Links for NST IB Physics A/B ‘Mathematical Methods’ 2025
Handouts |
Corrections |
Additions |
Resources |
Books/Formula Handbook
16 lectures, Michaelmas term, Friday and Monday, 10:00am, in Titan
Teaching Room 3, Cockcroft Building, New Museums Site (see this
map; use the entrance on the north side of the Cockcroft Building, in
the corner adjacent to the Austin Building). This room is not well
signposted, but follow the signs for Titan Teaching Room 1 instead
(upstairs on the 2nd floor) which will get you there, as it is next door.
The handouts and problem sheets for this course are
available from the course
page on the Cavendish Teaching Information System
(TiS) website, for registered users. (Spare copies will be put in
the filing cabinet in the corridor outside the IA/IB Practical
Laboratories.)
- Handout I, p1: in the note in the middle of the
page, ‘includedœ’ should just be ‘included’.
- Handout I, p2/3: a sketch to
illustrate why for the Fourier series of a square wave the amplitudes
of even values $n$ are zero (in this case for $n=2$).
- Handout I, p16: explanation of a 1-D Diffusion
equation (in terms of temperature/heat) (cf. 2.42).
- Handout I, p18: an justification
for equation 2.58.
- Handout I, p19: Fourier transform of cosine (and sine), to show symmetries
between $f(t)$ and $F(\omega)$.
- Handout I, p19. Section 2.7: using convolution (and Fourier
transforms) to explain the Borwein
integrals.
- Handout I, p20/21, Section 2.8: Fourier transforms of
multiple $\delta$ functions.
- Handout I, p22: the algebra
required to go from equation 2.93
and 2.94 to 2.95.
- Handout II, p14: alternative ways of writing curl in cylindrical
polar coordinates.
- Handout II, p15/16: a graph
for the example showing the stationary points for distance from the origin
with the constraint $y=1-x^2$.
- Handout III, p11/12: showing in a bit more detail how to derive equations 7.17 and 7.19
to 7.21
from 7.16.
- Handout III, p26: a visualisation
of low order spherical harmonics, and alternate ways of writing spherical
harmonics, to obtain $s, p, d$ orbitals
as used in chemistry.
- Convolution: a webpage
that illustrates the convolution of two functions with an animation,
which has a choice of various functions. Note, you can interactively
change the width of the functions before starting the convolution
animation by click on the dot in the plot of a function, and drag to
change.
- Zernike polynomials: here
is a visualisation of Zernike polynomials, which are orthogonal over a
unit circle. The left plot of each is the phase variation over the
circle, e.g. a lens, and the right plot shows the distortion in the
image from a lens due to such a phase variation. These are used to
characterise aberrations for optical instruments (hence the names).
- Waves (Bessel functions): webpage
visualising of waves on a circular membrane,
which is Q24.
(This is from this
website, which has
other useful visualising of various maths/physics, including
the links below for ‘Normal Modes’.)
- Spherical Harmonics: visualisations of spherical
harmonics (here used as the basis set to describe the
gravitational field/geoid (i.e. equipotential surface) of the
Earth).
- Normal Modes: webpages that visualise normal
modes for 1-D motion of multiple masses
coupled by springs,
and sideways oscillations of masses on a
string.
There are many books that cover the material in this course,
including the following.
- ‘Mathematical Methods in the Physical Sciences’,
by Boas M L (3rd edition, Wiley 2006).
- ‘Mathematical
Methods for Physics and Engineering’, by Riley, Hobson &
Bence (3rd edition, CUP 2006).
(This covers many more
advanced topics also. As this is published by CUP you can read this online.
Also available is the earlier
2nd edition, where
chapters are available in .pdf format.)
The ‘Mathematical Formula Handbook’ –
which is provided
in NST Physics examinations – is available
here (version 2.6), or on the
Cavendish Undergraduate
Intranet website.
Also you can purchase a copy for £1.50 from Mr Richard King,
in the Part IA practical laboratory.
Dave Green –
(last changed 2025 December 1st)
