The course is designed for graduate students in the engineering sciences to provide to them familiarity with perturbation methods, with special focus on how these methods provide useful insight in mathematical problems encountered in physics and engineering. The solution of ordinary differential equations with one small/large parameter will be analyzed, both within the framework of regular- or singular-perturbation theory, with special attention on boundary-layer theory, WKB approaches and multiple-scale analyses. The extension of the methods to partial-differential equations will also be discussed.
FSG3123 Perturbation Methods in Mechanics 7.5 credits
Information for research students about course offerings
The course is given once per year with start VT 2017.
Content and learning outcomes
Course contents
Intended learning outcomes
Once the course will be completed, the student should be able to:
- Explain basic concepts of perturbation techniques, such as order relationships, asymptotic sequences, asymptotic expansions and convergence issues.
- Propose a solution method for regular perturbation problems
- Explain the difference between a regular and a singular perturbation problem
- Analyze a singular problem by means of a balancing method, methods of strained coordinates and boundary-layer theory
- Determine inner and outer solutions for singular perturbation problems by means of boundary-layer theory and the composite form
- Use WKB methods to solve linear ordinary differential equations subjected to different length or time scales
- Perform a multiple-scale analysis on linear and non-linear problems
- Apply perturbation methods to partial-differential problems
Literature and preparations
Specific prerequisites
Basic knowledge of ordinary differential equations, Mechanics and Matlab.
Recommended prerequisites
Basic knowledge of ordinary differential equations, Mechanics and Matlab.
Equipment
Literature
- D. Wilcox (1995) Perturbation methods in the computer age. DWC Industries Inc.
- E. J. Hinch (1991) Perturbation methods. Cambridge University Press.
- C. Bender & S. Orszag (2010) Advanced mathematical methods for scientists and engineers. Springer
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
Examination
- DEL1 - Participation, 1.5 credits, grading scale: P, F
- INL1 - Assignment, 6.0 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
DEL1 Participating 1,5 hp (P, F)
INL1 Inlämningsuppgift 6,0 hp (P, F)
Other requirements for final grade
- Active participation to the lectures and, in particular, to the problem-solving classes.
- Homework assignment.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course room in Canvas
Offered by
Main field of study
Education cycle
Add-on studies
Contact
Supplementary information
Teachers:
· Dr. Antonio Segalini (KTH Mechanics)
· Docent Anders Dahlkild (KTH Mechanics)