Undergraduate - UnitMTH3110 - Differential geometry

This unit entry is for students who completed this unit in 2013 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

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6 points, SCA Band 2, 0.125 EFTSL

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Level	Undergraduate
Faculty	Faculty of Science
Organisational Unit	School of Mathematical Sciences
Offered	Clayton Second semester 2013 (Day)
Coordinator(s)	Dr Daniel Mathews

Synopsis

This unit will explore the metric structure of curves and surfaces, primarily in 3-dimensional Euclidean space. Concepts of curvature arise naturally, and the major focus will be on the inter-relationships of various definitions of curvature, such as the normal and binormal curvatures of a curve, and the extrinsic, principal and Gaussian curvatures of a surface. Links will be drawn with many other areas of mathematics, including complex analysis, linear algebra, differential equations, and general relativity.

Outcomes

On completion of this unit students will be able to:

Appreciate the significance of intrinsic measures of curvature, for curves and surfaces in R^3;

Compute curvature and related quantities, by hand and using computer software;

Understand tensors and their use in geometry;

Communicate mathematical ideas and work in teams as appropriate for the discipline of mathematics.

Assessment

Two assignments: 10% each
One project: 20%
Final examination: 60%

Chief examiner(s)

Dr Daniel Mathews

Contact hours

Three hours of lectures and one hour support class per week

Prerequisites

MTH2010 or MTH2015, and MTH2021

Prohibitions

MTH3132