Meets MTR 6-8.30pm at MCS B29; first meeting is 5/22 Instructor: A. Levichev, MCS 236, 3-1487(e-mail is more reliable), office hrs: TR 8.30-9.15pm and by an appointment.
E-mail: levit@math.bu.edu
levit@bu.edu (when the above does not work)
get to http://math.bu.edu/people/levit for an info about the Instructor and for the course updates. ("Mathhelp" file might be of interest, too)
To read and to understand the content of respective sections is part of each and every HW assignment (it goes "without saying").
VIEW YOUR GRADES ON-LINE (on the other website: http://courseinfo.bu.edu
navigate to our course)
From within the CourseInfo site, students should select Student Tools > Check Your Grade.
There will be three tests (Mon 6/2, Mon 6/16, Thursday 6/26), and the Final (on the 1st of July).
6/29 I am receiving questions like "Can my grade go down if I take the Final?" YES, it can go down. As I said, already (when presenting the No-Final Opt), typically, of those who take the Final, 1/3 go down, 1/3 stay, 1/3 go up (in terms of the letter grade).
6/27 Current letter grades posted. If you do not show up on the Final (and irrespectively of your Mon attendance) this letter will be entered into the grade sheet.
If a question on the Final is 13.5-13.8 related, it means that either you have to use one of the formulas (specified below, section per section), or use one of the (few) Theorems from these sections. Any other method (which you might have to know to take the question) is from 13.2 (or prior to it).
In 13.5(pp.957,958 won't be tested): 2,3,4,9,10,11. HW 13.5: 1,5,10, 17 (and 21,22,23,24 to be aware about).
In 13.6: 2 (4 is a special case of 2),9 (10 is a special case of 9), HW 13.6: 17.
In 13.7 (p.975 won't be tested): Stokes' Theorem (p.971) (to better understand its right side, check with (9) from 13.6). HW 13.7: 1,3,7.
In 13.8 (p.982 won't be tested): formula on p.978. HW 13.8: 4,7.
13.4 follows from 13.7.
6/26 Current attendance grade posted.
Test 3 covers 12.1-12.4, 12.6-12.9, 13.1,13.2.
L - 13 13.1, 13.2 discussed; 13.3 started. HW is below (see 6/23).
6/23 Questions taken. Recommended Chapter 13 reading is 13.1 (try to solve 21,23,29,30,31,32); in 13.2 the most important formulas are the one at the very bottom of p.929, and # 13. There is a lot of new notation (not too much new content!) in 13.1, 13.2. Try 13.2 ## 5,11,17,31,33.
6/21 The NoFinOption is formally announced (see the respective file).
L - 12 12.4,12.6,12.7,12.8,12.9. They have been presented in a much more compact way than it is done in the text. HW 12.4: 1-11odd, 12.6: 1-9odd,21; 12.7: 1-15odd; 12.8: 7,9,11,15,19; 12.9: 1,3,5,11,13.
6/18 Test 2 scores posted. Ave was 27.7 in the 16 to 37 range. T2 access is on Thursday, tomorrow, at the very end (and after) of the class (or some can do it on Mon after class).
L - 11 12.2, 12.3 (as well as some of Calc I notions recalled). HW 12.2: 1-11odd, 17,19,21; 12.3: 1-23odd,29-37odd.
Questions taken, Test 2, L - 10 5.2 (definite integral from Calc I recalled), 12.1. HW 12.1: 1,3.
Test 2 on Mon 6/16 covers 9.6,9.7,10.1,10.2,10.5, 11.1 - 11.7.
L - 9 11.7 finished, questions taken, a few examples discussed.
L-8 11.5(pp.790-794,only; Ex.2 won't be tested), 11.6,11.7 (not finished; 11.7 Ex.4 won't be tested). HW 11.5: 3,5,7,9; 11.6: 5-15odd,19-25odd, 33(enough to be aware about #33 formulas),35,37,41,45; 11.7: 1,3,5,9,,11,13,23,25,27,31,33.
L - 7 11.3 (omit pp.775,776), 11.4 (pp.779,780,787,788,only). HW 13-31odd,35,37; 11.4: 1,3,33,35.
L-6 10.5 finished, 9.7(Ex.8 optional),11.1(Ex.1,2,5,10 won't be tested), 11.2. HW 10.5: 1,3,17,19,21; 9.7: 5,7,9,21,23; 11.1: 5,7,13,15; 11.2: 1,7,9,11,15
6/5 Test 1 scores posted. 26 was the ave, in the 4 - 40 range. Test 1 access is today at the end of the meeting.
L - 5 10.1 (pp.708,709 won't be tested); 10.2, 10.5 (not finished). HW 10.1: 1,3,13,15,19,27 (also, be aware of 10.1 #33 laws); 10.2: 3,5,9,11,19,21,31,33; 10.5: 17.
Test 1, then L-4: 9.6 (Ex.3 won't be tested). HW 9.6: 3-25odd.
L-3 9.5 finished, some of the suggested methods are not in the text. HW 9.5: 11-39odd,43,45. Test 1 on Mon, 6/2, covers 9.1-9.5.
L-2 9.4 (pp.670,671 are VERY IMPORTANT), 9.5 (up to p.677, to be finished on Thursday). HW 9.4: 1,3,7-17odd,21,23,25,29,33; 9.5: 1,3,7,9.
L - 1 9.1,9.2, 9.3(omit p.665). HW 9.3: 1-15odd (when asked about an angle, it is enough to provide the cosine of that angle), 33(to be aware of that formula); HW 9.1: 3,7,9,11,13,15a,29,31; 9.2: 3,4,15,17,19,25.
Grading policy: attendance=2units; tests: 2,3,3 units (respectively); Final=6 units. The two lowest from these 16 grades will be dropped. The average of the remaining 14 will determine the grade for the class.
Text: Calculus by J. Stewart, 2nd edition
Most important pre-requisite sections from Calc I, Calc II (same 2nd edition) are 1.3, 1.7; 3.1,2,4,5; 4.2,3; 5.2,3,5; 6.1,2,3; 8.6,7,9.
Course Outline:
Chapter 9: Vectors and the Geometry of Space
Chapter 10: Vector Functions
Chapter 11: Partial Derivatives
Chapter 12: Multiple Integrals
Chapter 13: Vector Calculus
Homework will be assigned on a regular basis. It is not collected but you are welcome to turn (part of) it (you'll get it back with my comments which might be helpful as part of your tests' preparation).
THE STUDENTS HAVE THE RESPONSIBILITY TO KNOW THE PROVISIONS OF the CAS Academic Conduct code, copies of which are available in CAS 105. Cases of suspected academic misconduct will be referred to the Dean's Office.
Some of the students do not have BU ACS accounts: They can apply by following the directions found at http://www.bu.edu/computing/accounts/apply/ . Once they get ACS accounts, they will automatically be added to the site.
A (tentative) day-by-day coverage (below) is subject to change. (Read from below)
L-14 13.6 finished, 13.7 (p.975 won't be tested), 13.8 (p.982 won't be tested); 13.4 shown to be a special case of 13.7; p.985 Summary discussed. HW 13.7: 1,3,5,7; 13.8: 4,7.
L-13 13.2 (formula 13 is fundamental, overall: applications presented in Ch.13 won't be tested, just the theory; you are not responsible for the proofs), the notion of an arc length as a natural parameter has been presented from 10.3); 13.3(pp.942-943 won't be tested), 13.5 (omit pp.957,958), 13.6 (to be finished). HW 13.2: 5,11,13,17,31,33; 13.3: 3-9odd,13-21odd; 13.5: 1,5,10,17, (21,22,23,24 to be aware about their existence); 13.6: 9,17.
L-12 12.7(last two pages won't be tested),12.8,12.9(the presentation differs from the text's one, formulas remain the same),13.1. HW 12.7:1-15odd, 12.8: 7,9,11,15,17,19; 12.9: 1,3,5,11,13; 13.1: 21,23,29,30,31,32. Reading of 13.3-13.5 (in advance) will be helpful. In 13.2 formula 13 is the key.
L-11 12.3,12.4(with a more general presentation),12.6,12.7(up to Ex.1). HW 12.3: 1-23odd,29-37odd; 12.4: 1-11odd; 12.6: 1-9odd,21
Test 2, then L - 10. 12.1 (subsection on pp.844-846 won't be tested), 12.2. HW 12.1:1,3; 12.2: 1-11odd, 17,19,21. Also, a new portion of the text is attached (see the very bottom of this file).
L - 9 11.7 finished, questions taken, a few examples discussed.
L-8 11.6,11.7 (Ex.4 won't be tested) (the last 11.7 subsection to be covered on Thursday). HW 11.6: 5-15odd,19-25odd,33(enough to be aware about #33 formulas),35,37,41,45; 11.7: 1,3,5,9,,11,13,23,25,27,31,33.
L - 7 11.3 (omit pp.775,776), 11.3 HW is in L-6 below; 11.4 (pp.779,780,787,788,only), 11.5 (pp.790-794, only). HW 11.4: 1,3,33,35; 11.5: 3,5,7,9.
L-6 9.7(Ex.8 optional),11.1(Ex.1,2,5,10 won't be tested),11.2. In 11.3 the partial derivatives have been presented by examples. HW 9.7:5,7,9,21,23; 11.1: 5,7,13,15; 11.2: 1,7,9,11,15; (Try to start solving 11.3 ## like 13-310dd,35,37).
L-5 10.2, 10.5. HW 10.2: 3,5,9,11,19,21,31,33; 10.5: 1,3,17,19,21.
Test 1, then L-4: 9.6 (Ex.3 won't be tested), 10.1 (pp.708,709 won't be tested). HW 9.6: 3-25odd; 10.1: 1,3,13,15,19,27. Be aware of the #33 laws.
Homework will be assigned on a regular basis. You are not getting any formal credit for the HW. However, welcome to turn (part of) it in. I'll be returning with my comments (sometimes wrong approach provides correct answers; on tests I'll be looking for proper reasoning as well as for right answers)
1) MODERN introduction to DIFFERENTIALS
(not in the Stewart's book, those interested might check with the well-known Calculus by Kaplan. The Stewart's presents simplified version of differentials. I will design all test problems in such a way that technically a student will be able to get up to "A" on the basis of the Stewart's book alone). A more detailed version of this text is suggested as a "hand-out".
It is based on the important notion of DUALITY. A dual to a vector space V is the totality W of all linear functions on V. Of course, W, itself, is a vector space, since the sum f + g of two linear functions is a linear function; and, if s is a scalar, sf is a linear function. W contains a zero element (which assignes a number zero to each vector v from V). All usual properties of vector spaces take place for W. Always, they are of one and the same dimension: dim W = dim V. Consider the x-axis as a one-dimensional vector space V, "i" is its basic vector. By "dx" mathematicians denote such a basic element of the dual space W, that the value of dx on i is the number 1. Since dx is a linear function, this determines dx completely. "dx" is defined everywhere on V. The "d" can now be interpreted as an OPERATOR of DIFFERENTIATION. It maps functions into one-forms, one-forms into two-forms, etc. All usual rules apply (linearity, the product rule, etc.). Now, dx can also be interpreted as a result of application of an operator "d" to a coordinate function "x".