Komplex Analys, Fall 2007, Uppsala Universitet This page will be used for general announcements and the list of recommended "homework" problems. **** AND FOR LINKS TO EXAM SOLUTIONS, OLD EXAMS, ETC **** -------------------------------------------------------------------------- LAST UPDATE: 18 Feb 2008 -------------------------------------------------------------------------- EXAM dated 2008-01-11: SOLUTIONS ARE POSTED at www.math.uu.se/~hejhal/komplex.html %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 1) See www.math.uu.se/~hejhal/komplex.html for other supplemental course material (problems, solutions, duggor). THE SOLUTIONS FOR BOTH DUGGOR ARE NOW POSTED THERE. SO ARE SOME OLD FINAL EXAMS....but note that we only use Rouche's threorem, NOT the full argument principle on October 15. 2) FOR THOSE NOT OWNING A COPY OF SAFF & SNIDER: The Angstrom Library now has a copy for 24 hour loan. It can be taken out, eg for xeroxing... ------------------------------------------------------------------------- Prob. Class Date Typical Problems 4 Sept Prob Sheet: C2, C4, C6, C7, C8, C10, C15, C16, C17 S&S 1.2 7,16 1.3 11,16 1.4 12(a), 17(b), 18(b), 20 1.5 5(d), 10, 16 2.1 3, 13(ab) 2.2 11,17,25 2.3 7(d),11,13,16 2.4 2,3,4,6,9,12 2.5 3(cde), 7, 10,11,12,15,16,17 11 Sept Prob Sheet: B1-B19 except B7,B11,B12,B18,B19 El-E4 S&S 3.1 11(b), 13(ab), 15(abc) 3.2 9, 12(b), 13,18,19 3.3 1,3,11,12,13,15 (hejhal's problem: let D be the domain lying to the left of the parabola y*y = x + 4. find an explicit branch of log(z*z + 4) on D and compute its derivative. hint: factor.) 3.4 4,5 3.5 3,5,7,8,11 4.1 8,9,11 4.2 6,7,14(ad) 4.3 1(a-e) 18 Sept Problem Sheet: E5--E11, E13, E14, E16, E19--E21, E27 S & S 4.4 15--18 4.5 4 4.6 1,2,3,5,6,8,14,16 27 Sept (OLD) Problem Sheet: G2,G3,G5,G6,G8,G9 and I2 S&S 4.6 3,5,7,8 5.1 4,11,14 5.2 1(adef), 2(adef), 5(bce), 11(ab) 5.3 3--5 5.5 3,5,7(ab), 13 5 Oct (OLD) Problem Sheet: H(1,3,4,6,8,10) I(3,8,13,16,17) S&S 5.6 1(abcd,fgh), 3(d), **19** IMPORTANT 5.7 1(bcdfhi) 6.1 1(e) 9 Oct (OLD) Problem Sheet: K(4,6,8,9abc) S&S 6.1 3(ef) 6.2 4 6.3 3,4,6 11 Oct (OLD) Problem Sheet K9(cde), K11(ae), L5,L6,L12(ab),L11 S&S 6.4 6,8 6.7 6--10 [plus review of earlier problems; or discussing old exams] ========================================================================== (for reference) UPPSALA UNIVERSITET Komplex Analys (HT 2007) Matematiska Institutionen Prof. Dennis Hejhal Email: hejhal@math.uu.se ; phone: 471-3274 There will be 14 lectures and 6 problem-solving classes, each of 2 x 45 minutes. The official textbook for the course is: E. Saff & A. Snider, Fundamentals of Complex Analysis with Applications to Engineering and Science, 3rd Edition, Prentice-Hall. We will cover (roughly) chaps. 1--6. The lectures will basically follow the treatment given in Saff & Snider. (Saff & Snider's book is intended to give an introduction to komplex analys at a level just slightly higher than multi-variable calculus.) We will also make use of an old, extensive list of problems available at website "A" below. There will be a written final exam at the end of the course. There will also be two 45 minute "duggor" consisting of 3 problems each. A passing grade will be 8 points out of 15. For each dugga with a passing grade, there will be one bonusproblem on the final exam given on 15 October 2007. Obs!: the dates & times of the duggor will be announced in class and on this website. The duggor can *only* be taken at the times listed. Two websites with excellent supplemental material for this course are: A) www.math.uu.se/~andersk/ht2006/komplex_analys/ B) www.math.uu.se/~leifab/komplex_www/ ======================================================= APPROXIMATE COVERAGE OF THE LECTURES Lecture Saff & Snider 27 Aug 1.1--1.6 28 Aug 2.1--2.3 29 Aug 2.4--2.5 3 Sep 2.6--3.2 6 Sep 3.3--3.5 (3.4 lightly) 7 Sep 4.1--4.4 12 Sep 4.5--4.6 17 Sep 5.1 20 Sep 5.2--5.5 (in streamlined form; we omit 5.4) 25 Sep 5.5--5.6 2 Oct 5.6; 5.7 (lightly); omit 5.8 3 Oct 6.1--6.4 (6.4 lightly) 9 Oct 6.5; omit 6.6; 6.7 (lightly) 10 Oct Review