Differential calculus on manifolds

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Smooth manifold, tangent space differential forms, tensors, Riemannian metrics and manifold, covariant

derivative, parallel transport, orientation of manifold, itegration on manifold and Stokes theorem.

Requirements:

A good knowledge of linear algebra and multivariable differential and integral calculus, a basic knowledge of topological notions (e.g., in the extent of the courses 01MAN1-2, 01ANA/B3-4, 01LAL1-2, and 01TOP held at the FNSPE CTU in Prague).

Syllabus of lectures:

1. Smooth manifolds

2. Tangent and cotangent space

3. Tensors, differential forms

4. Orientation of manifold, integration on manifold

5. Stokes theorem

6. Riemannian manifold.

Syllabus of tutorials:

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Study materials:

Povinná literatura

1. L. Krump, V. Souček, J.A. Těšínský: Matematická analýza na varietách, skripta MFF UK, Karolinum, 1999.

Doporučená literatura

2. O. Kovalski: Úvod do Riemannovy geometrie, Univerzita Karlova, 1995.

3. M. Spivak: Calculus on Manifolds, CRC Press, 2018.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Aplikovaná algebra a analýza (compulsory course in the program)