MTH3110 - Differential geometry

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Overview

This unit will explore the metric structure of curves and surfaces, primarily in 3-dimensional Euclidean space. The major focus is on the various concepts of curvature and related notions, and the relationships between them. Curvature and torsion of a curve. First and second fundamental forms of a surface. Geodesic and normal curvatures of a curve on a surface. Gaussian, mean and principal curvatures of a surface. Important theorems relating these concepts. Links will be drawn with many other areas of mathematics, including real and complex analysis, linear algebra, differential equations, and general relativity.

Offerings

S1-01-CLAYTON-ON-CAMPUS

S1-FF-CLAYTON-FLEXIBLE

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Dr Daniel Mathews

Unit Coordinator(s)

Dr Daniel Mathews

Learning outcomes

On successful completion of this unit, you should be able to:

Explain the significance of intrinsic measures of curvature, for curves and surfaces in 3-dimensional space.

Perform calculations of curvature and related quantities for curves and surfaces in 3-dimensional spaces.

Explain and apply important concepts and theorems about the geometry of curves and surfaces in 3-dimensional space.

Apply results about differential geometry to write proofs and solve problems about curves and surfaces in 3-dimensional space.

Recognise many of the links between differential geometry and other areas of mathematics and physics, such as real and complex analysis, linear algebra, differential equations, and general relativity.

Communicate mathematical ideas relating to differential geometry in a clear, precise and rigorous manner.

Assessment summary

Examination (3 hours and 10 minutes): 60% (Hurdle)

Continuous assessment: 40% (Hurdle)

Hurdle requirement: If you would otherwise have passed the unit but you do not achieve at least 45% in the end of semester written examination and continuous assessment you will receive a Hurdle Fail (NH) grade and a mark of 45 on your transcript.

Workload requirements

Workload

Other unit costs

Costs are indicative and subject to change.
Miscellaneous Items Required (Unit Course Reader,Printing, Stationery)- $120.

Availability in areas of study

Applied mathematics
Mathematical statistics
Mathematics
Pure mathematics