Math 2263, Fall 2019, Professor D. Hejhal This page will be used for general announcements and the homework listing. Please check it regularly! ----------------------------------------------------------------------- LAST UPDATE: 12 DEC 2019 ======================================================================= CURRENT OFFICE HOURS: MWF 1:40-2:25pm. (note: 1:40pm) I can also answer some questions after lecture. ================================================================ FINAL EXAM, FRIDAY, DEC 13, 12 noon - 3PM RAPSON HALL 100; spread yourselves out in the room, it is a big room. FINAL EXAM HAS 12 MULTIPLE CHOICE PROBLEMS, 5 WRITE-OUT PROBS. ================================================================ *** The final exam is on fundamentals, not horribly long or complicated problems! *** As I said in lecture, SINGLE best advice is study our old hour exams, solution sheets, and your quizzes. PLEASE ALSO REVIEW THE ALGEBRA USED IN BOOK WITH LAGRANGE ON PAGES 973+975. Nonlinear equations often need a quick "refresher". THE MATH LIBRARY (website www.lib.umn.edu/math ) HAS OLD FINAL EXAMS FROM 2263. They can be used as a *GENERAL* sample. IT IS WORTH LOOKING. Some (by no means all) were written by DH. WE DO NOT PROVIDE ANY ANSWERS TO THOSE EXAM PROBLEMS. I think I "may have" taught 2263 in Spring **2009**; my memory is rusty. I like center-of-mass in R^2; it's a nice basic application. ------------------------------------- The Review Sheets (for hour exam material) from Carolynn Johnson are found under Handouts. Time is short. Here are the problems that "catch my eye" as relevant for a 'fundamental' final exam. CHECKLIST FOR YOU?? midterm 1 -- 1,3,6,8,9,10,11, 12(marginal), 13 (yes!), 14 midterm 2 -- 1,3,4,5,6,7,8 (can you guess u and v), 9 (a bit too long!) midterm 3 -- 1 (NO! but be able to do div, curl), 2, 4 (note z=3; and ds should be dr), 5 (ds should be dr), 6 (maybe), 7,8; (her sheet does not have a 3-dim Stokes as such) -------------------------- DOUBLE-CHECK YOUR MULTIPLE CHOICE ANSWERS! THERE HAVE BEEN "TRAPS" SET FOR YOU. This is a common cause of losing points. The problems may be easy, but still double-check your choice. ===================================================================== EXAM 3 STATS are: gradelines [90, [68 , [49, [40 100 (3); 95-99 (9); 90-94 (10) 85-89 (7); 80-84 (5); 70-79 (16); 60-69 (19); 50-59 (15) ; 40-49 (5); 30-39 (5); 20-29 (3); 10-19 (3); 0-9 (0) N = 100 exams ===================================================================== See recommended HW for Dec 12. ================================== DEC 6 LECTURE COMMENT: The 'slick/cheat' method I showed of getting rid of dz by writing it as g_x dx + g_y dy is NOT a universal simplifier. Most of the time, although it is correct, it creates many additional terms in the 'new' dx,dy line integral -- HENCE you get many more terms to do in Green's theorem (versus just using Stokes!). The situation depends very much on the problem -- especially on what g(x,y) is. I did the 'cheat' method since g(x,y) = 2-y is very simple!!! DEC 6 LECTURE COMMENT #2: Theorem 0 should be your favorite theorem in 2263 (... even if it is clearly FALSE). But, your second favorite should be Stokes' theorem. (Or else maybe Green's Theorem.) ====================================================================== RECOMMENDED HW PROBLEMS "for Dec 12" (even though none are handed in) 16.5 4,6 16.6 4,23,25,33,48-50 16.7 9,14,17,23,25-26, 31 16.9 7,10-11 (new:) 16.8 7,9,11; we will not give 13,15 - but these are nice. ================================================================ EXAM 2 STATS: (n = 105) approx gradelines 88*, 73*, 48], 40] (* = line down the middle) 100 (1) 95-99 (5) 90-94 (11) 85-89 (13) 80-84 (11) 75-79 (10) 70-74 (14) median 73 65-69 (2) 60-64 (9) 50--59 (12) 40--49 (11) 30--39 (4) 20--29 (0) 10--19 (1) 0--9 (1) A-range 20 B-range 35 C-range 36 D-range 8 F-range 6 =============================================================== IN ORDER TO FINISH THE SYLLABUS, A NEW DAY-BY-DAY SCHEDULE HAS BEEN INCLUDED BELOW (after the stuff about Exam 2) =============================================================== EXAM 1 DISTRIBUTION 90-99 (3) 80-89 (7) 70-79 (14) 60-69 (14) 56-59 (12) and 50-55 (21) 46-49 (10) and 40-45 (10) 30-39 (14) 20-29 (4) N = 109 (median is 54) gradelines: 80] {78,79?} 61] 46] 39] A range n = 13 (incl 78,79); B range n = 25; C range n = 43 D range n = 14; F range n = 14 (total n = 109) {this distribution is shifted about 4 points "downward" from 2017} ======================================================================== LATEST "DAY BY DAY" SCHEDULE ("or else we won't finish") 11-11 part of 16.2+16.3 11-13 rest of 16.2+16.3 11-15 16.4, feet wet in 16.5 11-18 16.5 11-20 16.6 11-22 16.7 (part 1) 11-25 16.7 (part 2), start 16.9 (skip 16.8 temporarily) 11-27 more stuff on 16.6, 16.7 and 16.9 (proofs?) = Wed before break! 12-2 review 16.9, start 16.8 12-4 reviewing for exam 3 (exam thursday, Dec 5) 12-6 more on 16.8; also 16.7 as need be 12-9 overflow stuff; begin review 12-11 review (and course evaluation) ======================================================================== It is very important to note that, in the Oct 14 lecture, I explained how making z-axis point out of the paper (sun at z = + infinity) allows us to set up double integrals for (signed) volume WITHOUT DRAWING the 3-d figure, i.e. only drawing the "base" B. The key is to determine where the light ray enters the solid and where it exits. This can be written in a sentence -- instead of drawn. ======================================================================== COURSE NOTES, COVERAGE "DIARY", READING LIST: Sept 4 did 798-815(box 7). Sept 6 811(box); 815(box 7)-831. Sept 9 820(box 14), 826(box 4); 834-839,888-898 Sept 11 893-899(look at 897 plots); then 903-920 Sept 13 907(example 4); 919-935 Sept 16 932-941(ex. 6) Sept 18 932-942(omitted ex. 7); 946-951; also 945(prob 49; WAVE EQUATION) Sept 20 942-943 (implicit diff); 952-960(reach start of sec 14-7) Sept 23 943 (differentials); 959-960; 965(bottom half)-966(top) Sept 25 959-967 Sept 27 959-967 Sept 30 952(box 15)-953; 971-973 Oct 2 971-977 Oct 4 971-977 Oct 7 971-979 (rounding out 14.8) Oct 9 988-998, 1002 box 3 (by a volume-by-slices method) Oct 11 1001-1008 Oct 14 1001-1011 Oct 16 1010-1014, start 15.4 and 15.5 Oct 18 1016-1021 (omit moment of inertia), 1026-1028 Oct 21 more 1026-1028, do 1021-1024 (on probability) DO MOT WORRY ABOUT 1024 (ex 8). Oct 23 wrap up 1021-1024 AND do 1015(prob 40), start 1029-1032 Oct 25 review of earlier sections; begin in 1034-1037 Oct 28 more review; work in 1029-1037 Oct 30 1040-1043 Nov 1 more 1040-1043; start 1045-1049 Nov 4 finish 1045-1049 Nov 6 15.9 (modified format to keep it simpler) Nov 8 15.9 (more; ex. 3)); some review; then started chap 16 [THERE WILL SOON BE A SHORT HAND-OUT ON 15.9] Nov 11 in Secs 16.1-16.3 Nov 13 talking more about 16.2+16.3 (see esp 1091, example 4, and 1092, example 5 [to be done on Nov 15]; OMIT 1093 (bottom half) Nov 15 start 16.4 Nov 18 16.4,16.5 Nov 20 16.6 (OMIT 1119 bottom half) Nov 22 16.7 (thru 1127) and 16.6 (example 10) ====================================================================== The lectures in this class are done in tandem with the Stewart book, Calculus Early Transcendentals, VOLUME TWO, 8th Edition. The book is quite readable (as many course evaluations have shown). In response to student input, I'll be deviating from the book as need be, so as to expedite things and to "mesh" more closely with the __actual__ content of our exams! ========================================================================= APPROXIMATE SCHEDULE (taken from Syllabus) Week Of Sections 9-2 12.4(review), 12.5-12.6 9-9 14.1-14.3 9-16 14.4-14.5; start 14.6 9-23 14.6-14.7 9-30 14.8; getting feet wet in 15.1 10-7 15.1-15.2 (exam 1: thurs/oct 10) 10-14 end of 15.2; 15.3-15.4; start 15.5 10-21 finish 15.5; and 15.6 10-28 (more on 15.6?); 15.7-15.8 11-4 15.9; start of 16.1 (exam 2; tentative) 11-11 more 16.1; 16.2-16.4 11-18 16.5-16.7 11-25 finish 16.7 and 16.9 (thanksgiving week) 12-2 more 16.9; 16.8 (+ exam 3; 12/5 tentative) 12-9 more on 16.8; review of earlier material ------------------------------------------------------------------ SPECIAL SCHEDULE NOTE The final exam is FRIDAY, Dec 13, 12:00-3:00pm. (The Common Final Day.) All registered students are expected to take the final exam at this time unless a special arrangement has been made, e.g., with Disability Services or the Undergraduate Math Office. [Read that sentence again!] The instructor is __NOT__ responsible for any problems with this. (See also the related comment in the course Syllabus below.) ========================================================================== CONCERNING HOMEWORK: If you are using any kind of manual -- online or hardcopy -- in doing your HW, I urge you in the strongest possible terms to try the problems on your own first BEFORE looking anything up to see the "full solution". If you wish to go 'intermediate' on this, look up only the ANSWER first: then try to get that answer. NOT following this advice will typically show up VERY(!) clearly on the hour exams. Remember: it is important to think through THE LOGIC on each homework problem that you do, not just "grind" or "plug and chug". ========================================================================== THE LATEST STARRED AND "HAND-IN" HOMEWORK A) Starred problems or things similar will appear on the Thursday quizzes. Pay particular attention to these. B) Hand-in problems (labelled "H") are the ones that Prof. Hejhal wants you to __hand in__ to your TA. A selection of these will be given a rough grade by your TA. Any "H" problems assigned during week N are due Thursday of week N+1. C) Cf. also the recommended/optional problems listed after the Syllabus. The following list shows the STARRED Problems!! (Those with "H" are hand-in.) ASSIGNED: week 1 [N.B.: I omit placing a star (*) in front of each to save space!!] 12.4 31 12.5 5,11,12,20-22,26,31,37,57,61,71,77,78 12.6 21-28, 33-38 p.843 23,25 "H" 12.5 #57 and #78 (a favorite; on exam?) week 2 14.1 10,18,20,28,52,70 14.2 9,11,15,16,27,35,36 14.3 15,31,37,42,45,48,50,55,59,61,76(skip e),77,99 "H" 14.3 #37,#45,#50 week 3 14.4 1,5,12,21,28,33-35 14.5 1,5,9,12,21,25,30,31,34,38,39,46,48,50(long but 'famous') 14.6 (tangent plane stuff) 41,46,51,56 "H" 14.4 #35 14.5 #21,34 14.6 #46 week 4 14.6 7,8,13,17,20,21,32,33,63 14.7 6,9,11,32,34,42,45,46,53 "H" 14.6 #20,#33,#63 14.7 #6,#45, #53 week 5 14.8 3,8,17,18,22,23,32,36,45 p.984 56,59,61 15.1 10, 20, 21 "H" 14.8 problems #18,#36,#45 week 6 15.1 32,40,50 15.2 9,18,22,30-31,36,48,49,51,56 "H" 15.1 #40 15.2 #30,48, 51 (not: 56!!) week 7 15.3 4,6,9,14,18,20,25,26,32,39,40 15.4 2,3,8,10,12,16,17 "H" 15.3 #14,26,32 15.4 #16 week 8 15.4 16,17,27,28 15.5 2,5,9 15.6 4,6,13-15,17-19,29 "H" 15.4 16(not 17!), 28 15.5 5 15.6 13,17,18 week 9 (week beginning Oct 28) 15.6 33,34(much harder but less crucial), 42,47-48 15.7 3,11,19,21,27,29,30 15.8 7,8, 12,20,23,25,30,31,35 "H" 15.6 42,47 15.7 27 (be sure to know 21 and 30, tho they are not "H") 15.8 23, 30 (both these problems have simple limits); 31(a) week 10 (week beginning Nov 4) 15.8 35 (both ways), 42 15.9 5,8,9,15,17-19,23-24,26,28 "H" 15.9 15,23,24 week 11 (week beginning Nov 11) 16.1 21,23,26,29-32 16.2 2-4,7-8,19,22, 34 16.3 3,5,7,13-17,20 "H" 16.1 23 16.2 #2,8,19,22 "H" 16.3 7,16,20 week 12 (week beginning Nov 18; DUE TUES NOV 26) 16.4 1,2,4,8-10,17-18 16.5 4-8,14-17,19 "H" 16.4 9,18 "H" 16.5 4,6. ============================================================================== COURSE SYLLABUS MATH 2263 (Lecture 020) Fall 2019 TEXT: Calculus, Early Transcendentals VOL TWO (2016, 8th ed.), by J.Stewart LECTURER: Prof. Dennis Hejhal Vincent Hall 220 Phone 625-4557 Email hejhal@math.umn.edu LOCATION AND TIME: Tate 105, MWF 2:30-3:20pm EXAMS, QUIZZES, HW: There will be 3 one-hour tests and approximately 11 weekly quizzes (10-15 minutes long depending on # of problems). The hour exams and quizzes will be given during the recitations. The sections in textbook covered by the tests will be announced in lecture. Quizzes will be based on homework problems. 3 tests 3 x 100 = 300 pts. (3 x 20%) HW + quizzes 50 pts. (10%) three hour final exam 150 pts. (30%) -------------------------------------------- TOTAL points 500 pts. Course grades will be based primarily on your exam performance. The HW+quizzes are vital to doing well on the exams; your scores here will also be used by your TA in rounding out borderline grades. Note: for each student, the 2 lowest quiz grades will be thrown out. The quizzes are given on THURSDAYS. There will be TWO types of homework: a) starred (QUIZ problems will be chosen from among these, either verbatim or else very similar: be warned!!) b) hand-in "H" (these problems must be handed in to your TA). A selection of the hand-in homework will be given an approximate grade. Hand in **only** those problems designated as 'hand-in'. TWO NOTES: (a) there are some [supplemental] recommended problems attached below; (b) in response to student input, certain "H" problems may be made up by Prof Hejhal so as to be closer to actual exam problems. :-) TENTATIVE Dates for Hour Exams: Oct 10(almost certain); Nov 7; Dec 3 (= a TUESDAY). DATE OF FINAL EXAM: Common final day, Friday, Dec 13, 12:00--3:00pm. There are both department and UM rules regarding the Common Final Day being used for the final exam in CERTAIN courses only. Professor Hejhal does ___NOT___ make exceptions to these rules!!! Students are expected to take the final exam for Math 2263 on the common final day. Plan accordingly with regard to any other classes you may have. ABSENCE FROM HOUR EXAMS: Missing an hour test is permitted only for the most compelling of reasons. Except in extraordinary situations, you should obtain permission to miss a test *in advance*. No make-up exams are given. If you are excused from taking an hour test, your score for that test will be determined from your performance on the final exam. N.B. a grade 'transference' of this kind will normally be granted by the instructor at most ONCE. (In addition: please note, there will also be __no__ make up quizzes!) CALCULATORS: It is expected that NO calculators of any kind will be permitted on the exams and quizzes. ELECTRONICS: No cell phones, laptops, or anything with networking capabililites are allowed on the exams or quizzes. NOTE SHEETS (CHEAT SHEETS): Unless _explicitly_ stated by Prof Hejhal and your TA, no note sheets are permitted on any exams or quizzes. WITHDRAWAL: See _Fall Semester 2019 Class Schedules_ for policies concerning cancellations/withdrawals. There are strict deadlines here! INCOMPLETES: Due to earlier abuse with this, Prof Hejhal adheres strictly to department and UM rules concerning the grade "INC". The upshot is that such grades are now given only very rarely, and, when given, the student's cumulative grade up til that point in the course MUST BE _clearly_ passing (ie, C- or better) on the exams and quizzes. GENERAL REMARKS: Though Stewart's book tends to be quite readable (as past years' course evaluations bear out), Prof Hejhal does occasionally deviate from the book in the interest of greater clarity and expediting things. It is therefore important to come to lecture -- or else have regular access to someone's notes. There may also be occasional hand-outs. Many years of experience have shown that it is VERY important to keep up-to-date in this class. The material covered (chaps. 12, 14-16) becomes increasingly difficult, also RUSHED at the end. (Students have made suggestions about how to avoid the 'crunch' at the end; I will try to use some so we can go slower there!) If you don't understand things in Math 2263, it is wise to visit office hours. Help __IS__ available. Prof Hejhal welcomes suggestions about how to improve the class; these can be left at any time in his department mailbox on the first floor of Vincent Hall (or else simply sent by email). OVERALL, in past years, the course evaluations for Math 2263, when taught by Professor Hejhal, have 'on average' stated: (a) the course is agreeable, but hard; (b) the book is not bad, and should be read; (c) it is very important to keep up-to-date; (d) the course is a steady uphill climb (be warned); (e) the hour exams basically have 'no gimmicks' PROVIDED you do the homework. ================================================================================ APPROXIMATE SCHEDULE Week Of Sections 9-2 12.4(review), 12.5-12.6 9-9 14.1-14.3 9-16 14.4-14.5; start 14.6 9-23 14.6-14.7 9-30 14.8; getting feet wet in 15.1 10-7 15.1-15.2 (exam 1: thurs/oct 10) 10-14 end of 15.2; 15.3-15.4; start 15.5 10-21 finish 15.5; and 15.6 10-28 (more on 15.6?); 15.7-15.8 11-4 15.9; start of 16.1 (exam 2; tentative) 11-11 16.1; 16.2-16.3 11-18 16.4-16.7 11-25 finish 16.7 and 16.9 (thanksgiving week) 12-2 more 16.9 (exam 3; tentative); 16.8 12-9 finish 16.8; review of earlier material ================================================================================ ================================================================================ SUPPLEMENTAL/RECOMMENDED HOMEWORK PROBLEMS (Interesting problems of variable difficulty.) (This list may be updated occasionally.) Section Problems 12.4 27,35,52,53 12.5 26,64 12.6 --- 14.1 --- 14.2 18,20 14.3 79,103,105 14.4 46 14.5 49,51,59 14.6 62 14.7 44,47 14.8 50 15.1 42 15.2 11,12,65,66 15.3 --- 15.4 --- 15.5 24 15.6 51 15.7 22,28 15.8 32,41-43,48-49 15.9 25 16.1 --- 16.2 50 16.3 31-34 16.4 31 16.5 28 16.6 20,24 16.7 45,48,49 16.8 16,18 16.9 29,30,31