\BOOKMARK [1][-]{section.1}{1. Oct 3, 2006: Introduction}{}
\BOOKMARK [2][-]{subsection.1.1}{1.1. Perspective}{section.1}
\BOOKMARK [2][-]{subsection.1.2}{1.2. \(Higher\) cohomology and physics}{section.1}
\BOOKMARK [2][-]{subsection.1.3}{1.3. Classical dynamics vs. open string statics}{section.1}
\BOOKMARK [2][-]{subsection.1.4}{1.4. The quantum case}{section.1}
\BOOKMARK [1][-]{section.2}{2. Oct 10, 2006: Lagrangian Mechanics}{}
\BOOKMARK [2][-]{subsection.2.1}{2.1. Introduction to the Lagrangian approach}{section.2}
\BOOKMARK [2][-]{subsection.2.2}{2.2. Deriving the Euler-Lagrange equations}{section.2}
\BOOKMARK [2][-]{subsection.2.3}{2.3. Physics notation}{section.2}
\BOOKMARK [2][-]{subsection.2.4}{2.4. Example: A particle in a potential}{section.2}
\BOOKMARK [2][-]{subsection.2.5}{2.5. ``Sneak preview"}{section.2}
\BOOKMARK [1][-]{section.3}{3. Oct 17, 2006: From Lagrangian to Hamiltonian Dynamics}{}
\BOOKMARK [2][-]{subsection.3.1}{3.1. Recap}{section.3}
\BOOKMARK [2][-]{subsection.3.2}{3.2. A matter of notation}{section.3}
\BOOKMARK [2][-]{subsection.3.3}{3.3. Switching to the Hamiltonian approach}{section.3}
\BOOKMARK [2][-]{subsection.3.4}{3.4. Energy}{section.3}
\BOOKMARK [2][-]{subsection.3.5}{3.5. Hamilton's Equations}{section.3}
\BOOKMARK [1][-]{section.4}{4. Oct 24, 2006: Hamiltonian Mechanics and Symplectic Geometry}{}
\BOOKMARK [2][-]{subsection.4.1}{4.1. Recap}{section.4}
\BOOKMARK [2][-]{subsection.4.2}{4.2. Some musical operators}{section.4}
\BOOKMARK [2][-]{subsection.4.3}{4.3. The Hamiltonian vector field}{section.4}
\BOOKMARK [2][-]{subsection.4.4}{4.4. Homework}{section.4}
\BOOKMARK [2][-]{subsection.4.5}{4.5. Coordinate-free formulations}{section.4}
\BOOKMARK [1][-]{section.5}{5. Oct 31, 2006: More on the canonical 1-form}{}
\BOOKMARK [2][-]{subsection.5.1}{5.1. Reconciling with the coordinate-based definition}{section.5}
\BOOKMARK [2][-]{subsection.5.2}{5.2. Symplectic manifolds}{section.5}
\BOOKMARK [2][-]{subsection.5.3}{5.3. Digression on five-body systems}{section.5}
\BOOKMARK [2][-]{subsection.5.4}{5.4. The 1-form and action}{section.5}
\BOOKMARK [1][-]{section.6}{6. Nov 07, 2006: The Extended Phase Space}{}
\BOOKMARK [2][-]{subsection.6.1}{6.1. Aside}{section.6}
\BOOKMARK [2][-]{subsection.6.2}{6.2. Bringing in spacetime}{section.6}
\BOOKMARK [2][-]{subsection.6.3}{6.3. Hamilton's equations and the conservation of energy}{section.6}
\BOOKMARK [2][-]{subsection.6.4}{6.4. Digression of the day: LIGO}{section.6}
\BOOKMARK [2][-]{subsection.6.5}{6.5. A look back at the special case t\(s\) = s}{section.6}
\BOOKMARK [1][-]{section.7}{7. Nov 14, 2006: From particles to strings and higher membranes}{}
\BOOKMARK [2][-]{subsection.7.1}{7.1. More derivations}{section.7}
\BOOKMARK [2][-]{subsection.7.2}{7.2. Generalizing the Lagrangian}{section.7}
\BOOKMARK [1][-]{section.8}{8. Nov 28, 2006: More on particles ``vs." membranes}{}
\BOOKMARK [2][-]{subsection.8.1}{8.1. \(Functorial\) construction of the multivelocity alternating tensor}{section.8}
\BOOKMARK [2][-]{subsection.8.2}{8.2. Volume forms}{section.8}
\BOOKMARK [2][-]{subsection.8.3}{8.3. The canonical p-form}{section.8}
\BOOKMARK [1][-]{section.9}{9. Dec 05, 2006: Phases and connections on bundles}{}
\BOOKMARK [2][-]{subsection.9.1}{9.1. When connections come in}{section.9}
\BOOKMARK [2][-]{subsection.9.2}{9.2. Phases and relative phases}{section.9}
\BOOKMARK [2][-]{subsection.9.3}{9.3. Example: Rigid rotor}{section.9}
\BOOKMARK [2][-]{subsection.9.4}{9.4. Integral cohomology and Max Planck}{section.9}