Instructor:Hans Wenzl email: hwenzl@math.ucsd.edu
office: APM 5256,
Office hours: M:3:30-4:30, W:4:30-5:30 Please show up at least 15 minutes before the end of the office hour. I may have another office hour after the given one, or I may have to go somewhere else.
Teaching assistants:
Sections B01 and B02: Jacob Rhodehamel, email: jrhodeha@ucsd.edu
Sections B03 and B04: Xin Tong, email xit040@ucsd.edu
Sections B05 and B06: Matvey Yutin, email: myutin@ucsd.edu
Sections B07 and B08: Chuqing Shi, email: chs139@ucsd.edu
It is important that you have a look at the material before the lectures since it will help you to follow the lectures, see below for a tentative syllabus. Please ask questions in lectures, since if you don't quite understand something others may not understand either, and the explanations will help everyone understand better and keep the lectures at a pace you can follow. The best way to learn math is by doing examples so try to do all the homework problems and more similar problems. Let us know if you have any complaints and suggestions for improvements.
Text: Marsden and Tromba, Vector calculus, 6th edition
homework (28%), 2 midterms (24% each) and the final, part A and B (24% for each part). We will pick the three best parts of midterms and finals to calculate your grade.
We will drop the two worst homework scores for the homework component. There will be no make-up exams.
| Week | Monday | Tuesday | Wednesday | Thursday | Friday |
|---|---|---|---|---|---|
| 0 |
Oct 2
Chap 1.1-3 (Review)
|
||||
| 1 |
Oct 5
Chap 2.3 |
Oct 7
Chap 2.5 |
Oct 8
Discussion
|
Oct 9
Chap 3.2
|
|
| 2 |
Oct 12
Chap 5.1-3 |
Oct 14
Chap 5.4 |
Oct 15
Discussion
|
Oct 16
Chap 5.5
|
|
| 3 |
Oct 19
Chap 6.1 |
Oct 21
Chap 6.2 |
Oct 22
Discussion
|
Oct 23
Chap 4.3
|
|
| 4 |
Oct 26
Chap 7.1 |
Oct 28
Review |
Oct 29
Discussion
|
Oct 30
Exam 1
|
|
| 5 |
Nov 2
Chap 7.2 |
Nov 4
Chap 7.3
|
Nov 5
Discussion
|
Nov 6
Chap 7.4
| |
| 6 |
Nov 9
Chap 7.5
| Nov 12
Discussion
|
Nov 13
Chap 7.5-6
|
||
| 7 |
Nov 16
Chap 7.6 |
Nov 18
Review |
Nov 19
Discussion
|
Nov 20
Exam 2
|
|
| 8 |
Nov 23
Chap 8.1 |
Nov 25
Chap 8.2 |
|||
| 9 |
Nov 30
Chap 8.4(4.4) |
Dec 2
Chap 8.4 |
Dec 3
Discussion
| Dec 4
Chap 8.3 |
|
| 10 | Dec 7
Catchup/Review |
Dec 9
Catchup/Review |
Dec 10
Discussion
| Dec 11
Review |
|
| 11 | Dec 14
Final Exam
11:30am-2:30pm |
Some lecture notes:
Lecture 6 Oct 14: x-simple regions, change of order of integration, mean value inequality
Lecture 8 October 19 Triple integrals, change of variables
Lecture 10 Oct 28: Change of variable theorem
Lecture 11 Oct 30: vector fields
Lecture 13 Nov 2: path integrals
Lecture 14 Nov: 4 line integrals
Lecture 15 Nov 6: Line integrals for gradient fields; parametrized surfaces
Lecture 16 Nov 9: Surface area
Lecture 17 November 13 Surface integrals of functions
Lecture 18 Surface intgrals of functions and of vector fields
Lecture 19 November 18 Review problems
Lecture 21 November 25 Curl, surface integrals for vector fields
Lecture 23 Dec 2 Stokes' Theorem, Conservative vector fields
Lecture 24 Ch 8.4 Gauss Divergence Theorem
Lecture 25 Surface integrals for functions and vector fields, Gauss Law
Lecture 26 Review Double Integrals, change of variables, path and line integrals
Homework assignments Homework is to be turned in via gradescope Grade Scope for HW this quarter. You will receive an email prompt some time during the second week notifying you of your gradescope enrollment and providing a link to set up your personal account.
You can watch this video which explains how to scan and submit HW online.
Attempt to solve all problems yourself to learn it. Homeworks are usually supposed to be turned in on Please turn in your homework on the given date by 8pm. Review homework need not be turned in as the material was covered in Math 20C.
But you are expected to be familiar with them:
Due October 10 (midnight):
Misprints and hints for homework assignment: 2.3 #20 This question
doesn't make sense! It should say "Consider, for each
function, the level set which passes through the point (1,0,1)
- in other words, the surface in R^3 defined by the equation
f(x,y,z)=c where c=f(1,0,1). Find the equation of the tangent
plane to this surface at the point (1,0,1)." Hint: if we move in R^3 from
(1,0,1) to the nearby point (1,0,1)+h (for some small vector
h), the linear approximation tells us that f changes by Df
(evaluated at (1,0,1)) multiplied by h. If we want f to _stay
constant_ - that is, h is moving us _along_ (=in a direction
tangent to) the surface, we need this change to be 0. 2.3. #28 For this exercise
"f: R^n -> R^m is a linear map" means that
f is of the form f(x) = Ax+b, where A is an mxn matrix and b
a fixed m-vector). Usually, in linear algebra f being linear
means satisfying the laws f(x_1+x_2) = f(x_1) + f(x_2) and
f(lambda.x) = lambda.f(x), i.e. it is of the form f(x) =
Ax without the b). I think they actually intended the linear
algebra sense, but you should be able to work out the
derivative in both cases and then see what is special about
the second... 2.5 #8 Use the matrix form
of the chain rule to do this. I know you can also do it by
direct substitution, but it's important to learn how to apply
the rule. (You have to do essentially the same calculations
either way, but the matrix rule organises them more clearly
and becomes more and more useful as the functions get more
complicated or the numbers of variables increase.) 2.5 #20 This is a
ludicrously badly-written question - I mean that without the
hint it makes absolutely no sense at all. It should probably
say something like this: "Consider three variables
x,y,z which are related by an implicit equation F(x,y,z) = 0.
In principle you ought to be able to solve for each variable
and write it as a function of the other two, obtaining
functions x=f(y,z), y=g(x,z), z=h(x,y), though in
practice it's probably impossible for us to do this using
explicit formulae. (Consider for example, something nasty like
F(x,y,z) = x^4 + y^4 + z^4 + xyz - 1! If you just
consider that F(x,y,z)=0
describes a surface in R^3 , you ought to be able to see why
functions f(y,z) etc ought to exist, whether or not we know
how to write them down explicitly.) By differentiating the three
formulae of the form F(f(y,z),y,z)=0, show that
(dg/dx)(dh/dy)(df/dz)= -1."
Due October 17:
Due October 24:
Information about first midterm
CONTENT: The midterm will be a 50-minute exam, similar in nature to the practice exams, see below. You will have an additional 15 minutes to scan and upload the exam (see details below). It will cover everything up to and including HW 3: in terms of the book, this means sections 2.3, 2.5, 3.2, 5.1-5.5 and 6.1-6.2.
RULES: It will be an open book exam: you will be allowed to consult the textbook, your own notes or previous homework, and the notes posted on Canvas or my webpage by me or by the TAs, but no other resources may be used. In particular, you may not use any online resources, any other printed material (such as solution manuals), or any form of calculator (all arithmetic on the exam will be easy!) and you must not communicate in any way with anyone else during the exam. You will be required to write, sign and submit with your work a statement certifying that you have followed the regulations. Breaches of the rules will be reported to the Academic Integrity office.
TECHNICAL INFORMATION: The exam will be presented through Gradescope in a form similar to a homework assignment, except that it will be timed. When you log in to Gradescope you will be able to see (and/or download) a pdf copy of the exam paper. You should write your answers on your own paper, scan and upload them to Gradescope within 65 minutes - that's 50 minutes official exam time, plus 15 minutes allowance for upload time. (Please assign the pages corresponding to the questions, just as you do for homework.)
DATE AND TIME: The exam will take place during normal class time: 1-1.50pm Friday Oct 30th PDT. Students who currently live in different time zones for whom the time would be very inconvenient should contact me about the possibility of taking the exam at another time by Tuesday, October 27. If you do so, please state where you currently live! Only students who have been approved before the exam can take it at a different time.
Some practice exams: The exam in this class may be different. Question 3 in the second practice exam has not yet been covered in this course. Practice1 Practice2
Due November 7 (get started soon):
Due November 14:
Information about Midterm 2 Essentially the same rules apply as for the first midterm,
so please read them again.
The material will go until including Section 7.5. So it will primarily cover
Sections 4.3 and Sections 7.1 until including 7.5. While I will not ask questions specific
to previous sections, you need to know the material as far as necessary for solving problems
from the relevant sections.
The following problems need not be
turned in, but will be relevant for the midterm:
Some practice exams. The second practice exam contains solutions. You need not worry
about problems involving integration of vector fields over surfaces and Green's Theorem.
But you do need to worry about integrating vector fields over curves and about parametrizing surface .
Exam2Practice1
Practice2
Due November 29 (Sunday only this time):
Due December 5:
Relevant for final; need not be turned in:
Some practice exams. The final in this class may be different. PracticeFinal1 PracticeFinal2
The following is a review sheet from another professor. It may help with reviewing the material: review sheet
For those of you who want to review their midterms, here are the problems: first midterm second midterm
Solutions to some practice final problems:
Some solutions