Applied Functional Analysis

Course aim

To have knowledge and understanding of advanced  techniques in analysis and apply them to a specific context, such as convex optimisation or partial differential equations.

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

Examination, Problem solving exercise

Fees

EFTSL*: 0.125
Commonwealth Supported program (Band 1)
To determine the fee for this course as part of a Commonwealth Supported program, go to:
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Fee-paying program for domestic and international students
International students and students undertaking this course as part of a postgraduate fee paying program must refer to the relevant program home page to determine the cost for undertaking this course.

Non-award enrolment
Non-award tuition fees are set by the university. To determine the cost of this course, go to:
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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.