An Introduction to smooth Manifolds
Offered By: Indian Institute of Science Bangalore via Swayam
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
Tags
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