Statistical Physics and Quantitative Biology
University of Cologne
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Classical Theoretical Physics II: Advanced Mechanics and Electrodynamics
Winter Semester 2009/2010
  1. Lagrange mechanics
    1. Least action principle
    2. Lagrangian of a free particle, Galilei invariance
    3. Lagrangian mechanics in generalized coordinates
    4. Systems with boundary conditions and with constraints
    5. Symmetries and conservation laws
  2. Hamilton mechanics
    1. Legendre transformations
    2. Hamiltonian function and canonical equations of motion
    3. Symmetries and conservation laws in Hamiltonian mechanics
    4. Phase space
    5. Least action principle in phase space
    6. Reduced action and Maupertuis' principle
    7. Canonical transformations
    8. Liouville's theorem
    9. Hamilton-Jacobi equations and outlook on quantum mechanics
  3. Relativistic mechanics
    1. Relativistic kinematics and Lorentz transformations
    2. Relativistic dynamics
    3. Relativistic least action principle
  4. Continuum mechanics and classical field theory
    1. Relativistic field theory
    2. Energy-momentum tensor
  5. Electrodynamics
    1. Vector potential and field tenso
    2. Lagrangian density and equations of motion
    3. Gauge invariance
    4. Energy-momentum tensor, energy of fields and matter
    5. Electromagnetic field in vacuum
    6. Field generated by a current density
    7. Potential and field of a point particle
    8. Radiation of an oscillating charge distribution
    9. Self-interaction and incompleteness of electrodynamics