Applied Functional Analysis
Course Level Undergraduate
Area/Catalogue
MATH 3026
Course Level
Undergraduate
Offered Externally
No
Course ID
101192
Unit Value
4.5
University-wide elective course
No
Course owner
School of Information Technology and Mathematical Sciences
Course aim
To discuss selected key theorems of mathematical analysis. The discuss should include the history of the theorems, their motivation, their impact on the systematic development of mathematical notation, their rigorous proof and their contribution to the study of particular topics.
Course content
Classical Abstract spaces in Modern Functional Analysis: Topological spaces, Metric spaces, Normed Vector spaces, Space of Lebesgue Measurable Functions, and Hilbert spaces; Fundamental Theorems of Analysis: Hahn-Banach Theorem, Uniform Boundedness Theorem, The Open Mapping Theorem. Dual Spaces: Weak and Weak* topology, Riesz’s Representation Theorem, Closed Graph Theorem, Adjoint Operators in Hilbert spaces, Lp spaces. Differential Calculus in Normed Vector Spaces: Differentiability of functionals (Gateaux and Frechet differentiability).
Textbook(s)
Kurdila, AJ & Zabarankin, M 2005, Convex Funtional Analysis, Birkauser
Prerequisite(s)
| Common to all relevant programs | |
|---|---|
| Subject Area & Catalogue Number | Course Name |
| MATH 2027 | Fundamentals of Real Analysis |
Corequisite(s)
Nil
Teaching method
| Component | Duration | ||
|---|---|---|---|
| INTERNAL, MAWSON LAKES | |||
| Lecture | 3 hours x 13 weeks | ||
| Tutorial | 1 hour x 13 weeks | ||
| Directed Study | N/A x N/A | ||
Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.
Assessment
Assignment 1, Assignment 2, Examination
Fees
EFTSL*: 0.125
Commonwealth Supported program (Band 2)
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Fee-paying program for domestic and international students
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Non-award enrolment
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* Equivalent Full Time Study Load. Please note: all EFTSL values are published and calculated at ten decimal places. Values are displayed to three decimal places for ease of interpretation.
Course Coordinators
Degrees this course is offered in
