Asymptotic Methods

Summer Semester 2019

Lecture: M.A. Efremov

Exercise: M.A. Efremov


Monday, 13:00-16:00N24/252


The aim of this special lecture series is to provide students with a Bachelor or Master degree with advanced mathematical tools to solve different problems faced by physicists, engineers, and applied mathematicians. Each method is illustrated by both well‐known and completely new examples of physics problems appeared within classical and quantum mechanics.

Methods include but are not limited to

  • approximate solutions of transcendental equations,
  • asymptotic calculus for integrals and sums,
  • the saddle‐point and contour integration methods,
  • the WKB method and its generalizations for differential equations of different types,
  • the methods of averaging.


  • N.G. de Bruijn, Asymptotic methods in analysis (Dover, 2010)
  • C.M. Bender and S.A. Orszag, Advanced asymptotic methods for scientists and engineers: asymptotic methods and perturbation theory (Springer, 1999)
  • A.H. Nayfeh, Perturbation methods (Wiley, 2007)
  • E.J. Hinch, Perturbation methods (Cambridge University Press, 1995)


oral examination, 50% of exercise credits required


Tuesday, 12:00-14:00N24/227

Exercise sheets (.pdf files)

Sheet No. Date of issueDiscussion
Sheet 123-04-201930-04-2019
Sheet 2
Sheet 307-04-201914-05-2019
Sheet 4
Sheet 529-05-201904-06-2019
Sheet 605-06-201925-06-2019
Sheet 726-06-201902-07-2019
Sheet 803-07-201909-07-2019
Sheet 910-07-201916-07-2019