There are no announcements



This course is part of the MAGIC core.


This is a core applied module. The aim of the course is to pool together a number of advanced mathematical methods which students doing research (in applied mathematics) should know about. Students will be expected to do extensive 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 time available, most will be covered. The course proceeds at a fairly fast pace.
Assessment The assessment for this module will be in the form of a take-home exam at the end of the course.

Recommended books:
  • Bender and Orsag, Advanced mathematical methods for scientists and engineers
  • Bleistan and Handlesman, Asymptotic expansions of integrals
  • Hinch, Perturbation methods
  • Ablowitz & Fokas Complex Variables, C.U.P.
  • Lighthill Generalised Functions, Dover paperback.


Autumn 2011 (Monday, October 10 to Friday, December 16)


  • Mon 12:05 - 12:55
  • Thu 10:05 - 10:55


It is assumed that students have done some real and complex analysis.


  • 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 formuale.
  • 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.


Jitesh Gajjar
Phone (0161) 2755895
Interests Stability theory, theoretical and computational fluid dynamics, R>>1 flows.
Photo of Jitesh Gajjar


Photo of Azwani  Alias
Azwani Alias
Photo of Cisem Bektur
Cisem Bektur
Photo of Michael Bennett
Michael Bennett
Photo of Ashley Brereton
Ashley Brereton
Photo of Daniel Colquitt
Daniel Colquitt
Photo of Tom Croft
Tom Croft
Photo of Boris Dadachev
Boris Dadachev
Photo of Matthew Edgington
Matthew Edgington
Photo of Mariano Galvagno
Mariano Galvagno
Photo of Kostas Georgiadis
Kostas Georgiadis
Photo of Christopher Jeavons
Christopher Jeavons
Photo of Thorpe Maria
Thorpe Maria
Photo of Aniayam  Okrinya
Aniayam Okrinya
Photo of Charlotte Page
Charlotte Page
(East Anglia)
Photo of Pearce Philip
Pearce Philip
Photo of Harvind Rai
Harvind Rai
Photo of Rahifa Ranom
Rahifa Ranom
Photo of Xavier Riedinger
Xavier Riedinger
Photo of Lucy Sherwin
Lucy Sherwin
Photo of Jonathan Stone
Jonathan Stone
Photo of Julian Thompson
Julian Thompson
(East Anglia)
Photo of Desislava Todorova
Desislava Todorova
Photo of Daniel Wacks
Daniel Wacks
Photo of Martin Walters
Martin Walters
(East Anglia)
Photo of Derek Watson
Derek Watson
Photo of nicolas werning
nicolas werning
Photo of Xizheng Zhang
Xizheng Zhang


Advanced Mathematical Methods for Scientists and EngineersBender and Orszag
Asymptotic Expansions of IntegralsBleistein and Handelsman
Perturbation methodsHinch
Complex variables: introduction and applicationsAblowitz and Fokas
Introduction to Fourier analysis and generalised functionsLighthill


Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.)


Assessment for this course will be via a take-home examination which will be put online towards the end of the course (8th December) and for which the deadline for completion will be 15th January. The exam paper will require the completion of 4 out of 6 questions and to pass one is required to obtain at least 50%.

MAGIC022 take home exam

Files:Exam paper
Deadline: Monday 16 January 2012 (2042.7 days ago)

MAGIC Take-home exam. Click on the problems in the box above to see the paper.

Recorded Lectures

Please log in to view lecture recordings.