Relativity
| Code | School | Level | Credits | Semesters |
| MATH3018 | Mathematical Sciences | 3 | 20 | Spring UK |
- Code
- MATH3018
- School
- Mathematical Sciences
- Level
- 3
- Credits
- 20
- Semesters
- Spring UK
Summary
The course is an introduction to Einstein's theory of special and general relativity. When velocities are a significant fraction of the speed of light, the concepts of spatial distance and elapsed time need to be modified; they become relative to the observer. In this course the relativistic laws of mechanics are described in a unified framework of space and time and some implications, such as Einsteins famous equation E=mc2, are explained. Gravitational effects require that space-time is warped or curved. The relevant mathematical machinery to describe this curvature is introduced and is used to discuss its physical effects. Topics covered:
- Lorentz transformations.
- Minkowski space.
- Relativistic particle mechanics.
- Special relativity continuum mechanics.
- Elementary differential geometry.
- Newtonian gravitation.
- General relativity.
- Einstein field equations.
- Examples of spacetimes, including Schwarzschild geometry.
Target Students
Single and Joint Honours students from the School of Mathematical Sciences and Mathematical Physics students. Available to Natural Sciences students.
Assessment
- 100% Exam 1 (3-hour): Written examination
Assessed by end of spring semester
Educational Aims
The aim of thecourse is to give the student a sound and modern understanding of the mathematics and physical principles of special and general relativity at an introductory level. Thecourse will include a comparison to the previous framework of Newtonian physics, and also explain the new phenomena which occur in relativity. The module is also a preparation for students that choose to study later more advanced topics in relativity such as black holes.Learning Outcomes
A student who completes this course successfully will be able to:
L1 - derive results and solve problems in the special theory of relativity, and use these to demonstrate its relationship to Newtonian mechanics;
L2 - state and apply relevant concepts of differential geometry;
L3 - solve problems in tensor calculus and apply it to calculations in general relativity;
L4 - derive results and solve problems describing the main observed phenomena of general relativity using the appropriate theoretical concepts;
L5 - derive results and solve problems comparing the descriptions of gravitational phenomena in Newtonian gravity and general relativity.