Mathematical Classical Mechanics
Prerequisites:
This course is intended to complement classical mechanics
courses like Physics 206 in the sense that the physical background
will be developed but the emphasis will be on the resulting mathematical
analysis. Students should already have some experience with rigorous mathematics
(like Math 320 and 321) and with classical mechanics (like Physics 206)
although these prerequisites may be waived at the discretion of the instructor.
Instructor
Joel Feldman
Text

V. I. Arnold, Mathematical Methods of Classical Mechanics,
I will post all handouts, problem sets, etc. on the web
here.
Other References

G. Gallavotti, The Elements of Mechanics.

H. Goldstein, Classical Mechanics.
Topics

Newtonian Mechanics:
The principles of relativity and determinacy, the gallilean group,
Newton's equations
Examples: the harmonic oscillator, pendulum and central fields
An introduction to phase space, conservation of energy, momentum and
angular momentum

Constraint Free Lagrangian Mechanics:
Variational problems and the EulerLagrange equation
The lagrangian and Hamilton's principle of least action
The hamiltonian and Hamilton's equations
Liouville's theorem
Poincaré recurrence theorem

Lagrangian Mechanics on Manifolds:
The introduction of manifolds through constraints
Differentiable manifolds and tangent bundles
Lagrangian dynamics
Symmetry and Conservation laws: Noether's theorem

Differential Forms:
Exterior algebra, differential forms on manifolds, exterior
differentiation, vector analysis
Chains, integration of differential forms
Stokes' theorem
Poincaré lemma
Grading

There will be weekly problem sets accounting for about 50% of the final mark.

The final exam will account for about 50% of the final mark.

Grades will probably be scaled.
Policies

The final examination will be strictly
closed book: no formula sheets or calculators will be allowed.

There is no supplemental examination in this course.

Late homework assignments normally receive a grade of 0.
Missing a homework normally results in a mark of 0.
Exceptions may be granted in two cases: prior consent of the instructor
or a medical emergency.