Math 428/609E: Mathematical Classical Mechanics

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

Spring Term 2025

General Information

Office: MATX 1112, 604-827-3031
Email: "lior" (at) Math.UBC.CA (please include the course number in the subject line, if applicable)
Office hours (Winter 2025):

Time Location Zoom Meeting ID Zoom Password
TTh 12:30-13:00 ESB 4127 and on Zoom 684 2674 1683 101671

F 10:30-11:30 My office and on Zoom

Time	Location	Zoom Meeting ID	Zoom Password
TTh 12:30-13:00	ESB 4127 and on Zoom	684 2674 1683	101671
F 10:30-11:30	My office and on Zoom

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 223, 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.

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 428/609 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.

Problem Set 1 (LyX, TeX), due 16/1/2025. Note: problem F(c) fixed in PDF version.
Problem Set 2 due 30/1/2025. Version updated.
Problem Set 3 due 30/1/2025. Version updated.
Problem Set 4

Lecture-by-Lecture information

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

Chapter	Week	Date	Material	In-class	Notes
Kinematics	1	T 7/1	Introduction Configuration space	Scan
Kinematics	1	Þ 9/1	Coordinates Tangent vectors	Scan
Newtonian Mechanics	2	T 14/1	Dynamics Differential Equations	Scan
	2	Þ 16/1	The Galilean Group Conservation Laws	Scan	PS1 due
	3	T 21/1	Examples	Scan
Lagrangian Mechanics	3	Þ 23/1	Calculus of Variations	Scan
	4	T 28/1	"Direct" appraoch Sobolev spaces	Scan
	4	Þ 30/1	Examples	Scan
	5	T 4/2	Constraints	Scan
	5	Þ 6/2	Symmetry	Scan
	6	T 11/2	Angular momentum	Scan
	6	Þ 13/2	Small Oscillations	Scan
	Feb 17-21		UBC Winter break
	7	T 25/2	Rigid Body Motion	Scan
Hamiltonian Mechanics	7	Þ 27/2	Convex Geometry The Legendre transformation	Scan
	8	T 4/3	Symplectic Geometry The Hamiltonian Flow	Scan
	8	Þ 6/3	Dynamics	Scan
	9	T 18/3	Thermodynamics ensembles	Scan
	9	Þ 20/3	Integrable Systems Hamilton--Jacobi	Scan
Quantum Mechanics	10	T 25/3	Introduction	Scan
	10	Þ 27/3	Fourier Transform Pseudodifferential calculus	Scan
	11	T 1/4	Quantization Egorov's Theorem	Scan
	11	Þ 3/4	WKB QUE	Scan
	13	T 8/4	Review
Final exam		F 25/4	8:30-11:30 @ BUCH B318

Back to my homepage.

Clarification: the writings on these pages are generally my own creations (to which I own the copyright), and are made available for traditional academic reuse. If you wish to republish substantial portions (including in "derivative works") please ask me for permission. The material is expressly excluded from the terms of UBC Policy 81.

Last modified Tuesday April 15, 2025