Analysis

Course code MATH2330Units 10Level 2000Faculty of Science and Information TechnologySchool of Mathematical and Physical Sciences

Makes precise the notions of convergence and continuity and examines the validity of intuition about these notions. The course thus puts calculus on a firm foundation and establishes the range of its application. Convergence and continuity form the foundation for much more than elementary calculus and the course also aims to orient students towards these further developments. This course is therefore appropriate for those intending to teach mathematics, as well as those who wish to pursue further study in mathematics.

Available in 2015

Callaghan CampusSemester 1
Previously offered in 2014
Objectives1. To provide students with the fundamental mathematical skills underlying the areas of mathematics broadly described as "analysis".

2. To give students a deeper understanding of the structure of calculus.

3. To develop students' skills in constructing and communicating rigorous arguments.
Content. Convergence of sequences; first principles, the algebra of limits, monotone convergence, Cauchy sequences.

. Convergence of functions: algebra of limits, continuity, the Intermediate Value Theorem.

. Convergence of series

. Differentiable functions, the algebra of differentiation, the Mean Value Theorem and its applications.

. The Riemann integral and the Fundamental Theorems of Calculus.
Replacing Course(s)n/a
Transitionn/a
Industrial Experience0
Assumed KnowledgeMATH1220
or
MATH1120
or
195/200 in HSC Extension 2 Mathematics plus concurrent enrolment in MATH1210.
Modes of DeliveryInternal Mode
Teaching MethodsLecture
Tutorial
Assessment Items
Examination: ClassMid-semester Exam
Essays / Written Assignments
Examination: Formal
Contact HoursTutorial: for 1 hour(s) per Week for Full Term
Lecture: for 3 hour(s) per Week for Full Term
Timetables2015 Course Timetables for MATH2330