Forelesningsplan, gjelder også som pensumliste. Dessuten er øvingene pensum.

De første ukene vil jeg forsøke å følge Seips forelesningsplan:

• During Week 2 we cover I.1-I.3, II.1.-II.2 in Gamelin's book and some basics about the set of complex numbers as a metric space; see pp. 1-16 in Hanche-Olsen's notes.

• During Week 3 we cover II.2-II.6 in Gamelin's book. (We also cover I.4-6 through examples of analytic functions and inverse functions.)

• During Week 4 we cover II.7 and then we begin discussing the core of chapters III and IV in Gamelin's book. We take a more direct route to complex integration, following mainly Ahlfors' book.

• During Week 5 we will cover the remaining part of chapters III and IV. (We will postpone discussing III.6, III.7, and we will not consider IV.8.) We will also begin the discussion of power series (Chapter V).

• During Week 6 we will discuss Chapter V and and then move to Chapter VI.

• During week 7 we will study VI.2-4 and VI.6, and then we will discuss Cauchy's theorem as presented in Ahlfors's book.

• During Week 8 we will cover Chapter VII.

NB! UKE 9,10 er midtsemester-uker hos Seip. Så vi fortsetter med denne tempoplanen:

• Uke 9: Kap VII (Residueregning). Repeterer vindingstall i VIII.6.

• Uke 10: Kap VIII(Argumentprinsippet,Rouche,Hurwitz,Open mapping,Kritiske punkt,Enkelt-

sammenhengende områder). Kap IX.1 (Schwarz' Lemma)

• Uke 11: Kap IX.2,3(Konforme selvavbildinger, hyberbolsk geometri). Ser på ukens øving.

• Uke 12: Kap X.1,2. Kap XI.1,2,5,6(Riemanns avbildingssats). Det siste først!

• 09.04: Kap X.3 (Schwarz'refleksjonsprinsipp). Utsetter Schwarz -Cristoffel.

• 12.04: Kap XIII.3(Uendelige produkt)

• 16,04: Kap XIV.1(Gammafunksjonen)

• 19.04: Kap XI.3(Schwarz-Christoffel)

• 23.04: Oppsummeringer
• 26.04: Oppsummeringer forts.