MATH416-21S1 (C) Semester One 2021

Differential Systems

15 points

Details:
Start Date: Monday, 22 February 2021
End Date: Sunday, 27 June 2021
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 7 March 2021
  • Without academic penalty (including no fee refund): Friday, 14 May 2021

Description

Differential Systems

Moving frames and exterior differential systems form a natural backdrop for the study of problems in geometry and partial differential equations. In particular, most (if not all) physical systems exhibit symmetry and so embody geometric content in the differential equations that describe the physics. These systems are naturally described in the coordinate free approach of moving frames. Integrability conditions, the "size" of the solution space and the existence of "singular" branches of the solution space for systems of partial differential equations can be readily found in the moving frame approach.

This course will introduce moving frames and exterior differential systems with an emphasis on the conceptual and operational issues. The "standard" vector calculus will be revisited with the aid of differential forms. Their application to simple geometric problems and the reformulation
of Maxwell’s equations as an exterior differential system will be considered. If time permits (and depending on student interest) either the exterior differential system formulation of Einstein’s field equations or application of moving frames to computer recognition of objects will be considered.

Prospective students should have familiarity with partial differential equations and vector calculus.

Pre-requisites

Subject to approval of the Head of School.

Timetable 2021

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Friday 09:00 - 10:00 Jack Erskine 505
22 Feb - 28 Mar
26 Apr - 6 Jun
Lecture B
Activity Day Time Location Weeks
01 Wednesday 09:00 - 10:00 Jack Erskine 505
22 Feb - 4 Apr
26 Apr - 6 Jun
Lecture C
Activity Day Time Location Weeks
01 Tuesday 11:00 - 12:00 Jack Erskine 505
22 Feb - 4 Apr
26 Apr - 6 Jun

Course Coordinator

Mark Hickman

Lecturer

Mark Hickman

Indicative Fees

Domestic fee $1,000.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All MATH416 Occurrences

  • MATH416-21S1 (C) Semester One 2021