A geometric view of classical physics (MAGIC024) |
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 GeneralDescription
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 R^{n}.) Similarly, it is more useful to treat 3-dimensional space or 4-dimensional 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. SemesterSpring 2010 (Monday, January 11 to Friday, March 19) Timetable
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
Students
Bibliography
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.) AssessmentNo assessment information is available yet.
No assignments have been set for this course. FilesFiles marked L are intended to be displayed on the main screen during lectures. Recorded LecturesPlease log in to view lecture recordings. |