GAS2611

Real analysis

Offered for the last time in 1998

Dr John Arkinstall

3 points
* First semester
* 2 hours per week
* Gippsland/Distance (even numbered years only)
* Prerequisites: GAS 1615 or GAS1611, preferably with a grade of at least credit
* Corequisite: GAS2614 is desirable
* Prohibitions: MAP2011

Objectives The objectives for this subject are for students to learn the discipline of axiomatic proof, and understand the meta-mathematical properties of axiom systems; understand the Dedekind cut model for the real numbers, and its status in relation to an axiomatic specification for the real numbers; build an understanding of analytic proof, sufficient to be able to apply this to new tasks; use the concept of uniform convergence to justify mathematical methods of calculus involving sequences and series of functions, and apply this to examples; understand the basis for the Riemann integral, and prove the existence of functions which are Riemann integrable and of functions which are not.

Synopsis This subject provides an introduction to classical real analysis, a formal treatment of the methods of calculus. Introduction to proof in axiomatic systems; an axiom system for the real numbers; convergence of sequences and series, decimal representation, power series; limits of functions, continuity, differentiability, the mean value theorem and its consequences; uniform convergence, continuity of the limit function, differentiation and integration of infinite series term by term, application to power series; the Riemann integral; improper and infinite integrals, Cauchy principal value.

Assessment Assignments: 40%
* Examination: 60%

Recommended texts

Gaughan E D Introduction to analysis Brooks Cole, 1987