| Area of Mathematics: | Physics (EPh) |
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| Semester: | 6o | ||
| Course ID: | 62501 | ||
| Course Type: | Elective | ||
| Teaching hours per week: | Theory: 3 | Practice: 2 | Laboratory: 0 |
| ECTS : | 6 | ||
| Eclass: | For the course’s material, click here. | ||
| Instructors: | Vasilios Zarikas | ||
Description
- Tensors: Concept of the Cartesian tensor, second, third, and higher order tensors, tensor transformations, product, generalized tensors, general coordinate transformations, tensor invariance. Tensile Algebra, tensile contraction. Pseudo-tensors. Tensile Analysis. Christoffel symbols, parallel transport and covariant derivative. Tensile fields, geodesics and geodesic coordinates. Riemann curvature tensor and its algebraic properties, Ricci tensor and gradient, Bianchi identities. Applications from the theory of elasticity, hydrodynamics, and theoretical mechanics. Applications from General Relativity.
- Partial Differential Equations of Waves and Heat: Linear differential equations of second order. Solution of the Laplace equation. One-dimensional wave equation and heat equation: separation of variables, solutions with various boundary conditions. Two-dimensional wave equation and heat dissipation equation: separation of variables, solutions with various boundary conditions.
Bibliography
- Mathematical Methods in the Physical Sciences, Mary Boas
- Mathematical Methods for Physics and Engineering των K.F. Riley and M.P. Hobson.
- Abraham R., Marsden J. E., Ratiu T., Manifolds, Tensor Analysis, and Applications, Springer, 1988.
