Mathematics 428/609D, Section 101

Mathematical Classical Mechanics

Department of Mathematics University of British Columbia

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.


Joel Feldman

 Office  Math 221
 Phone  822-5660
 Home page
 Office hours  Mon 10:00-11:00, Wed 10:00-11:00, Fri 10:00-11:00


I will post all handouts, problem sets, etc. on the web here.

Other References


  1. 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
  2. Constraint Free Lagrangian Mechanics:
         Variational problems and the Euler-Lagrange equation
         The lagrangian and Hamilton's principle of least action
         The hamiltonian and Hamilton's equations
         Liouville's theorem
         Poincaré recurrence theorem
  3. Lagrangian Mechanics on Manifolds:
         The introduction of manifolds through constraints
         Differentiable manifolds and tangent bundles
         Lagrangian dynamics
         Symmetry and Conservation laws: Noether's theorem
  4. Differential Forms:
         Exterior algebra, differential forms on manifolds, exterior differentiation, vector analysis
         Chains, integration of differential forms
         Stokes' theorem
         Poincaré lemma