• Offered by Department of Mathematics
• ANU College ANU Joint Colleges of Science
• Classification Advanced
Specialist
• Course subject Mathematics
• Academic career PGRD
• Course convener
• Dr Scott Morrison
• Mode of delivery In Person
• Offered in Second Semester 2014
Analysis 3: Functional Analysis, Spectral theory and Applications (MATH6214)

This course is intended both for continuing mathematics students and for other students using mathematics at a high level in theoretical physics, engineering and information technology, and mathematical economics.

Topics to be covered include:

• Measure theory
• Functions of bounded variation over R
• Absolute continuity and integration
• Examples of more general measures (Radon, Hausdorff, probability measures)
• Fubini-Tonelli theorem
• Radon-Nikodym theorem
• Banach spaces and linear operators
• Classical function and sequence spaces
• Hahn-Banach theorem
• Closed graph and open mapping theorems
• Uniform boundedness principles
• Sequential version of Banach-Alaoglu theorem
• Spectrum of an operator and analysis of the compact self-adjoint case
• Fredholm alternative theorem.

Note: Graduate students attend joint classes with undergraduates but will be assessed separately.

## Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Explain the fundamental concepts of functional analysis and their role in modern mathematics and applied contexts
2. Demonstrate accurate and efficient use of functional analysis techniques
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from functional analysis
4. Apply problem-solving using functional analysis techniques applied to diverse situations in physics, engineering and other mathematical contexts

## Indicative Assessment

Assessment will be based on:

• Three assignments (30% total; LO 1-4)
• Essay paper (20%; LO 1-4)
• Take home exam (50%; LO 1-4)

The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.

## Workload

36 lectures, tutorials by arrangement

## Requisite and Incompatibility

You will need to contact the Department of Mathematics to request a permission code to enrol in this course.

## Fees

Tuition fees are for the academic year indicated at the top of the page.

If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Students continuing in their current program of study will have their tuition fees indexed annually from the year in which you commenced your program. Further information for domestic and international students about tuition and other fees can be found at Fees.

Student Contribution Band:
2
Unit value:
6 units

If you are an undergraduate student and have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). You can find your student contribution amount for each course at Fees.  Where there is a unit range displayed for this course, not all unit options below may be available.

Units EFTSL
6.00 0.12500

## Course fees

Domestic fee paying students
Year Fee Description
1994-2003 \$1650
2014 \$2946
2013 \$2946
2012 \$2946
2011 \$2946
2010 \$2916
2009 \$2916
2008 \$2916
2007 \$2520
2006 \$2520
2005 \$2520
2004 \$2160
International fee paying students
Year Fee
1994-2003 \$3606
2014 \$3762
2013 \$3756
2012 \$3756
2011 \$3756
2010 \$3750
2009 \$3618
2008 \$3618
2007 \$3618
2006 \$3618
2005 \$3618
2004 \$3618
Note: Please note that fee information is for current year only.

## Offerings, Dates and Class Summary Links

ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.

The list of offerings for future years is indicative only.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.

### Second Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary
7325 21 Jul 2014 08 Aug 2014 31 Aug 2014 30 Oct 2014 In Person N/A

Responsible Officer: Registrar, Student Administration / Page Contact: Website Administrator / Frequently Asked Questions