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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Classical Mechanics for Mathematicians (MATH10106)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 3 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryClassical mechanics deals with the mathematical description of the motion of bodies, or point-like objects. By understanding the forces that are exerted on a body we can construct Newton's equation that describes the motion of the object in question. There are however, other mathematical approaches to this class of problems, known as the Lagrangian and Hamiltonian descriptions of classical mechanics. This course will introduce these various perspectives, and in the process cover the subject of the calculus of variations. Furthermore this course is the first in a series of mathematical physics courses, such as Quantum Mechanics, Classical Field theory, Quantum Information, Geometry of General Relativity and Topics in Mathematical Physics A/B.
Course description This course is an introduction to the subject of classical mechanics. It will cover Newton's equation, the motion of point particles, including planetary motion, and an introduction to the notion of variational calculus for point particles. In particular the course will cover Hamilton's principle of least action, Lagrangians for systems with conservative forces, and Noether's theorem. The latter provides a conserved quantity whenever there exists a continuous symmetry. Finally, an introduction to the Hamiltonian formalism will be given which prepares the ground for the follow-up course on quantum mechanics for mathematicians. The classical mechanics for mathematicians course is a great opportunity to learn about many classical differential equations and physical problems that helped shape many developments in mathematics. It is also a nice arena to practise one's knowledge of several variable calculus and differential equations.

The course will include the following topics:

- Newton's equations for simple mechanical systems
- Celestial mechanics
- Lagrangians and Euler-Lagrange equations
- Noether's theorem and continuous symmetries
- Hamiltonians and Hamilton's equations
- Poisson brackets
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Honours Differential Equations (MATH10066)
Prohibited Combinations Students MUST NOT also be taking Lagrangian Dynamics (PHYS10015)
Other requirements None
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Academic year 2023/24, Available to all students (SV1) Quota:  None
Course Start Semester 2
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 18, Supervised Practical/Workshop/Studio Hours 5, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 73 )
Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Additional Information (Assessment) Coursework: 20%, Examination 80%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Solve Newton's equation for simple mechanical systems
  2. Construct Lagrangians for simple mechanical systems
  3. Compute conserved charges using Noether's theorem
  4. Construct Hamiltonians starting from a Lagrangian
  5. Compute with Poisson brackets
Reading List
The course will be based on lecture notes. Recommended in addition to materials provided:
- (*) Herbert Goldstein, Classical Mechanics
- (*) Landau and Lifshitz, Mechanics, Course of Theoretical Physics, Volume 1
- (*) Marion and Thornton, Classical Dynamics (of particles and systems)
¿- Arnold, Mathematical Methods of Classical Mechanics (chapters 1 to 3)
(*) are available to download from the University Library
Additional Information
Graduate Attributes and Skills Not entered
KeywordsCMech,Classical Mechanics,Lagrangians,Hamiltonians,Noether¿s theorem
Course organiserDr Timothy Adamo
Course secretaryMiss Greta Mazelyte
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