Analytic Functions
Analytiska funktioner

FMA131F, 6 högskolepoäng

Gäller från och med: Spring 2020
Beslutad av: FN1/Anders Gustafsson
Datum för fastställande: 2014-01-27

Allmänna uppgifter

Avdelning: Mathematics
Kurstyp: Ren forskarutbildningskurs
Undervisningsspråk: English

Syfte

The course is primarily intended to bridge the gap between the requirements of the course FMAF01 Analytic Functions and the prerequisites for standard postgraduate courses on analytic functions in one or several variables.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• in his/her own words be able to describe the concepts in the course and their properties.
• in his/her own words be able to explain the logical connections between the concepts (definitions, theorems and proofs).

Färdighet och förmåga

För godkänd kurs skall doktoranden

• be able to show capability to identify problems which can be modelled with the concepts introduced in the course.
• be able to use the concepts in the course in problem solving.
• with proper terminology, in a well structured way and with clear logic be able to explain the solution to a problem.
• be able to show capability, in the context of problem solving, to develop the theory somewhat further.
• have developed his or her ability independently to read and judge mathematical text.

Kursinnehåll

Analytic continuation. Complex integration. The argument principle. Conformal mappings. Polynomials and their zeroes. Partial fractions, meromorphic functions. Infinite products. Ordinary differential equations. Integral transforms. Asymptotic methods. Potential theory.

Kurslitteratur

Lecture notes.

Kursens undervisningsformer

Undervisningsform: Föreläsningar

Kursens examination

Examinationsformer: Skriftlig tentamen, muntlig tentamen
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvariga: