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Analysis and geometry ( 6 points, SCA Band 2, 0.125 EFTSL)


Leader: Associate Professor Hans Lausch

Clayton Second semester 2006 (Day)

Synopsis: Basic concepts of topology; advanced topics on functions of several variables; advanced topics in linear algebra; geometry of surfaces in Euclidean space; higher dimensional integration theory; infinite dimensional linear spaces; Fourier expansions; spectral theory; applications to differential equations.

Objectives: On completion of this unit, students will: understand basic concepts in nonlinear analysis and linear algebra within a geometric context; become familiar with the basic concepts of Hilbert spaces; recognise the limitations of Euclidean space and the power of geometry and topology in studying spaces of functions; understand the elements of spectral theory and appreciate its role in applications; be able to carry out explicit calculations in specific situations and design proofs of basic mathematical statements.

Assessment: Examination (3 hours): 70% + Assignments: 30%

Contact Hours: Three 1-hour lectures and an average of one 1-hour support class per week

Prerequisites: MTH2021 and MTH2111 or MTH3111 or MTH2140 or MTH3140.