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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.


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

Many more recorded lecture can be found here
Last modified: Friday 02-02-2018 at 11:35:06 (CET)