University Course Planner The University of Adelaide Australia

PURE MTH 3009 - Integration and Analysis III

Career: Undergraduate
Units: 3
Term: Semester 2
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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Student Status

Domestic
International

What type of place are you studying in

Commonwealth supported
Full fee paying

Study Level

Undergraduate
Postgraduate Coursework
Non Award

Program of Study

Study Abroad student tuition fees are available here

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

Units
EFTSL
Amount
3
0.125
          
  


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
Semester 2 Mon 08/08/2022 Wed 17/08/2022 Fri 16/09/2022 Fri 28/10/2022


Class Details

Enrolment Class: Workshop
Class Nbr Section Size Available Dates Days Time Location
20585 WR01 25 5 28 Jul - 15 Sep Thursday 1pm - 2pm Hughes, 113, Teaching Room
6 Oct - 27 Oct Thursday 1pm - 2pm Hughes, 113, Teaching Room
Note: This class will be delivered both online and face to face. Please refer to MyUni for details once enrolled.
Related Class: Tutorial
Class Nbr Section Size Available Dates Days Time Location
20584 TU01 25 5 26 Jul - 13 Sep Tuesday 1pm - 2pm Barr Smith South, 2032, Teaching Room
4 Oct - 25 Oct Tuesday 1pm - 2pm Barr Smith South, 2032, Teaching Room
Note: This class is only available for face-to-face (on-campus) students.
20590 TU02 10 10 26 Jul - 13 Sep Tuesday 3pm - 4pm MyUni, OL, Online Class
4 Oct - 25 Oct Tuesday 3pm - 4pm MyUni, OL, Online Class
Note: This class is for offshore/interstate students only. Please refer to MyUni for details once enrolled.