Links for NST IB Physics A/B ‘Mathematical Methods’ 2024
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.
(This room is not well signposted, and is not included on the University
online map. Follow the signs for Titan Teaching Room 1 instead, which will get you there.)
The handouts and problem sheets for this course are
available from the
course
page of the Cavendish Teaching
Information System (TiS) website, for registered users. (Spare
copies are in the filing cabinet in the corridor outside the IB
Practical Laboratory.)
- Handout II, p13: just before Section 5.2, ‘reciprocols’ should be
‘reciprocals’.
- Handout II, p14: after equation 5.24, there
is a space missing and it should read ‘To simplify…’
- Handout IV. p15: the text just before 11.5
should refer to 11.3 (not 11.1).
Here are links to some additional material presented in the lectures.
- Handout I, p14: alternative ways of writing curl in cylindrical
polar coordinates.
- Handout I, p15/16: a graph
for the example showing the stationary points for distance from the origin
with the constraint $y=1-x^2$.
- Handout II, 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 II, p18: an explanation
for equation 5.58.
- Handout II, p18/19: Fourier transform of cosine (and sine), to show symmetries
between $f(t)$ and $F(\omega)$.
- Handout II, p19. Section 5.7: using convolution (and Fourier
transforms) to explain the Borwein
integrals.
- Handout II, p20/21, Section 5.8: Fourier transforms of
multiple $\delta$ functions.
- Handout II, p22: the algebra
required to go from equation 5.93
and 5.94 to 5.95.
- Handout III, p11/12: showing in a bit more detail how to derive equations 7.16, 7.19,
7.20 and 7.21.
- 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.
- 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’.)
- 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).
- 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 website.
Also you can purchase a copy for £1.50 from Mr Richard King,
in the Part IA practical laboratory.
Dave Green –
(last changed 2024 November)
