Part II Further Complex Methods
Handouts and examples sheets (pdf format)
Example Sheets
Examples sheet 1
Examples sheet 2
Examples sheet 3
Examples sheet 4
Revision examples sheet
NEW: solution to harmonic plot question on sheet 2
Handouts
Plan of the course (Lecture 1)
Recommended books (not handed out)
Functions defined by integrals (Lecture 3)
Analytic continuation by contour deformation (Lecture 4)
Integration using a branch cut (not handed out: covered in Lecture 6)
The arcsin as an integral (Lecture 6)
Cauchy Principle Value (Lecture 7)
Causality using harmonic response plot (Lecture 8)
Waves on a string (Lecture 9)
The wave equation with source (Lecture 10)
The Airy equation (Lecture 11
The Hermite equation (Lecture 12)
and
video in windows media format
(There is a mistake at 8:54 - I said `If the real part of nu is negative'; I should have said `If the real part of nu is less than minus one'.)
*Product formulae for the Gamma function* (Lecture 13)
The Hankel representation for the Gamma function (Lecture 14)
Wielandt's theorem (Lecture (15)
*Prime number formula for the Gamma function* (Lecture (16)
Proof of the functional equation for the zeta function (Lecture 17)
Solution of de's by series (Lecture (18)
*Obtaining the log solution via the Wronskian* (Lecture 19)
The Papperitz equation (Lecture 20)
The Legendre equation (Lecture 22)
The hypergeometric equation: second solution and solution near infinity (Lecture 23)