# wi4243AP-CA: Recorded lectures (2014)

## The lectures

Here are the recordings of the lectures of the course Complex Analysis
(part of Mathematical Methods for Physics), taught in the fall of 2014.
- 2014-09-05: Lecture (start at about 14:00),
slides
- Introduction to and refresher of the algebra and geometry of the complex numbers.
- 2014-09-08: Lecture,
slides
- More geometry, roots of unity, infinity and the Riemann sphere,
Moebius transformations
- 2014-09-12: Lecture,
slides
- Some topological notions, functions of a complex variable, differentiability
(complex versus real), the Cauchy-Riemann equations
- 2014-09-15: Lecture,
slides
- Analyticity, harmonic functions, exponential functions, trigonometric functions,
logarithmic functions
- 2014-09-19: Lecture,
slides
- Inverse trigonometric and hyperbolic functions, exponential and power functions,
branch points, branch cuts
- 2014-09-22: Lecture,
slides
- Complex integrals, a fundamental inequality, the theorem of Cauchy and Goursat
and some applications (independence of path, existence of primitives).
- 2014-09-26: Lecture,
slides
- The Fresnel integrals, Cauchy's integral formule and some applications:
infinite differentiabilty of analytic functions, Gauss' mean value theorem,
Liouville's theorem, Fundamental Theorem of Algebra, the Maximum Modulus theorem.
- 2014-09-29: Lecture,
slides
- Sequences and series of functions, uniform convergence, power series;
power series expansions of analytic functions

Here is a weblecture on power series
and the logarithm.
- 2014-10-03: Lecture, slides
- Laurent series for analytic functions, analytic continuation,
uniqueness results, singularties
- 2014-10-06: Lecture
- A question-and-answer session
- 2014-10-10: Lecture,
slides,
worksheet
- Residues and the Residue theorem; calculation of integrals using residues
- 2014-10-13: Lecture, slides
- More integrals, Fourier transforms using residues, Jordan's Lemma,
an example from PDE (Klein-Gordon), the Laplace transform and its
inversion formula
- 2014-10-17: Lecture,
slides
- Inversion of the Laplace transform, finishing up Green's function for the
Klein-Gordon equation, the Cauchy principal value of integrals
- 2014-10-20: Lecture,
slides
- A question
from the Wisfaq site,
my favourite formula,
another Laplace
inversion

## The exam

Here is the exam of 30-10-2014
## The text

The course uses
Applied Complex Variables for Scientists and Engineers by
Yue Kuen Kwok.
The numbering of the problems on the slides is as in the second edition,
for those who have the first edition: the problem pages from the second edition
can be found here.
## Exams

Here are the exams referred to during the lectures:
- First exam (2013-10-31)
- Resit (2014-01-22)

Many more recorded lecture can be found
here

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Last modified: Friday 02-02-2018 at 11:35:06 (CET)