Module Code & Title: MATH1A Calculus of One Variable
Availability: Semester 1
Academic Unit: 4
Pre-requisite: A level Mathematics or equivalent
Module Description: Lecture: 13 x 3 hrs; Tutorial: 12 x 1 hrs; Laboratory: 3 x 2 hrs
Content
Functions from R to R, their limits, continuity, Intermediate Value Theorem. Differentiability, chain rule, critical points, Rolle’s Theorem and Mean Value Theorem. Inverse functions and derivatives of inverse functions. Integrability and integrals. Fundamental Theorems of Calculus. Trigonometric, logarithm and exponential functions. Techniques of integration. Taylor’s formula. Infinite sequences. Infinite series. Power series and radius of convergence.
Objectives
This is an intensive introduction to calculus of one variable and (plane) analytic geometry for Science and Engineering scholars.
Learning Outcomes
Upon successful completion of the module, the students will know:
a. basic properties of real number and functions, in particular elementary transcendental functions, continuous functions, differentiable functions;
b. limits and sequences, and their relationship to continuity and differentiability (univariate case);
c. basic properties of continuity and derivatives, methods to determine derivatives.
d. the role of derivatives in analytic geometry;
e. basics of (Riemann) integration, techniques for finding (in)definite integrals;
f. basics of infinite series and in particular power series.
Module Assessment
Students will be assessed by:
a. A final 2-hour written examination (70%)
b. Continuous assessment (30%)