## Announcements

Welcome to MAGIC024! Today (8 Jan) I have posted two phorum topics (course format and course content), and I have uploaded the 2007/08 course overview and 2007/08 lecture notes. Do not print the complete lecture notes, as they will change. Please read the phorum posts and reply!
Carsten

Forum

## General

#### Description

Theoretical physics is dominated by partial differential equations such as the Euler equation, which you have probably seen written out in Cartesian coordinates. But what form does it take in spherical polar coordinates? Or in an arbitrary coordinate system? What if space (or spacetime) is curved, as general relativity tells us it is?

A fundamental idea of modern physics is that all its laws should be geometric in nature, that is they should be relations between geometric quantities such as a velocity vector field, independent of the coordinates used to describe this object. These objects could live in the 3-dimensional space of our experience and of Newtonian physics, or they could live in the the 4-dimensional spacetime of relativistic physics.

A more abstract example is the state of a gas in thermodynamical equilibrium. Its state is fixed by any three of the following properties: its volume, pressure, temperature, internal energy, entropy, chemical potential. All remaining properties can then be treated as functions of the selected three. A lot of the mathematical difficulty in elementary thermodynamics can be avoided by treating the space of all equilibrium states as a (3-dimensional, in this case) manifold. (As you will learn, a manifold is, roughly speaking, a space that is locally like Rn.) Similarly, it is more useful to treat 3-dimensional space or 4-dimensional spacetime as manifolds, rather than as vector spaces R3 or R4.

This course will teach you all the core mathematical concepts you need for writing physical laws in geometric form first, and only then use them to introduce a few selected areas of physics where a geometric view is either essential, or really makes things easier.

#### Semester

Spring 2010 (Monday, January 11 to Friday, March 19)

#### Timetable

• Mon 12:05 - 12:55
• Fri 09:05 - 09:55

#### Prerequisites

Undergraduate calculus, in particular integration in several variables. Undergraduate linear algebra, in particular abstract vector spaces. Vector calculus would be useful but is not essential.

#### Syllabus

• Differential geometry (6 lectures)
• Special relativity and Electrodynamics (5 lectures)
• Thermodynamics (3 lectures)
• Fluids (4 lectures)
• General relativity (2 lectures)

## Lecturer

 Email cjg@soton.ac.uk Phone 023 8059 5116

## Students

 Lamia ALQAHTANI (Leeds) Andrew Bailey (Birmingham) Jack Campbell (Exeter) Sam Dolan (Southampton) Matt Ferguson (York) Michael Hogg (Southampton) Muhammad Anjum Javed (Newcastle) Lucy Keer (Southampton) Carl Kent (Sheffield) Yi-Ping Lo (Loughborough) Paul Mackay (Newcastle) Niels Warburton (Southampton)

## Bibliography

 General relativity Wald Geometrical methods of mathematical physics Schutz Ph 136 Applications of Classical Physics Roger Blandford and Kip Thorne

Note:

Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.)

## Assessment

No assessment information is available yet.

No assignments have been set for this course.

## Files

Files marked L are intended to be displayed on the main screen during lectures.

Week(s) magic024_exercises1.pdf magic024_exercises10.pdf magic024_exercises11.pdf magic024_exercises12.pdf magic024_exercises13.pdf magic024_exercises14.pdf magic024_exercises15.pdf magic024_exercises17.pdf magic024_exercises18.pdf magic024_exercises19.pdf magic024_exercises2.pdf magic024_exercises20.pdf magic024_exercises3.pdf magic024_exercises4.pdf magic024_exercises5.pdf magic024_exercises6.pdf magic024_exercises7.pdf magic024_exercises8.pdf magic024_exercises9.pdf magic024_lecturenotes_0910.pdf magic024_overview.pdf MAGIC024_slides_1.pdf MAGIC024_slides_10.pdf MAGIC024_slides_11.pdf MAGIC024_slides_12.pdf MAGIC024_slides_13.pdf MAGIC024_slides_14.pdf MAGIC024_slides_15.pdf MAGIC024_slides_16.pdf MAGIC024_slides_17.pdf MAGIC024_slides_19.pdf MAGIC024_slides_2.pdf MAGIC024_slides_20.pdf MAGIC024_slides_3.pdf MAGIC024_slides_4.pdf MAGIC024_slides_5.pdf MAGIC024_slides_6.pdf MAGIC024_slides_7.pdf MAGIC024_slides_8.pdf MAGIC024_slides_9.pdf