Course11110813468 lectures

An Introduction to Smooth Manifolds

Prof. Harish Seshadri · IISc Bangalore

About

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.

Lectures

Week 1 Review of linear algebra and multivariable calculus

Week 2 Smooth manifolds and Smooth maps

Week 3 Tangent spaces

Week 4 Tangent Spaces (Contd.)

Week 5 Submanifolds

Week 6 Vector Fields and Lie Groups

Week 7 Flows of vector fields

Week 8 Lie Brackets and Lie Algebras

Week 9 Differential forms and Symmetric tensors.

Week 10 Alternating tensors

Week 11 Differential Forms

Week 12 Orientation on manifolds.

Syllabus and materials

At NPTEL, as the course publishes them.

Syllabus

Credits and licence

Institution: IISc Bangalore
Department: Mathematics
Teacher: Prof. Harish Seshadri
Level: Graduate
Language: English
Subjects: Mathematics
Source: NPTEL
Licence: CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution: NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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