Prospectus

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Introduction to Perturbation Methods (BM)

Course
2022-2023

Admission requirements

Ordinary differential equations.

Description

When available, explicit solutions are fundamental to the understanding of differential equations, but for many problems of interest, such closed-form exact solutions can not be found. Even when they do exist, often the understanding and interpretation of explicit solutions requires computational and/or further approximation. The study of asymptotic and perturbation methods offers a systematic analysis of solutions to differential equations when tractable solutions are unavailable. The goal of perturbation methods is to replace an exact problem that does not have a tractable solution, by a series of approximate problems that do have (simpler) explicit solutions. We will cover a range of topics including asymptotic expansions for algebraic and differential equations and multiple scales for initial and boundary value problems. The methods all rely on there being a parameter in the problem that is relatively small. Such a situation is relatively common in applications and this is one of the reasons that perturbation methods are a cornerstone of applied mathematics.

Course Objectives

After the course you will be able to study differential equations with a small parameter

  • using the methods of matching, multiple time scales and WBKJ method.

  • with multiple solutions.

Timetable

The schedule for the course can be found on MyTimeTable.

Mode of Instruction

lectures

Assessment method

The examination consists of homework, a written final exam, and an oral retake exam. No minimum grade is required for
the homework in order to take the exam or to pass the course. The homework counts as a practical and there is no retake
for it. The final grade based on the final exam and the retake consists of homework (40%) and the final (or retake) (60%); to pass the course,
the grade for the final exam (and the retake) should be at least 5 and the (unrounded) weighted average of the two partial grades at least 5.5.

Reading list

Introduction to Perturbation Methods by M.H. Holmes
ISBN-13:978-1461454762

Registration

From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.
Extensive FAQ's on MyStudymap can be found here.

Contact

Vivi Rottschafer vivi@math.leidenuniv.nl
Arjen Doelman doelman@math.leidenuniv.nl