units

MTH3110

Faculty of Science

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6 points, SCA Band 2, 0.125 EFTSL

Undergraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Coordinator(s)

Dr Daniel Mathews

Offered

Clayton

  • First semester 2016 (Day)

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:

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

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

  1. Understand tensors and their use in geometry;

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

Assessment

Final examination (3 hours): 70%
Assignments: 30%

Workload requirements

Three hours of lectures and one 2-hour support class per week

See also Unit timetable information

Chief examiner(s)

This unit applies to the following area(s) of study

Prerequisites

Prohibitions

MTH3132