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In general I judge the quality to be satisfactory. In particular, the textbook is of high quality, is available online, and is followed closely for most of the course. There is room for improvement especially in creating some more and easier calculation exercises.

Learning outcomes are updated and relevant. Learning outcomes are available on NTNU's official course page. I judge the fulfillment of learning outcomes as satisfactory. This is supported by the responses to the student survey for FY3107/FY8304 to "Learning outcome fulfillment": Out of 6 respondents, 5 answered "To a large extent", and 1 answered "To a very large extent". I judge the correspondence between the learning outcomes of this course and those of other relevant courses to be satisfactory. This is supported by the responses to the student survey for FY3107/FY8304 to "Overlap": 6 out of 6 respondents answered "Appropriate".

Lectures were given on Blackboard Collaborate Ultra. As I did not have hardware for writing on the screen in real time, lectures consisted of me going through my pre-prepared handwritten or typewritten notes. This probably made the pace a bit too high at times. On the upside, unlike in previous years the lectures were recorded. Attempting enough calculation exercises is crucial for acquiring the necessary skills. Several students perceived the problem sets (there were 6 of them) as very challenging, and expressed a wish for more and easier problems to practice on. Developing problem sets with more and easier problems would probably be the most useful change in the course. Out of 6 responses to the student survey for FY3107/FY8304 to the question "My benefit of calculation exercises", 2 answered "Very good", 2 answered "Good", 1 answered "Average", and 1 answered "Bad". My impression based on questions and some other feedback is that some students were highly motivated. However, there may also have been some that were less motivated. All lectures and tutorial sessions were held on Blackboard. There was generally very low (including zero) attendance at the weekly one-hour tutorial session (but having them scheduled on Friday morning at 8:15 probably did not help either). I would certainly imagine that the corona situation in general and the lack of physical lectures and tutorial sessions in particular gave a far from optimal learning environment. I was not able to recruit students for a reference group. As a replacement, I set up a Google sheet for the students to submit anonymous feedback, and this feedback was discussed in a lecture around the middle of the semester.

The evaluation is restricted to a final written exam. I judge the correspondence between learning outcomes and the evaluation form to be satisfactory in general. This semester was unusual since the exam was a home exam with merely a "Pass/Fail" grade scale.

NTNU:TIA:REST

Institutt for fysikk

Department of Physics

Spesifiserte trykte og håndskrevne hjelpemidler tillatt. Bestemt, enkel kalkulator tillatt.

Engelsk

Anbefalte forkunnskaper

Standard kunnskap og modenhet i matematikk, som for 3-4 års studier i fysikk.

Mer om vurdering

Ved utsatt eksamen kan skriftlig eksamen bli endret til muntlig.

Link til informasjon om emnet

Faglig innhold

Emnet undervises annethvert år, neste gang høsten 2020. Emnet tar sikte på å gi en innføring og trening i nyttige metoder for å finne tilnærmede løsninger på fysiske problemer, især slike der regulære perturbasjonsutviklinger ikke kan benyttes. Også i de tilfeller der et gitt problem må behandles numerisk, kan approksimative løsninger gi verdifull opplysning om kvalitativt forløp for valg og implementering av numerisk metode. Kurset behandler bl.a. lokal analyse av differensiallikninger, approksimativ evaluering av integraler, asymptotiske utviklinger, singulær perturbasjonsteori, grensesjiktmetoden, WKB-metoden, flerskalautviklinger.

Kursmateriell

Pensumlitteratur: C.M. Bender og S.A. Orszag: Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill 1978.

Læringsformer og aktiviteter

Forelesninger og regneøvinger. Endel av øvingene vil bli lagt opp for å utføres v.hj.a. datamaskin algebra programmer. Når undervisning og undervisningsmateriell er på engelsk, vil eksamen normalt bli gitt kun på engelsk. Forventet arbeidsinnsats i emnet er 225 timer.



Læringsutbytte

Kunnskapar - kandidaten skal ha kunnskap om
- dei nyttigaste metodane for å finna approksimative analytiske løysingar av matematiske problem som ofte oppstår i modellering av fysiske system
Ferdigheiter - kandidaten skal vera i stand til å
- identifisera ymse klassar av matematiske problem
- forenkla eller omskriva problemet til ei form som gjer det mogeleg å bruka ein relevant metode
- bruka metoden for å finna ei approksimativ analytisk løysing
Generell kompetanse - kandidaten skal
- kjenna til relevante matematiske referansekjelder og programvare
- vera i stand til å bruka desse til å finna/ekstrahera informasjon effektivt



Matematiske approksimasjonsmetoder i fysikken

Fysikk

Fysikk og matematikk - masterstudium (5-årig)

Physics (Master's Programme)

Web/Lists(guid'8b698a2d-6ad0-4f7d-b3be-219cc1979f02')/Items(7567)/FieldValuesAsText

Matematiske approksimasjonsmetoder i fysikken - FY3107