Sample lecture schedule
(based on 25 lectures each
of duration 75 minutes).
- Lecture 1:
Review
of basic Newtonian mechanics.
- Lecture 2:
Variational
calculus.
- Lecture 3:
Generalized
coordinates and constraints.
- Lecture 4:
Hamilton’s
principle and the Lagrange equations of motion.
- Lecture 5:
Conservation
theorems and symmetries.
- Lecture 6:
Central
forces; scattering in a central force.
- Lecture 7:
Hamiltonian
formulation and the Principle of Least Action.
- Lecture 8:
Canonical
transformations and Poisson brackets.
- Lecture 9:
Hamilton-Jacobi
method; action-angle variables.
- Lecture 10:
Adiabatic
invariance; Liouville’s theorem.
- Lecture 11:
Kinematics
of rigid body motion – tensor notation.
- Lecture 12:
Rotation
matrices, rotating frames, Coriolis force.
- Lecture 13:
Rigid
body dynamics 1.
- Lecture 14:
Rigid
body dynamics 2.
- Lecture 15:
Linear
oscillations 1 – normal modes.
- Lecture 16:
Linear
oscillations 2 – the role of symmetries and symmetry groups.
- Lecture 17:
Nonlinear
oscillations.
- Lecture 18:
Secular
perturbation theory.
- Lecture 19:
Dissipative
nonlinear systems and chaos.
- Lecture 20:
Transition
from discrete to continuous systems; the Lagrangian density.
- Lecture 21:
Lagrangian
formulation for continuum systems; waves on a one-dimensional
string, sound waves in three dimensions.
- Lecture 22:
Hamiltonian
formulation for continuum systems.
- Lecture 23:
Stress-energy
tensor and conservation theorems.
- Lecture 24:
Special
topics.
- Lecture 25:
Special
topics
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