Ngô Quốc Anh

MAT3318 – Calculus on manifolds

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 \mathbb R^n, 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 \mathbb R^n
  • Weeks 4–6: Manifolds in \mathbb R^n
  • Weeks 7–9: Differential forms
  • Week 10: Stokes’ theorem
  • Mid-term Test
  • Weeks 12–13: Stokes’ theorem (cont.)
  • Weeks 14–15: Life outside of \mathbb R^n
  • Exam

Assessment:

  • Participation \approx 5%
  • Assignments \approx 15%
  • Mid-term Test \approx 30%
    Coverage: Weeks 1-9
  • Exam \approx 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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