PARTIAL LIST OF CONCEPTS/IDEAS/METHODS FOR 601
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- constants of the motion, scalar and vector
- => reduction of order of ODEs
- equivalent 1-D problem, V_eff
- turning points and forbidden zones
- constraints and generalized coordinates
- Lagrangian formulation and derivation
- extension to q_dot as independent variable
- q_j -> \vec r etc for no constraints
- Lorentz force "fits" into T-V formulation
- calculus of variations
- Lagrange multipliers 
- 2 body problem
- counting initial conditions, ODE's, and constants of motion
- regular perturbation theory
- small oscillations about equilibrium
- secularities and failure of perturbation theory
- Bertrand's Theorem

- Legendre Transforms
- Hamilton's Equations
- Constructing H from L
- phase space
- analogy to v = z x grad(phi)
- motion along constant H surface
- Hamiltons Eqns from Variational Principle
- General transformations in phase space
- desirability of P = P(H) transformations
- point and contact transformations
- covariance of H eqns under canonical transformations
- generating functions
- examples: H.O.,  NL pendulum
- O-points, X-points, passing and trapped orbits, separatrix
- restrictions on P(H) if Q is to be periodic (Action-Angle vars)
- regular/singular perturbation theory for algebraic eqns/ode's
- WKB, eikonal method, validity
- Hamilton-Jacobi eqn in eikonal methods
- dispersion relation from WKB w=w(k,x)
- parameterizing k(t) and x(t)
- choice of dx/dt = dw/dk as parameterization
- geometric optics, 1D and 3D
- constants of the motion in G.O.
- classical mechanics as G.O. limit of QM
- transform from [p,q] to [alpha,beta] constants of motion
- canonical transformation for the above and Hamilton-Jacobi Theory
- solutions to simple mechanics problems from H-J theoory
- > 1D problems in H-J theory

- small oscillations, eigenvalues and eigenvectors
- decoupled normal modes
- real eValues, orthogonal normal modes
- small oscillations for general U(p,q), stability
- zero frequency modes

- rotations and rigid-body dynamics

Special Relativity: 
- Symmetry and Covariance 
- Rotation and Inertial Frame Symmetry
- Coordinate transformations and Covariance
- Manifest Covariance 
- Scalars, vectors, Tensors 
- Contraction 
- Gradient vectors 
- Co- and contravariant vectors 
- metric tensor
- raising/lowering operators
- Covariant EM eqns in the {phi,A} representation
- 4-vectors:  A, j, U, d 
- 4-Tensor:   F = dA - dA 
- "obvious generalization" to 4-vec covariance