For all vectors A, B, C in 3-space:
     There are scalars r, s, t (depending on the vectors) that are not all zero with rA + sB + tC = 0
                                               if and only if
     the scalar triple product is zero, that is,  [A,B,C] = 0.

Sec. 2.2:  2, 4

Due 4/13:  Sec. 3.1:  1, 4, 10(a,d), 16
Sec. 3.2:  2, 4
Sec. 3.3:  1, 3, 5, 6
Sec. 3.4:  4, 6, 7, 11
Sec. 3.5:  4, 5, 6
Sec. 3.6:  5
Sec. 3.8:  5, 10(a,b,g,h)
Sec. 4.1:  1, 3, 4, 5, 14, 15

Due 4/20:  Sec. 4.2:  3, 4, 7, 8
Sec. 4.3:  2(a,c,e), 3(a,c,e), 6, 8
Sec. 4.4:  1, 2, 7, 11 (Hint: (3.37)?)

I have been getting questions relating to reading and understanding mathematics.  In mathematics (and often in other subjects), the best way to develop an understanding of ideas is to look at examples, asking yourself what it means, if it is similar to things you've already seen, and how to calculate with it.  The course web page has a link near the top to material on reading and understanding mathematics (which is important in all math classes, especially starting with 20E) and on doing proofs (which is less important for 20E, but more important for later classes).
 

Due 4/27:  Sec. 4.6:  2, 4, 5, 6, 10 (Possible Hint: Consider |AXB|^2 + (A.B)^2 )
Sec. 4.7:  1, 8, 13
Sec. 4.8: 3(also describe region), 5(a)

GRADE GUIDELINES: A rough idea of how you are doing based on the midterm grade:  40 A / B break,   32 B / C break,  24 C / D-F break.  Congratulations to the 5 people who had a perfect paper and the several of you who missed only 1 or 2 points!

Due 5/4:  Sec. 4.7: 2(b) and Sec. 4.9: 2(b)
Sec. 4.9: 11, 22, 23
Sec. 5.1: 1, 6, 7, 8, 9  You may save calculation by noting that   F  =  |R|^{-3} R   in 9(e) and using (3.28) and (3.33).
Sec. 5.4: 7, 9, 11
Sec. 5.5: 2, 3 (Hint: (3.29)), 5

When I wrote up my notes after thinking about how to present Stokes' for class today, it was clear to me what I should say.  Somehow, between the note writing and class I "lost it" and made a mess of things even with my notes.  I apologize.  Here, I hope, is the way I intended to present the material.  ps   pdf

Change of variables in multiple integrals is not covered in the text and is only partially covered in 20C.  Homework will be assigned from Stewart (Calculus: Early Transcendentals, 5th ed.).  Copies of the problems will be available in pdf and ps formats on this web page.
If you have Stewart, I recommend reading at Section 15.9.  You may also want to look at 15.4 and 15.8.

Due 5/11:  Sec. 3.10: 11, 12  In #12 either, the answers are wrong or the problem has a typo.  You can either (i) solve the given problem or (ii) solve the problem with the typo fixed so that you get the answers in the book.
Sec. 3.11:  3(first part), 6(a,b,c), 9(a)
Stewart, 5th ed.  Sec. 15.9:  12, 14, 16, 17, 18 and two supplementary problems.  All online:   ps    pdf

Due 5/18:  Sec. 4.5: 2, 8, 9(a,b)
Supplementary problems for Section 4.5   ps   pdf

Due 5/25:  Sec. 5.2: 1, 9
Sec. 5.3:  3, 4

Wed. 5/26:  Exam covering material since last exam---through 5.3 plus know what Green's Theorem is.  (5.5 is just proof of Stokes' Theorem)   Solutions
Q: When and where is it?
A: At lecture time (11AM).
    If your last name starts with A-P: CSB 002.
    If your last name starts with R-Z: APM 2402.
Q: What can I use on the exam?
A: You may have one side of one sheet of notes --- handwritten, xeroxed, cut & pasted, or any combination.
You may NOT use your text or a calculator.
Q: What should I bring to the exam?
A: Your notes, your student ID, a blue book, and pen or pencils.
Q: Are we responsible for the material from the first exam which was through Section 4.4?
A: You're responsible in the sense that later material builds on earlier material.
Q: What about sections 5.2 and 5.3 --- they were on the recent homework?
A: You should be familiar with the terminology and the results in the theorems, but you will not be asked to apply them or to do any calculations requiring those sections.
Q: Do you have practice exams?
A: I post old exams, but since I have not taught this course for some time, none are posted.   I obtained the following link by asking other members of the department for old exams.

       http://www.math.ucsd.edu/~lindblad/20e/20e.html

ANNOUNCEMENT:  When your second exam is returned in section, it will contain your grade in the course up to that time, based on the two exams and the homeworks.  You will have the option of either accepting that grade or taking the final exam.
To check your grade, add your 7 highest homeworks, multiply by 0.3 and add your two exam scores.  (This weights homework about 16%.)  The maximum possible is 129.  Grade breaks are as follows:
                           A+/A/A-   above 95;     B+/B/B-   above 75;    C+/C/C-   above 60.
Q: How can I get an idea how I did on the exam before section?
A: I expect people to do about as well on this exam as on the first, so look at the solutions, estimate points, multiply by 0.8 to convert to first exam scale and look at the grade guidelines for the first exam.
Q: What if I take the final and do poorly on it?
A: If you hand in the final to be graded, it will count, regardless of how you do on it..  (Obviously, if you take it but do not hand it in, then it will not count.)
Q: How will the final compare with the midterms?
A: I expect it to be about twice as long.  Since you'll have had longer to understand the course material and since you'll have 3 hours for the exam, the problems will be somewhat harder.  There will be some short proofs.  However, I expect people to do as well on the final as on the midterms.
Q: Do the restrictions on notes and calculators still apply?
A: Yes, except that you may have BOTH sides of one sheet of notes.

Finals week office hours:  Prof. Bender Wed. 8-11    TA Shopple Thur. 1-5
 

Final exam solutions are available