Math 20E. Vector Calculus - Fall 2011
- Lectures: MWF 9-10 in PCYNH 109
Lecture schedule and notes available below.
- Sections: Tuesdays and Homework
due in box on 6th floor of AP&M, solutions below.
- Office Hours:
Instructor: Hans Wenzl:
Email: Hans Wenzl
MW: 2:30-3:30 and by appointment (just talk to me after class, or email)
TA for sections A01, A02:
James Hall in AP&M 5748
Email: James Hall
TA for sections A03, A04:
Maximilian Metti M1-2 in AP&M 5768
Email: Maximilian Metti
TA for sections A05, A06: Jon Middleton Th3-5pm AP&M 6432
Email: Jon Middleton
It is important that you have a look at the material
before the lectures since it will help you to follow the lectures,
see the schedule
where you also find lecture notes.
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.
It can be helpful with different perspectives:
Multivariable calculus texts
give an easy introduction.
Davis, Snider, Vector analysis
used to be the text.
Colley, Vector calculus
is similar to the text.
Shey, Div, grad, curl and all that
is a popular introduction from a physics perspective.
Kettler Multivariable calculus, applications and theory
is free. Online
Lectures in Multivarible Calculus
Further study:
150A Differential geometry of curves & surfaces,
B Vector calculus on manifolds, differential forms
Partial Differential Equations
110A,B,
Physics classes.
Analysis-proofs 140, 142 or
Hubbard, Hubbard,
Vector calculus, linear algebra, and differential forms
-the Honors Calculus 31 text.
- Midterm 1 will be on 10/19, 9-10am
in WLH 2005 for sections A01, A02, A03 and in the class room for sections
A04, A05, A06.
- Midterm 2 will be on 11/16, 9-10am
in .
- Final Exam will be on 12/07/2011, 8:00-11:00am
in .
Bring identification to exams.
No calculators, books or notes are allowed in exams, but
you will be allowed one hand-written 'cheat sheet'.
The exams cover material in homeworks due before the exams,
and corresponding lectures and reading.
Questions about the grading should be brought up with your TA.
Calculation of Grade
Your grade will be calculated
as the better of the two options as follows:
Option 1:
homework (10%), 2 midterms (20% each) and the final (50%).
Option 2: homework (10%), the better of the 2 midterms (20%) and the
final (70%)
For both options
we will drop your worst homework score for the homework component.
Below you find a tentative syllabus for the class. We may possibly go a little
faster or slower in the course.
It is important that you have a look at the material before it is covered
in the lectures. For additional info, see below this table.
wk |
date |
Monday |
Wednesday |
Friday |
0 |
9/19 |
No Class |
No Class |
1.1-3 Overview, vector operations |
1 |
9/26 |
1.3 Cross product, determinants,
1.5 Matrices-linear maps |
2.1 Graphs-surfaces, (2.2 Limit) |
2.3 Derivative matrix,
2.4 curves, 2.5 chainrule |
2 |
10/3 |
2.5 Chain rule, 2.6 Gradient |
3.2 Taylor's theorem-vector func. |
4.1-2 Curves, arc length |
3 |
10/10 |
4.3-4 Vector fields-flow lines |
4.4 Divergence and curl |
5.1-3 Double-, iterated-integrals |
4 |
10/17 |
5.4 Changing order of intergration 5.5 Triple integrals |
Exam |
6.1 Change of variables,geometry
of maps in plane(3.5 Inv Func Th) |
5 |
10/24 |
6.2 Change variables in integrals |
7.1 Path-, 7.2 Line-integrals |
7.2-3 Parametrized surface |
6 |
10/31 |
7.4 Area of surface |
7.5 Integrals over surfaces |
7.6 Integrals over surfaces |
7 |
11/7 |
7.6 Integrals over surfaces |
8.1 Green's thereom |
Holiday |
8 |
11/14 |
8.2 Stokes' theorem |
Exam |
8.3 Conservative fields |
9 |
11/21 |
8.4 Gauss' theorem |
8.5 Electromagnetism, Fluids |
Holiday |
10 |
11/28 |
8.6 Differential forms |
3.5 Implicit Function Theorem |
Review |
11 |
12/8 |
No class |
Final 8-11am |
No class |
The schedule was taken from
Professor Lindblad's
course page.
If you go to this page, you will find a similar syllabus (with slightly
different dates); if you click on the appropriate chapter, you will find
Lindblad's LECTURE NOTES which may still be useful for our lectures as well.
All homeworks should be handed in, but we only have resources to grade 3-4 problems
per set and some sets might be returned ungraded.
The lowest homework score will be discarded.
Attempt to solve all problems yourself to learn it.
Homeworks are usually supposed to be turned in on
Wednesdays. An exception will be the first week,
when it is on Friday. There may be no homework due in
exam weeks. Mailboxes will be available on the 6th floor
of APM. Please turn in your homework on the given date
by 5pm.
for 9/30: Sec. 1.1: 16, Sec. 1.2: 8, 14, 22, Sec. 1.3: 6, 7, 12, 16a, Sec. 1.5: 4, 18
for 10/5: Sec. 2.1: 6, 11 (level sets only), 21, 28, Sec. 2.3: 6a, 8cd, 12c, 18, 20, Sec. 2.4: 8, 18, Sec. 2.5: 4, 5c, 15, 8, 12,
for 10/12: Sec. 2.6:3c,4a, 5c, 6a,9,12, Sec. 3.2:2,6, Sec. 4.2:2,8,10,
Sec 4.3: 5,6,9,14, (Recall that x'' = a^2 x for a function x=x(t) has
the solution x(t)= c exp(at) + d exp(-at) for constants c and d).
for 10/19: need not be turned in, but relevant for midterm:
Sec. 4.4: 4, 8, 20, 26.
for 10/26: Sec. 5.1: 1a, 10, Sec. 5.2: 2d, 4, Sec. 5.3: 2b, 8,
Sec. 5.4: 2b, 8, Sec. 5.5: 4, 11, Sec. 6.1: 2, 3, 4, 10
Midterm I: The first midterm takes place on October 19 in class
for students in sections A04, A05, A06, and in WLH 2005 for students in
sections A01, A02, A03. The material will go until Section 4.4. Exam problems
will be similar to homework problems (+ problems listed above for
Section 4.4) or problems in the practice exam posted below.
You are allowed one hand-written cheat-sheet (you can use both sides),
but no further notes, books or calculators.
Practice test
for Midterm I
for 11/02: Sec 6.2: 1,4a,,8,9,19, 25, 29, Sec 7.1: 2a,4a,
Sec 7.2: 1c, 2a, 3, 12,15,18,
for 11/09: Sec 7.3: 2, 5, 12, 14, Sec 7.4: 1, 4, 6, 11, Sec 7.5: 2, 4, 6, 8, 10,
for 11/23: Sec 7.6: 2(look at example 4 in book),3, 5, 7, 10,
Sec. 8.1: 1, 3d, 4(see Theorem 4), 9, 12, 13, Sec, 8.2: 11
for 11/30: Sec 8.2: 3, 6, 10, Sec. 8.3: 4, 7, 13ac, Sec. 8.4: 2, 3, 5a, 8
Review Session: Given by Max Metti at CENTR 109 on Friday, 4-5.
Solution to Problem 5 in Section 7.6
Final: The final will be cumulative, with an emphasis on
the material after the second midterm. I have posted a practice final
below which should give you some idea. The usual rules apply for the
final: one cheat sheet (both sides OK), no calculators, no books.
Location:
Students from Section A01, A02 (TA: Jimmy Hall): PCYNH 122
Students from the other sections (TA: Max Metti, Jon Middleton): class room PCYNH 109
Office hours in finals week: M1-2, T4-5
Practice final
Unfortunately, there is no official solution set available for the practice
exam. But you are welcome to ask questions about the practice exam problems
in my or the TAs' office hours.
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Midterm II: The second midterm will take place on November 16
in class for students in sections A01, A02, A03 and in CENTR 212
for students in sections A04, A05 and A06.
Same rules will apply as for the first midterm. So, in particular, you
are allowed one hand-written cheat sheet, but no further notes, books or
calculators. The material will go until the last homework assignment,
i.e. until Section 7.5.
Practice test
for Midterm II