Table of contents

The course is connected to the following study programs

Teaching language

English.

Prerequisites

The course requires advanced knowledge in physics and/or applied mathematics.

Learning outcomes

After the course is completed, the student will be familiar with taking analytical approaches to solving differential equations and integrals. The student will be able to perform local analysis of equations, simplify them and find mathematical methods for obtaining approximate solutions. In particular, to find analytical solutions to differential equations and integrals that often occur in mechanics and that cannot be solved exactly (classical, quantum and celestial mechanics).

Contents

  • Asymptotics
  • Perturbation theory
  • Summation of series
  • Local analysis of linear and nonlinear differential equations in mechanics
  • Asymptotic expansion of integrals

Teaching and learning methods

Lectures and tutorials.

Examination requirements

In order to take the final exam, the student must have an approved paper/report describing examples from own engineering discipline where the theory from the course is applied.

Examinations

Oral examination.

Student evaluation

The course will be evaluated in accordance with the quality assurance system for education, chapter 4.1.

Offered as a free-standing course

Yes. Subject to availability or capacity.

Admission Requirement if given as a free-standing course

The candidate must be admitted to a PhD programme

Admission for external candidates

No.

Other information

The course is based on the first part of the book by C.M. Bender and S.A. Orszag: «Advanced Mathematical Methods for Scientists and Engineers», McGraw-Hill 1978.
Last updated from FS (Felles studentsystem) Oct. 15, 2026 10:09:50 AM