Alan Sokal

Professor of Mathematics, University College London

Office: Maths Dept (UCL Union), Room 800

Office hours: MONDAYS 3-4 PM
E-mail: sokal@math.ucl.ac.uk

MATH0054: Analytical Dynamics, Spring 2024

• Syllabus

• Handout #1: Newton's First Law and the Principle of Relativity
• Handout #2: Newton's Second Law
• Handout #3: Newton's Third Law
• Handout #4: How to Do Mechanics Problems
• Handout #5: Solvable Cases of One-Dimensional Motion
• Handout #6: Momentum, Angular Momentum, and Energy; Conservation Laws
• What is energy?, Section 4-1 of Volume I of the Feynman Lectures on Physics
• Handout #7: More on Central-Force Motion
• Problem Set #1 (due 18 January)
• Problem Set #2 (due 29 January) NOW DUE AT BEGINNING OF AFTERNOON CLASS

• Handout #8: Coupled Oscillations and Normal Modes
• Handout #9: Introduction to Waves
• Problem Set #3 (due 8 February)

• Handout #10: Introduction to Perturbation Theory
• Problem Set #4 (due 19 February)

• Handout #11: The Lagrangian Approach to Mechanics 8 FEB 2024: I HAVE ADDED ADDITIONAL COMMENTS IN SECTIONS 1 AND 2
• Problem Set #5 (due 26 February)
• The principle of least action, Chapter 19 of Volume II of the Feynman Lectures on Physics
• Problem Set #6 (due 7 March)

• Gregory, Chapter 14
• Handout #12: The Hamiltonian Approach to Mechanics 5 MAR 2024: I HAVE ADDED EXAMPLE 2 ON P. 10    11 MAR 2024: I HAVE POINTED OUT A GAP IN EXAMPLE 2 ON P. 10; AND I HAVE ADDED A NEW SECTION 5 (PP. 14-18)    13 MAR 2024: I HAVE FIXED ANOTHER ERROR IN EXAMPLE 2 ON P. 10; COMPLETING THE PROOF IS STILL AN OPEN PROBLEM
• Problem Set #7 (due 18 March)

• Handout #13: Introduction to the Rotation Group

  
  PAST FINAL EXAMS:

• 2022 final exam
• 2023 final exam

MATH3103: Functional Analysis, Spring 2013

• Syllabus

• Handout #0: Review of Set Theory
• Handout #1: What is Functional Analysis?
• Problem Set #1
• Handout #2: Compactness of Metric Spaces
• Problem Set #2
• Handout #3: Introduction to Normed Linear Spaces
• Problem Set #3
• Handout #4: Introduction to Hilbert Space
• Problem Set #4
• Handout #5: Spaces of Continuous Functions
• Problem Set #5
• Handout #6: The Hahn-Banach Theorem and the Duality of Banach Spaces
• Problem Set #6
• Handout #7: The Baire Category Theorem and its Consequences
• Problem Set #7

Inaugural lecture, 10 March 2010

"Between combinatorics and analysis (with a little help from statistical physics)" (PDF file, 4 MB)