units

MTH3110

Faculty of Science

18 September 2017 22 November 2024
Monash University

Undergraduate - Unit

This unit entry is for students who completed this unit in 2015 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.

print version

6 points, SCA Band 2, 0.125 EFTSL

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

LevelUndergraduate
FacultyFaculty of Science
Organisational UnitSchool of Mathematical Sciences
OfferedClayton First semester 2015 (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:

  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 hour support class per week

See also Unit timetable information

Chief examiner(s)

Dr Daniel Mathews

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

Mathematics and statistics

Prerequisites

MTH2010 or MTH2015, and MTH2021 or MTH2025

Prohibitions

MTH3132