CTP PAS

Mathematical Structure of Time and Space I

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Oct. 2, 2019

10 a.m. - noon

Time and space, Euclidean geometry

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Oct. 9, 2019

10 a.m. - noon

The structure of space-time according to Newton; The string equation, i.e. the wave equation in two-dimensional space-time; Mathematical properties of the wave equation in two dimensions

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Oct. 16, 2019

10 a.m. - noon

Initial-boundary problem for the wave equation (string equation); Hyperbolicity and ellipticity of partial differential equations.

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Oct. 23, 2019

10 a.m. - noon

Fourier transform and its applications; Euclidean rotation group; Lorentz transformations as symmetries of the wave equation; Equation of sound propagation

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Oct. 30, 2019

10 a.m. - noon

Sound propagation equation II. Continuity equation; Initial problem for the wave equation in three spatial dimensions

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Nov. 6, 2019

10 a.m. - noon

Exponential function and trigonometric functions: key facts

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Nov. 13, 2019

10 a.m. - noon

The Michelson-Morley experiment and the metric structure of space-time; Lorentz group and its effect on the electromagnetic field

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Nov. 20, 2019

10 a.m. - noon

Maxwell's equations and their symmetries: Lorentz transformations; Clock synchronization. Time measurement and distance measurement

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Nov. 27, 2019

10 a.m. - noon

Electromagnetic field. How to describe a vector in a curvilinear system; A short excursion into differential geometry: vectors and covectors; Tensors and differential forms. Geometric description of t

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Dec. 4, 2019

10 a.m. - noon

Geometric digression: external differential. Maxwell's first pair of equations; Lorentz transformation of the electromagnetic field; Equations of motion of a charged particle in an electromagnetic fie

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Dec. 11, 2019

10 a.m. - noon

Four-shoot. Relativistic law of conservation of energy: E=mc^2

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