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

Books

• 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.
• Boas:
  Mathematical Methods in the Physical Sciences by Boas (John Wiley & Sons, 3rd Edition, 2005).
• Riley & Hobson:
  In addition to Riley, Hobson & Bence, there is a somewhat less daunting related book Foundation Mathematics for the Physical Sciences (CUP, 2011).

Java Applets

• 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.