Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

Online Course

An introduction to smooth manifolds.

Indian Institute of Technology Bangalore and NPTEL via Swayam

(0)
11

Taken this course? Share your experience with other students. Write review

Overview

The goal of this course is to introduce the student to the basics of smooth manifold theory. The course will start with a brief outline of the prerequisites from topology and multi-variable calculus. After the introducion of differentiable manifolds, a large class of examples, including Lie groups, will be presented. The course will culminate with a proof of Stokes' theorem on manifolds.     INTENDED AUDIENCE : Masters and PhD students in mathematics, physics, robotics and control theory, information theory and climate sciences. PREREQUISITES : Real analysis, linear algebra and multi-variable calculus, topology. INDUSTRY SUPPORT : Nil

Syllabus

COURSE LAYOUT Week 1 : Review of topology and multi-variable calculus Week 2 : Definition and examples of smooth manifolds Week 3 : Smooth maps between manifolds, submanifolds Week 4 : Tangent spaces and vector fields Week 5 : Lie brackets and Frobenius theorem Week 6 : Lie groups and Lie algebras Week 7 : Tensors and differential forms Week 8 : Exterior derivative Week 9 : Orientation Week 10 : Manifolds with boundary Week 11 : Integration on manifolds Week 12 : Stokes Theorem

Taught by

Prof. Harish Seshadri

Reviews for Swayam's An introduction to smooth manifolds. Based on 0 reviews

  • 5 star 0%
  • 4 star 0%
  • 3 star 0%
  • 2 star 0%
  • 1 star 0%

Did you take this course? Share your experience with other students.

Write a review

Class Central

Get personalized course recommendations, track subjects and courses with reminders, and more.

Sign up for free

Never stop learning Never Stop Learning!

Get personalized course recommendations, track subjects and courses with reminders, and more.

Sign up for free