University Course Planner The University of Adelaide Australia

PURE MTH 3009 - Integration and Analysis III

Career: Undergraduate
Units: 3
Term: 3820
Campus: North Terrace
Contact: Up to 3 hours per week
Available for Study Abroad and Exchange: Yes
Available for Non-Award Study: Yes
Pre-Requisite: MATHS 2100
Assessment: Ongoing assessment, exam
Syllabus:

The Riemann integral works well for continuous functions on closed bounded intervals, but it has certain deficiencies that cause problems, for example, in Fourier analysis and in the theory of differential equations. To overcome such deficiencies, a "new and improved" version of the integral was developed around the beginning of the twentieth century, and it is this theory with which this course is concerned. The underlying basis of the theory, measure theory, has important applications not just in analysis but also in the modern theory of probability. Topics covered are: Set theory; Lebesgue outer measure; measurable sets; measurable functions. Integration of measurable functions over measurable sets. Convergence of sequences of functions and their integrals. General measure spaces and product measures. Fubini and Tonelli's theorems. Lp spaces. The Radon-Nikodym theorem. The Riesz representation theorem. Integration and differentiation.

Course Fees

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Only some Postgraduate Coursework programs are available as Commonwealth Supported. Please check your program for specific fee information

  Commonwealth Supported Student Contribution
Tuition Fees
Units EFTSL Pre-2010 2010 Onwards Domestic International
3 0.125 Band 2 $1,169 Band 2 $1,169 select program select program


Course Outline

A Course Outline which includes Learning Outcomes, Learning Resources, Learning & Teaching for this course may be accessed here


Critical Dates

Term Last Day to Add Online Census Date Last Day to WNF Last Day to WF
3820 Mon 06/08/2018 Fri 31/08/2018 Fri 14/09/2018 Fri 26/10/2018


Class Details

Enrolment Class: Lecture
Class Nbr Section Size Available Dates Days Time Location
20867 LE01 25 11 23 Jul - 10 Sep Monday 11am - 12pm Benham, G25, Peter Martin Room
24 Jul - 11 Sep Tuesday 12pm - 1pm Engineering Nth, N132, Teaching Room
25 Jul - 12 Sep Wednesday 10am - 11am Engineering & Mathematics, EMG07, Teaching Room
1 Oct - 22 Oct Monday 11am - 12pm Benham, G25, Peter Martin Room
2 Oct - 23 Oct Tuesday 12pm - 1pm Engineering Nth, N132, Teaching Room
3 Oct - 24 Oct Wednesday 10am - 11am Engineering & Mathematics, EMG07, Teaching Room