Course details
Semester
- Autumn 2024
- Monday, October 7th to Friday, December 13th
Hours
- Live lecture hours
- 20
- Recorded lecture hours
- 0
- Total advised study hours
- 80
Timetable
- Tuesdays
- 15:05 - 15:55 (UK)
- Wednesdays
- 15:05 - 15:55 (UK)
Course forum
Visit the https://v2.maths-magic.ac.uk/forums/magic022-mathematical-methods
Description
Students will be expected to undertake reading from selected texts, as well as try out example problems to reinforce the material covered in lectures. A number of topics are suggested below and depending on the time available, most will be covered.
- Bender and Orsag, Advanced mathematical methods for scientists and engineers. McGraw Hill.
- Bleistan and Handlesman, Asymptotic expansions of integrals
- Hinch, Perturbation methods. C.U.P.
- Ablowitz & Fokas Complex Variables, C.U.P.
- Lighthill Generalised Functions, Dover.
Prerequisites
Syllabus
- Advanced differential equations, series solution, classification of singularities. Properties near ordinary and regular singular points. Approximate behaviour near irregular singular points. Method of dominant balance. Airy, Gamma and Bessel functions.
- Asymptotic methods. Boundary layer theory. Regular and singular perturbation problems. Uniform approximations. Interior layes. LG approximation, WKBJ method.
- Generalised functions. Basic definitions and properties.
- Revision of basic complex analysis. Laurent expansions. Singularities. Cauchy's Theorem. Residue calculus. Plemelj formula.
- Transform methods. Fourier transform. FT of generalised functions. Laplace Transform. Properties of Gamma function. Mellin Transform. Analytic continuation of Mellin transforms.
- Asymptotic expansion of integrals. Laplace's method. Watson's Lemma. Method of stationary phase. Method of steepest descent. Estimation using Mellin transform technique.
- Conformal mapping. Riemann-Hilbert problems.
Lecturer
-
Professor Andrew Gilbert
- University
- University of Exeter
Bibliography
No bibliography has been specified for this course.
Assessment
The assessment for this course will be released on Monday 13th January 2025 at 00:00 and is due in before Friday 24th January 2025 at 11:00.
Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).
You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).
If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.
Please note that you are not registered for assessment on this course.
Files
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Lectures
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