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GEOMETRIC METHODS
IN PHYSICS
dynamical systems
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The order of handouts is:
1. LINEAR ALGEBRA:
Basic notions (1 page)
Numbers (4 pages)
Linear space, etc. (14 pages)
From lectures of.... (comix) (1 page)
Exterior forms and multivectors (4 pages)
Hodge star (4 pages)
2. DIFFERENTIAL GEOMETRY:
Differential geometry (diagram) (1 page)
Dictionary (1 page)
Differential manifolds (4 pages)
Note on grad, div and curl (4 pages)
Induced maps (6 pages)
Differential forms and integration (8 pages)
Geometry of Maxwell's equations (35 pages)
Summary of e-m (4 pages)
Three faces of dynamical systems; Lie derivative (2 pages)
Distributions and the Frobenius theorem (1 page)
NEW
Tensors (6 pages)
NEW
The rank of a 1-form (2 pages)
NEW
3. DYNAMICAL SYSTEMS AND PHYSICS:
Examples of dynamical systems (4 pages)
More on dynamical systems (equilibria, symmetries, first integrals, etc) (4 pages)
Newtonian mechanics (geometry of tangent bundle) (12 pages)
The last 300 years (mini-poster) (1 page)
Symplectic description of a dynamical system (Hamilton's mandala) (2 pages)
Symplectic geometry and the Hamilton eqns (16 pages -- revised version)
The Symplectic Revolution (by Ian Stewart)
(7 pages)
Hamilton's vs Lagrange's eqns (3 pages)
Symplectic geometry of phenomenological thermodynamics (12 pages)
The magic cube of thermodynamics (4 pages)
PTE: the method (2 pages)
Symplectic geometry and the Gaussian optics (9 pages)
Schroedinger equation and symplectic structure (8 pages)
Poisson geometry (10 pages)
Hamilton/Lagrangee equation reconsidered (20 pages)
The history of variational principle (18 pages)
3. GROUPS, ALGEBRAS, CONNECTIONS, ETC:
Groups, groups, groups... (8 pages)
The Kepler problem (2 pages)
The Graph repressentation of SO(n) (2 pages)
Lie mandala (6 pages)
Connections on fiber bundles (16 pages)
Symplectic Structures -- a New Approach to Geometry (by Dusa McDuff)
(10 pages)
Euler's equations (rigid body) -- summary (4 pages)
Natural operations in differential geometry (9 pages)