MAU34214 Calculus on manifolds

Module Code	MAU34214
Module Title	Calculus on manifolds
Semester taught	Semester 2
ECTS Credits	5
Module Lecturer	Prof. Florian Naef
Module Prerequisites	MAU23203 Analysis in several real variables

This module is examined in a 2-hour examination at the end of Semester 2.
Continuous assessment contributes 10% towards the overall mark.
The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows:
1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session;
2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam;
3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.
Capping of reassessments applies to Theoretical Physics (TR035) students enrolled in this module. See full text at https://www.tcd.ie/teaching-learning/academic-affairs/ug-prog-award-regs/derogations/by-school.php Select the year and scroll to the School of Physics.

11 weeks of teaching with 3 lectures per week.

On successful completion of this module, students will be able to

Prove theorems about manifolds in Euclidean space.
Prove theorems about differential forms and perform calculations with them.
Carry out integration on manifolds in Euclidean space.
Explain the relation between scalar, vector, tensor fields and differential forms.
Explain, prove and apply Stokes' theorem for differential forms.
Explain and apply the Poincaré lemma.