SG2123 Mathematical Methods of Mechanics, General Course 6.0 credits

Mekanikens matematiska metoder, allmän kurs

Basic mathematical methods together with mechanical applications to nonlinear oscillations and waves.

Offering and execution

Course offering missing for current semester as well as for previous and coming semesters

Course information

Content and learning outcomes

Course contents *

Asymptotic series, local and uniform expansions. Strongly damped systems, boundary layer theory, WKB method. Periodic and transient motion, Lindstedt's method and multiple scales. Non-linear phenomena and theory of stability. Averaging approximations. Wave equation and Green functions. Approximations for short and long wave lengths. Non-linear waves, kinematic waves. Hyperbolic waves and 1D gas dynamics. Dispersive waves and the method of steepest descent.

Intended learning outcomes *

The course aims at an understanding of important phenomena and methods of modern mechanics, introduced in the contexts of oscillations-ODE and waves-PDE.

Course Disposition

No information inserted

Literature and preparations

Specific prerequisites *

Compulsory courses within the competence program Mechanics.

Recommended prerequisites

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Equipment

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Literature

Karl-Erik Thylwe: Kompendium Mek. Mat. Met. Ordinära diff. ekv. med tillämp. svängningsteori.

Bengt Enflo: Math. Meth. Mech. Partial diff. eqs with application to wave theory.

Examination and completion

Grading scale *

A, B, C, D, E, FX, F

Examination *

  • INL1 - Hand in Task, 1.5 credits, Grading scale: P, F
  • TENA - Examination, 4.5 credits, Grading scale: A, B, C, D, E, FX, 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.

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Examiner

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Further information

Course web

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Offered by

SCI/Mechanics

Main field of study *

Mechanical Engineering

Education cycle *

Second cycle

Add-on studies

No information inserted

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.