2000

Complex variable functions. Cauchy-Riemann equations. Cauchy integral. Laurent series. Residual theorem. Linear partial differential equations. Special functions. Green´s functions. Fourier analysis. Laplace transform.

Linear equation systems. Interpolation and extrapolation. Roots. Integration. Derivation. Series. Special functions. Random numbers. Fouriere Transform. Integration of differential equations. Eigenvalues, eigenvectors. Frontier problems.

Simple thermodynamics systems. Postulates of thermodynamics in balance systems. Energy and its preservation. Ideal gas. Kinetic theory. Applications in various systems. Thermal machines. Thermodynamic potentials. Phase transitions. Applications. Chemical balance.

We will conduct several experiments as: Photoelectric effect. Millikan experiment. Specific charge of the electron. Speed of light. Franck-Hertz experiment. Interferometry (Michelson, Fabry-Perot). Gamma rays-spectroscopy. Electrical-spin resonance. Cosmic-rays detection. X-rays. Rutherford experiment with Alfa rays. Hall effect.

Black bodies radiation and energy quantization by Planck. Einstein´s light quantum model. Bohr´s hydrogen-atom model. Bohr-Sommerfeld quantum rules. Broglie´s postulates. Schrodinger´s equation. 1D potential well. Hydrogenoid atoms. The spin of the electron. Pauli´s exclusion principle. Periodic table of the elements. Molecular covalent and ionic bonds. The hydrogen molecule. Complex molecules. Vibrational, rotational and electronic spectrum of the molecules.

Revision of Newton’s mechanics. Kinematics in cylindrical and spherical coordinates. Central Forces. Non-inertial systems. Lagrangian model. Hamiltonian Model. Rigid body mechanics: Orthogonal transformations, Euler´s angles, inertia tensor, main axes, free movement of rigid bodies, spinning top. Mechanical oscillations. Collisions. Special relativity. 4 vectors. Relativist collisions.

Maxwell´s equations. Electrostatic and magnetostatic with frontier values. Energy on the electromagnetic field. Multipoles. Electromagnetic waves in conductive and dielectric media. Reflection, refraction and Fresnel´s equations. Guides of waves. Lienard-Wiechert´s potentials and electromagnetic radiation. Antennas. Interference, Kirchoff´s theory and diffraction. Covariant formulation of Maxwell´s equations.