Math 20E. Vector Calculus - Fall 2011


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.


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.

Syllabus, Schedule and summary of lectures.

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.

Homework Assignments

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. -------------------------------------------------------------------------------

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