Math 428/513: Mathematical Classical Mechanics

This course is a PIMS Network Course and is also open to the public

Spring Term 2027

General Information

Office: MATX 1112, 604-827-3031
Email: lior@math.ubc.ca; please include the course number in the subject line, if applicable.
Office hours (AY 2025-2026): by appointment (I'm on sabbatical)

Classes: TTh 11-12:30 at ESB 4127 and on Zoom – see schedule below.
Syllabus (PDF)
(Rough) lecture notes (PDF)
There is a Piazza discussion board; contact the instructor for the sign-up link.

This course presents classical mechanics to a mixed audience of mathematics and physics undergraduate and graduate students. It is complementary to regular phsyics courses in that while the physics concepts will be developed the emphasis will be on the underlying mathematical analysis. Students should already have some experience with rigorous mathematics (at UBC via courses like MATH 131, 320, 321), and with classical mechanics (at UBC via courses like PHYS 216). Pre-requisites can be waived: contact the instructor if you wish to discuss this.

This is a PIMS Network Course; students at Canadian PIMS member universities can register for credit via the Western Dean's Agreement (see the PIMS page for details).

In addition anyone in the world is welcome to join the Zoom sessions and learn. The course is truly open to anoyne interested in mathematics. In general the instructor will only mark the homework of registered students, but in compelling situations arrangements can be made for students in any university: have your advisor contact me on your behalf.

References

Arnol'd, Mathematical Methods of Classical Mechanics, available from SpringerLink
Cushman & Bates, Global Aspects of Classical Integrable Systems, available from SpringerLink
Giaquinta & Hildebrandt, Calculus of Variations, available from SpringerLink
Goldstein, Classical Mechanics
Landau & Lifshitz, Course of Theoretical Physics vol. 1: Mechanics
Spivak, Physics for mathematicians—mechanics I

Problem Sets

Problem sets are due at 11:00 Vancouver time (start of class) on the date indicated. Please submit typeset solutions as PDF files, either on Canvas or by email. In the second case the subject line must be: "MATH 428/513 PSxx submission" where xx is the number of the problem set.
- The source files for the problem sets rely on my macro file. Feel free to use it for your submissions as well.
We will figure out how to distribute solutions.

Lecture-by-Lecture information

Warning: the following information is tentative and subject to change at any time

Chapter	Week	Date	Material
Newtonian Mechanics	1	T 5/1	Introduction; Dynamics Differential Equations
	1	Þ 7/1	The Galilean Group Conservation Laws
	2	T 12/1	Examples
Kinematics	2	T 7/1	Configuration space
Kinematics	3	Þ 19/1	Coordinates Tangent vectors
Lagrangian Mechanics	3	Þ 21/1	Calculus of Variations
	4	T 26/1	"Direct" appraoch Sobolev spaces
	4	Þ 28/1	Examples
	5	T 2/2	Small Oscillations
	5	Þ 4/2	Constraints
	6	T 9/2	Symmetry
	6	Þ 11/2	Angular momentum
	Feb 17-21		UBC Winter break
	7	T 23/2	Rigid Body Motion
Hamiltonian Mechanics	7	Þ 25/2	Convex Geometry The Legendre transformation
	8	T 2/3	Symplectic Geometry The Hamiltonian Flow
	8	Þ 4/3	Dynamics
	9	T 16/3	Thermodynamics ensembles
	9	Þ 18/3	Integrable Systems Hamilton--Jacobi
Quantum Mechanics	10	T 23/3	Introduction
	10	Þ 25/3	Fourier Transform Pseudodifferential calculus
	11	T 31/3	Quantization Egorov's Theorem
	11	Þ 1/4	WKB QUE
	12	T 6/4	Review
	12	Þ 8/4	Review
Final exam		F 25/4	8:30-11:30 @ BUCH B318

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Last modified Saturday July 25, 2026