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Semester 2
Classical Mechanics for Mathematicians (MATH10106)
Subject
Mathematics
College
SCE
Credits
10
Normal Year Taken
3
Delivery Session Year
2023/2024
Pre-requisites
Course Summary
Classical 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
Assessment Information
Written Exam 80%, Coursework 20%, Practical Exam 0%
Additional Assessment Information
Coursework: 20%, Examination 80%
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