas.
Sequences and Series
Convergence of sequences. Fundamental theorem on monotonic sequences. Convergence of series. Tests for convergence. Power series.
Lectures supported by problem-solving sessions and the use of mathematical software packages.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Formal Examination | 70 |
| Other Assessment(s) | 30 |