Analysis
Description
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.
Availability
Callaghan
- Semester 1 - 2016
- Semester 1 - 2017
Learning Outcomes
On successful completion of the course students will be able to:
1. 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.
Assumed Knowledge
MATH1220 or MATH1120 or 195/200 in HSC Extension 2 Mathematics plus concurrent enrolment in MATH1210.
Assessment Items
Written Assignment: Assignments
Formal Examination: Examination
Quiz: Quiz
Contact Hours
Callaghan
Lecture
Face to Face On Campus 3 hour(s) per Week for Full Term
Tutorial
Face to Face On Campus 1 hour(s) per Week for Full Term