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Om kursen

Kursens syfte är att ge den matematikintresserade teknologen möjlighet att utvidga sina kunskaper i en gren av matematiken som är relevant för tillämpningar eller modern forskning.

Kursplan - läsperiod - litteraturlista LTH.se

Spring 2024

During the second half of the spring semester 2024, the course FMAN90 Advanced Course in a Selected Area of Mathematics, 7.5 Credits, will be given by Erik Andreas Martens (email erik.martens@math.lth.se).

The subject is Advanced Dynamical Systems --- Applications and Methods in Science/Engineering, including topics in Neuroscience. The course could be seen as a continuation of FMAN15 Nonlinear Dynamical Systems (though, not all parts are strictly required). (The course may complement FMAN01 Biomathematics, but this course is not a pre-requisite.)

Elements may include: foundations of dynamical systems (brief repetition), nonlinear oscillations / limit cycles, introduction to bifurcation theory, numerical continuation of fixed points and detection of bifurcations, regular perturbation methods (incl. averaging). Phase oscillator models, dimensional reduction methods. Elements of network theory. Basic dynamical models of neurons / intro to neuroscience.

The course will be based on selected chapters from a combination of sources, such as:

1. Lecture notes on Advanced Dynamical Systems Applications and Methods in Science and Engineering, P.G. Hjorth, E.A. Martens, M.P.Sørensen, U.H. Thygesen
2. Richard H. Rand, Lecture notes on Nonlinear Vibrations, https://hdl.handle.net/1813/28989
3. John H. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, https://link.springer.com/book/10.1007/978-1-4612-1140-2
4. Mathematical Neuroscience (book to be determined)

The precise literature list may be subject to few changes. Further details will follow.

The examination will most likely consist of a take home exam (OR a project, to be determined), followed by an oral exam.

(Contact your programme coordinator (programplanerare) if you want to take the course, and it is not listed in Studentportalen.)

Spring 2023

During the second half of the spring semester 2023, the course FMAN90 Advanced Course in a Selected Area of Mathematics, 7.5 Credits, will be given by Jacob Stordal Christiansen (email Jacob_Stordal.Christiansen@math.lth.se).

The subject is complex analysis, so the course could be seen as a continuation of FMAF01 Function Theory.

The course will be based on chapters 5—8 of the book

Murali Rao et al, Complex analysis. An invitation.

Second edition. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2015. x+414 pp. ISBN: 978-981-4579-59-9

More precisely:

Chapter 8. The Riemann Mapping Theorem
Chapter 7. Picard’s Theorem
Chapter 10. Infinite Products and Factorization Theorems
Chapter 9. Runge’s Theorem
Chapter 5. The Global Cauchy Theorem.

The examination will most likely consist of a take home exam followed by an oral exam.

(Contact your programme coordinator (programplanerare) if you want to take the course, and it is not listed in Studentportalen.)