MATH2330Analysis

Course handbook

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

Learning outcomes

On successful completion of the course students will be able to:

1. Apply real mathematical analysis to solve problems in calculus

2. Carefully state and prove key theorems in calculus using real analysis techniques

3. Construct and communicate rigorous mathematical 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

In Term Test: Mid-semester test

Quiz: Online quiz

Contact hours

Callaghan