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An Introduction to smooth Manifolds

Offered By: Indian Institute of Science Bangalore via Swayam

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Mathematics Courses Calculus Courses Stokes' Theorem Courses Topology Courses Tensors Courses Lie Groups Courses Lie Algebras Courses Differential Forms Courses

Course Description

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

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