Course details
Semester
 Autumn 2007
 Monday, October 8th to Friday, December 14th
Hours
 Live lecture hours
 20
 Recorded lecture hours
 0
 Total advised study hours
 0
Timetable
 Wednesdays
 09:05  09:55
 Thursdays
 13:05  13:55
Announcements
I have uploaded scanned model answers to the exercises for lectures 1 and 2 as pdf.
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 3dimensional space of our experience and of Newtonian physics, or they could live in the the 4dimensional 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 (3dimensional, in this case) manifold. (As you will learn, a manifold is, roughly speaking, a space that is locally like R^{n}.) Similarly, it is more useful to treat 3dimensional space or 4dimensional spacetime as manifolds, rather than as vector spaces R^{3} or R^{4}.
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.
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 3dimensional space of our experience and of Newtonian physics, or they could live in the the 4dimensional 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 (3dimensional, in this case) manifold. (As you will learn, a manifold is, roughly speaking, a space that is locally like R^{n}.) Similarly, it is more useful to treat 3dimensional space or 4dimensional spacetime as manifolds, rather than as vector spaces R^{3} or R^{4}.
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.
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

CG
Dr Carsten Gundlach
 University
 University of Southampton
Bibliography
No bibliography has been specified for this course.
Assessment
Attention needed
Assessment information will be available nearer the time.
Lectures
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