PURE MTH 3009 - Integration and Analysis III
Career: | Undergraduate |
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Units: | 3 |
Term: | 3720 |
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 |
Biennial Course: | Offered in even years |
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
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.
The fees displayed below for international students are for students commencing a program in 2024 only. International students who commenced a program in 2023 or prior can find their fee here.
EFTSL | |||
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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 |
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3720 | Mon 07/08/2017 | Thu 31/08/2017 | Fri 15/09/2017 | Fri 27/10/2017 |
Class Details
Enrolment Class: Lecture | |||||||
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Class Nbr | Section | Size | Available | Dates | Days | Time | Location |
20860 | LE01 | 25 | 8 | 24 Jul - 11 Sep | Monday | 1pm - 2pm | Barr Smith South, 3022, Polygon Lecture Theatre |
26 Jul - 13 Sep | Wednesday | 1pm - 2pm | Hughes, 309, Hughes Lecture Theatre | ||||
28 Jul - 15 Sep | Friday | 1pm - 2pm | Barr Smith South, 3022, Polygon Lecture Theatre | ||||
2 Oct - 23 Oct | Monday | 1pm - 2pm | Barr Smith South, 3022, Polygon Lecture Theatre | ||||
4 Oct - 25 Oct | Wednesday | 1pm - 2pm | Hughes, 309, Hughes Lecture Theatre | ||||
6 Oct - 27 Oct | Friday | 1pm - 2pm | Barr Smith South, 3022, Polygon Lecture Theatre |