MATH20512 Classical Mechanics

This page will contain links to the lecture notes and problem sheets for the 2nd year Classical Mechanics course. You will need your University username and password to download any of the linked PDFs.

The course syllabus can be found here.

Full set of notes (249 pages, 1.4MB) available for download here.


The coursework assignment is available to be downloaded here. Please hand in your completed assignments to reception by 1pm on Wednesday 18th April 2018 (week 9).

4th May 2018: The marks are now available on Blackboard, and the solutions are available to read here.

Lecture notes

I will add a link to printed notes corresponding to each lecture after that lecture has taken place. These notes will contain much the same material as the lecture, but will not be an exact copy. For that reason it is important that you take notes during the lecture as it is on these that you will be examined.

The original version of these notes was originally written by Dr James Montaldi; all credit goes to him. Please do let me know if you spot any inaccuracies or typos.

Complete lecture notes for each part (note the revision checklist at the end):
  • Part 1 (Newton’s Laws)
  • Part 2 (The Calculus of Variations)
  • Part 3 (Lagrange’s Equations)
  • Part 4 (Potential Wells & Oscillations)
  • Part 5 (Hamiltonian Mechanics)

Problem sheets

Change of format: I will henceforth be uploading question sheets for each of the five parts. The questions I expect you to be able to complete after each week's lectures will be indicated below. Solutions will also be uploaded by part, but each file will only include those questions attempted to date.

Questions that can be attempted after the lectures for that week (these are the ones for the following week's tutorial):
  • Week 1: (1.1)–(1.8)
  • Week 2: (1.9)–(1.14)
  • Week 3: (1.15)–(1.16) and (2.1)–(2.4)
  • Week 4: (2.5)–(2.9)
  • Week 5: (2.10)–(2.12) and (3.1)–(3.2)
  • Week 6: (3.3)–(3.7)
  • Week 7: (3.8)–(3.13)
  • Week 8: (4.1)–(4.5)
  • Week 9: (4.6)–(4.12)
  • Week 10: (5.1)–(5.7)
  • Week 11: (5.8)–(5.13)

Past papers

The 2015, 2016, and 2017 past papers for this module can be found through the university's Past Exams site. Simply search for MATH20512 to get the links. Note that rotating frames are no longer on the syllabus (i.e. question A5 on the 2015 and 2016 papers).

Important topics

These will be used again and again in the course, so make sure you’re familiar with them:

  • vectors, vector products,
  • line, surface, and volume integration,
  • vector calculus (div, grad, curl),
  • Taylor’s theorem,
  • partial derivatives,
  • linear algebra, especially eigenvalues/eigenvectors.


There are two textbooks recommended for this course. They cover a lot more of the subject than we do in lectures, but they do offer further information about the concepts we discuss, and some examples of how they are used.

  • T.W.B. Kibble and F.H. Berkshire. Classical Mechanics. Imperial College Press.
  • R.D. Gregory. Classical Mechanics. Cambridge University Press.

Copies are available by searching the library catalog, or the Gregory book is available for reading online (requires university username and password: choose Shibboleth login with the University of Manchester as your institution).


Tutorials will provide an opportunity for your work to be discussed, and to provide feedback on your understanding. The coursework assignment will also provide an opportunity for you to receive feedback. You can also get feedback on your understanding of the work directly from me — please come and see me in my office hour (see “Contact details” below) or send me an email with a question, which I will do my best to answer.

Thanks for your feedback forms from week 3. I have uploaded a summary and a response for you to read at your convenience.

Contact details

My office hours are 10:00–11:00 on Thursdays. If you cannot make this time please feel free to contact me to arrange a meeting.