1. Introduction to tensor analysis, vectors and tensors, continuity of tensors and Cartesian coordinates, tensors and anisotropy of materials.
2. Orthogonal transformations, rotation of vectors and tensors, basis and Cartesian coordinate system, scalar, vector and tensor (dyadic) products, summation conventions.
3. First-, second- and M-order tensors, symmetry of tensors, operations on tensors, Kronecker delta and Levi-Civita symbol. Examples of tensors in physics.
4. Tensor field, derivative and differential of tensor function. Gradient, divergence, rotation, compound operators.
5. Characteristics of tensor fields: rarefaction, vorticity and field flux. The Gauss-Ostogradsky theorem.
6. Description of stress, strain and elasticity, thermal expansion.
7. Permittivity tensor of an anisotropic medium, relations between electric field E, electric induction D and material polarization P. Susceptibility tensor of an anisotropic medium, relations between magnetic field H, magnetic induction B and material magnetization M.
8. Crystallographic systems and their description by second order tensors. Symmetry operations in crystallography.
9. Piezoelectric and thermoelectric phenomena.
10. Magneto-optical phenomenon. Derivation of the linear magneto-optical tensor for various crystallographic configurations, description of higher order contributions in magnetization by fourth and fifth order tensors.
11. Pockels (linear) and Kerr (quadratic) electro-optic effect.
12. Tensor calculus in Python. Writing custom script I.
13. Tensor calculus in Python. Writing custom script II.
2. Orthogonal transformations, rotation of vectors and tensors, basis and Cartesian coordinate system, scalar, vector and tensor (dyadic) products, summation conventions.
3. First-, second- and M-order tensors, symmetry of tensors, operations on tensors, Kronecker delta and Levi-Civita symbol. Examples of tensors in physics.
4. Tensor field, derivative and differential of tensor function. Gradient, divergence, rotation, compound operators.
5. Characteristics of tensor fields: rarefaction, vorticity and field flux. The Gauss-Ostogradsky theorem.
6. Description of stress, strain and elasticity, thermal expansion.
7. Permittivity tensor of an anisotropic medium, relations between electric field E, electric induction D and material polarization P. Susceptibility tensor of an anisotropic medium, relations between magnetic field H, magnetic induction B and material magnetization M.
8. Crystallographic systems and their description by second order tensors. Symmetry operations in crystallography.
9. Piezoelectric and thermoelectric phenomena.
10. Magneto-optical phenomenon. Derivation of the linear magneto-optical tensor for various crystallographic configurations, description of higher order contributions in magnetization by fourth and fifth order tensors.
11. Pockels (linear) and Kerr (quadratic) electro-optic effect.
12. Tensor calculus in Python. Writing custom script I.
13. Tensor calculus in Python. Writing custom script II.