MAT3318 **Calculus on Manifolds**

Sem2 AY 2016-2017

Syllabus

**Aims & Objective**: This module studies the calculus on manifolds. It covers the following topics: manifolds in , tensor and exterior algebras, orientation of manifolds, integration on manifolds, Stokes’ theorem. The course is designed for mathematics undergraduate students with interest in analysis or geometry.

**Prerequisite**: The minimal requirement is the knowledge of multivariable calculus and linear algebra. More advanced knowledge from mathematical analysis also helps.

**Class**:

- Timetable: Wednesday, 9am-12pm, 303 T5
- Contact via ngoquocanh at gmail dot com or website http://wp.me/P4uAr-2YX

**Teaching Modes**: Lectures, assignments, tutorials.

**Schedule**:

- Weeks 1–3: Review of calculus on
- Weeks 4–6: Manifolds in
- Weeks 7–9: Differential forms
- Week 10: Stokes’ theorem
- Mid-term Test
- Weeks 12–13: Stokes’ theorem (cont.)
- Weeks 14–15: Life outside of
- Exam

**Assessment**:

- Participation 5%
- Assignments 15%
- Mid-term Test 30%

Coverage: Weeks 1-9 - Exam 50%

Coverage: Weeks 1-15

**Text & Readings**:

- (Main textbook) James R. Munkres,
*Analysis on manifolds*(Advanced books classics), Westview Press. - (Further reading) Michael Spivak,
*Calculus on manifolds: a modern approach to classical theorems of advanced calculus*, Westview Press.

Note: This schedule is very tentative and will be adjusted as necessary.

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