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Classical Mechanics

Lecture 1 Discrete systems, continuos physics: motion of a particle
Lecture 2 Conservation of energy and momentum, principal of least action (part I)
Lecture 3 Integration by parts, principal of least action (part II), examples
Lecture 4 Radial potential, definition of variation, Noether theorem, Hamiltionian
Lecture 5 Simple pendulum, double pendulum, harmonic oscillator, Hamiltonian formulation
Lecture 6 Legendre transformation, Hamilton's equations, Poisson brackets
Lecture 7 Liouville's theorem, chaotic systems, particle in a magnetic field
Lecture 8 Lorenz' force law, Gauge invariance, Hall effect, Poission algebra (part I)
Lecture 9 Poission algebra (part II), symmetries and generators

Statistical Mechanics

Lecture 1 Introduction, information, entropy, thermal eqilibrium, temperature
Lecture 2 Lagrange's multipliers, Sterling's approximation, multinominal coefficients
Lecture 3 Boltzmann distribution, partition function, fluctuations
Lecture 4 Pressure (control parameters), ideal gas
Lecture 5 Ideal gas of non point particles, kindergarden black hole thermodynamics
Lecture 6 Second law of thermodynamics, quantum oscillator
Lecture 7 Generalized uncertainty principle, black body radiation, radiation pressure
Lecture 8 Ising Models, mean field approximation
Lecture 9 Review of Ising models, chemical potential, critical point
Lecture 10 Adiabatic variation of parameters, gravitation and thermodynamics, negative temperature

Quantum Mechanics

Lecture 1 Classical and quantum bits (Qbit), vectors and matrices
Lecture 2 Example of a Qbit, vector spaces, observables
Lecture 3 Quantum mechanic axioms and theorems, spin polarisation
Lecture 4 Spin polarisation, eigenvectors and commutators, entanglement part I
Lecture 5 Entanglement part II, Bell's inequality, no-cloning theorem
Lecture 6 Subspaces, projections, interference, measurement and entanglement
Lecture 7 Two slit experiment, density matrix, entropy
Lecture 8 Entropy, time evolution
Lecture 9 Time evolution, Schrödinger equation, spin in a magnetic field

Special Relativity

Lecture 1 4-vector, Lorenz transformation, proper time
Lecture 2 Principal of least action, classical field theory (introduction)
Lecture 3 Forms of frame invariant laws: 4-vectors and derivatives
Lecture 4 Continuing classical field theory: Euler-Lagrange equation, symmetries and conservation laws
Lecture 5 Noether's theorem, energy, linear momentum and charge in field theory
Lecture 6 Conservation of charge and continuity equation, energy and momentum
Lecture 7 Gauge theory, electro-magnetic field tensor, charged particle
Lecture 8 Summation: Lorentz and gauge invariant formulation of Maxwell's equations

Einstein's Theory -- General Gravity

Lecture 1 Galileo's and Newton's gravity, gravitational field, Gauss' theorem
Lecture 2 Review of gravitational field, equivalence principle, geometry
Lecture 3 Introduction to multivariable calculus Part 1: basics, metric tensor
Lecture 4 Introduction to multivariable calculus Part 2: application to space-time
Lecture 5 Tensor calculus, Chrisoffel symbols, line integral
Lecture 6 Curvature, parallel transport
Lecture 7
Lecture 8
Lecture 9
Lecture 10
Lecture 11
Lecture 12
lectures/start.txt · Zuletzt geändert: 2012/05/18 15:05 von vaumann
 
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