GO TO: http://www.math.uu.se/~hejhal/komplex.html FOR MORE KOMPLEX ANALYS INFO....... Komplex Analys, Fall 2008, Uppsala Universitet This page will be used for general announcements and the list of recommended "homework" problems. **** ALSO FOR LINKS TO EXAM SOLUTIONS, OLD EXAMS, ETC **** -------------------------------------------------------------------------- LAST UPDATE: 7 Oct 2008 IMPORTANT: NEW PROBLEMS POSTED! HEJHAL LEKTION OCTOBER 6 SWITCHED TO OCTOBER 9, 13:15-15, Room 80127 Angstrom. THERE IS *NO* LEKTION OCTOBER 6 at 8:15. THE EXAM IS OCTOBER 13, 9-14, Gimogatan 4 Sal 2. IT IS FOR ALL STUDENTS, NOT JUST F3 B,E. ---------------------------------------------------------------- A) the course material is now getting denser and denser. regrettably, the lectures lately have been 'back to back'. it really is valuable to think about this material, and to see some examples. it makes it MUCH easier to follow. i will continue to try to streamline the class so that we can EFFICIENTLY get to our goal,and be ready for the exam in October. i will minimize some of the proofs, freeing up more time to see EXAMPLES. it **does** help to look at the book, too, as i go through the successive sections. the book is not bad. B) do not hesitate to ask me math questions outside of class if you do not understand something, or need help. email is ok. i) %%%%%%%% DUGGA SOLUTIONS ARE NOW POSTED %%%%%%%%%%% See other site! There's also a new hand-out on integrals. ii) PLEASE LOOK AT THE HOMEWORK PROBLEMS BELOW; ALSO GO TO WEBSITE www.math.uu.se/~hejhal/komplex.html TO DOWNLOAD THE "OLD" PROBLEM COLLECTION! iii) THIS COURSE MOVES FAIRLY QUICKLY THROUGH THE MATERIAL IN SAFF and SNIDER; PLEASE LOOK AT THE BOOK (especially after each lecture)!! ######################################################################### 1) See www.math.uu.se/~hejhal/komplex.html for supplemental course material (problems, solutions, duggor, old exams)!! WE WILL USE THE *OLD* PROBLEM SHEET IN OUR LEKTIONER. PLEASE DOWNLOAD A COPY FROM THIS UU WEBSITE!! 2) IT IS *STRONGLY RECOMMENDED* THAT YOU REFER TO THE TEXTBOOK OF SAFF & SNIDER AS THE COURSE PROGRESSES. 3) FOR THOSE NOT OWNING A COPY OF THIS BOOK, the Angstrom Library now has a copy for 24 hour loan. It can be taken out, eg, for xeroxing... ------------------------------------------------------------------------- Prob. Class Date Typical Problems 10 Sept Old 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 17 Sept Old 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) 23 Sept Old 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 29 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 2 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) 8 Oct OLD Problem Sheet: K(4,6,8,9abc) S&S 6.1 3(ef) 6.2 4 6.3 3,4,6 9 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 2008) Matematiska Institutionen Professor Dennis Hejhal Email: hejhal@math.uu.se ; phone: 471-3274 Website: www.math.umn.edu/~hejhal/ (click on Kplx Analys) There will be 13 lectures and 7 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, Pearson (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 complex analysis 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 one 45 minute "dugga" consisting of 3 problems. A passing grade will be 8 points out of 15. Students who pass the dugga will receive one bonus problem on the final exam given on 13 October 2008. OBS!: the date & time of the dugga will be announced in class and on this website. The dugga can *only* be taken at the time listed. Three websites with excellent supplemental material for this course are: A) www.math.uu.se/~hejhal/komplex.html B) www.math.uu.se/~andersk/ht2006/komplex_analys/ C) www.math.uu.se/~leifab/komplex_www/ ======================================================= APPROXIMATE COVERAGE OF THE LECTURES Lecture Saff & Snider 1 Sep 1.1--1.5 2 Sep 1.6, 2.1--2.3 3 Sep 2.4--2.5 8 Sep 2.6, 3.1--3.2 11 Sep 3.3--3.5 (3.4 very lightly) 15 Sep 4.1 (lightly), 4.2--4.4 18 Sep 4.5--4.6 22 Sep 5.1, 5.2 24 Sep 5.2--5.5 (in streamlined form; we omit 5.4) 25 Sep 5.5--5.6 30 Sep 5.6; 5.7 (lightly); omit 5.8 1 Oct 6.1--6.4 (6.4 lightly) 7 Oct 6.5 (very lightly); 6.7 (especially Rouche); omit 6.6