Theoretical Physics: Classical Mechanics and Special Relativity

In this course, you will learn how to use symmetries to analyse mechanical systems. You will learn to reformulate Newtonian mechanics into Lagrangian and Hamiltonian mechanics. The path there goes via the principle of least action and calculus of variations. Through this reformulation of ordinary mechanics, the role of symmetries suddenly becomes clear. Noether’s theorem states that for every continuous symmetry there is a conserved quantity. Conservation of momentum, energy, and angular momentum can be derived from symmetries.

The second part of the course deals with special relativity theory. Here you will gain tools for understanding spacetime, Lorentz transformations, and relativistic kinematics—important concepts in modern physics.

The course provides a solid foundation for further studies in physics, or related fields. It is particularly relevant if you want to continue with general relativity, particle physics, quantum field theory, or more advanced classical mechanics. The course can be included in a programme, but it can also be studied as a free-standing course.

The course covers:

• Lagrange formalism: principle of least action, Euler-Lagrange equations, conservation laws, and generalized coordinates
• Introduction to Hamilton formalism
• Constraints and Lagrange multipliers
• Two-body problem and Kepler's laws
• Lorentz transformations
• Four-vectors and relativistic kinematics

The teaching consists of lectures and problem-solving sessions where you practice solving problems and understanding the underlying theory. You also work on mandatory written assignments that help you deepen your knowledge step by step.

A project is included in which you present a modern application of classical mechanics or relativity. You will also give feedback on another student’s presentation, which trains your ability to evaluate and communicate physical reasoning.

The course ends with a written exam that tests the entire course content. All parts of the course are mandatory in order to receive a final grade.

Prerequisites

General eligibility, English proficiency corresponding to English 6/B from Swedish upper secondary school, and 30 ECTS credits in physics and 45 ECTS credits in mathematics, including knowledge corresponding to: FYSA12 Introduction to University Physics, with Mechanics and Electricity, 15 credits, NUMA01 Computational Programming with Python, 7.5 credits, MATB21 Analysis in Several Variables 1, 7.5 credits, and MATB22 Linear algebra 2, 7.5 credits, alternatively 75 ECTS credits in mathematics, including knowledge corresponding to: NUMA01 Computational Programming with Python, 7.5 credits, MATB21 Analysis in Several Variables 1, 7.5 credits, MATB22 Linear algebra 2, 7.5 credits, MATB23 Analysis in Several Variables 2, 7.5 credits, and MATB24 Linear Analysis, 7.5 credits.

Selection criteria

Seats are allocated according to: The general average (GPA) of your higher secondary school leaving certificate: 20 %, The Swedish national university aptitude test: 10 %, number of previous ECTS at application deadline (up to 165): 70 %.

Tuition fees for non-EU/EEA citizens

Citizens of countries outside:

• The European Union (EU)
• The European Economic Area (EEA) and
• Switzerland

are required to pay tuition fees. You pay an instalment of the tuition fee in advance of each
semester.

Tuition fees, payments and exemptions

Full programme/course tuition fee: SEK 23,125
First payment: SEK 23,125

Convert currency – xe.com

Note that you may also need to pay an application fee, or provide proof of exemption.

Application fee

No tuition fees for citizens of the EU, EEA and Switzerland

There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.