MAU11201 Single-variable calculus

This module is examined in a 3-hour examination at the end of Semester 1.
Continuous assessment contributes 15% towards the overall mark.
The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows: 1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session; 2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam; 3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.

11 weeks of teaching with 5 lectures and 1 tutorial per week.

On successful completion of this module, students will be able to

Compute limits and determine whether a given function is continuous or not.
Determine the intervals on which a given function is increasing/decreasing and concave up/down.
Use derivatives to solve optimisation problems and related rates problems.
Integrate functions using the standard techniques of integration.
Use integrals to compute areas, volumes and length.
Determine whether a given series converges or not.

Limits and continuity: epsilon-delta definition, Bolzano's theorem, applications.
Differentiation: Rules of differentiation, mean value theorem, optimisation problems, related rates.
Integration: Fundamental theorem of calculus, techniques of integration, area, length, volume.
Sequences and series: Tests for convergence, power series.