Links for NST IB Physics A & B `Mathematical Methods'

Books

There are many books suitable for this course, including the following.

Riley, Hobson & Bence: Mathematical Methods for Physics and Engineering: A Comprehensive Guide (CUP, 3rd Edition, 2006).

From cam.ac.uk machines, this can be accessed as an eBook.

Riley & Hobson: in addition to Riley, Hobson & Bence, there is a somewhat less daunting related book Foundation Mathematics for the Physical Sciences (CUP, 2011).

Boas: Mathematical Methods in the Physical Sciences by Boas (John Wiley & Sons, 3rd Edition, 2005).

Java applets that illustrate aspects of the course material.

Fourier series (with various examples).
Convolution: either here or here (or I am sure there are others that you could search for).
Spherical Harmonics:
- the Solar photospheric magnetic field reconstructed with spherical harmonics;
- visualisation in terms of a gravitational distortion to the suface gravity of the Earth.
  (The background picture is an optical image of the Crab Nebula, which is the remains of a star that was seen to explode as a Supernova in AD 1054, see: this, or this.)
Normal modes:
- transverse waves on weighted string;
- longitudanal waves for masses connected by springs;
- waves on a square membrane;
- waves on a circular membrane.

Also see this site for other useful Java applets for visualising various maths/physics.

Dave Green -- dag@mrao.cam.ac.uk (October 2012)