Click here
for the Department's AMV module page
and here
for duo.
-
Suggested books for the course:
-
Riley,
Hobson and Bence,
Mathematical Methods for Physics and Engineering, CUP 2006
(ISBN 9780521679718).
-
Salas, Hille and Etgen,
Calculus in One and Several Variables, Wiley 2007 (ISBN 9780471698043).
-
Boas,
Mathematical Methods in the Physical Sciences, Wiley 2005 (ISBN
9780471365808).
- Kreyszig,
Advanced Engineering Mathematics, Wiley 1988 (ISBN 0471627879).
-
The notations used in vector calculus date back to the 19th
century, and the works of
Hamilton,
Tait,
Maxwell,
Gibbs
and Heaviside
(mugshots below).
See
here
for some
discussion of the origin of the nabla (∇) symbol, and here
for James Clerk Maxwell's 1871 paper where he suggests the word
'curl'.
-
In the unlikely event that
you're finding index notation a bit too easy, or just to reassure
yourself that things might be even worse, you can have a look
at Penrose
graphical notation, a.k.a. birdtrack diagrams (or
fornicating
ostriches). Birdtrack diagrams will not be in the exam! For abstruse goose's
not-totally-serious take on these notational issues, see
here,
here, and finally
here (but not if you're
offended by strong language).
-
The (rather brief) entry
in mathworld
about the summation convention
contains a quote from Einstein about his invention.
-
There's a discussion of multidimensional differentiability at mathinsight.org
including some nice animated illustrations
(which need Java, unfortunately).
-
Some nice pictures of three-dimensional
level sets and their singularities
can be found here.
-
To hear Will Self trying to get to grips with some bits of vector
calculus, see (or rather hear) around 4:10 here.
-
Click here
to see a Mexican hat.
-
Stokes' theorem was set as a question in the 1854 Smith's prize exam
which was taken by Maxwell. It had been pointed out
to Stokes by Kelvin in a
postscript to a letter dated July 2,
1850; this is why it is sometimes called the
Kelvin-Stokes theorem.
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