Math 20E: Vector Calculus, Winter 08, (Hans Lindblad)

Meetings  Texts  Exams  Review  Practice Exams  Syllabus  Schedule  Lecture summary  Homeworks
ANNOUNCEMENTS:


Meetings

It is important that you have a look at the material before the lectures since it will help you to follow the lectures, Why? 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.

Texts

Follow the link above for more study material. It can sometimes be helpful with a different perspective: Many multivariable calculus texts contain an easy introduction to vector calculus. Davis, Snider, Vector Analysis, Quant Systems 1995, used to be the text for 20E, see old syllabus/notes. Shey, Div, grad, curl and all that Norton 2005 is a popular introduction from a physics perspective. Colley, Vector Calculus Prentice Hall 2006, is similar to Marsden-Tromba. For further study, of the geometry of curves and surfaces / vector calculus on manifolds Math 150A/B, of partial differential equations 110,132A or physics classes. For deeper analysis and proofs 140, 142, or Hubbard & Hubbard, Vector Calculus, Linear Algebra, and Differential Forms which is the text for the Honors Calculus sequence 31ABC.

Exams

Bring identification to exams. No calculators, books or notes are allowed in exams. No make-up exams. The exams cover material in homeworks due before the exams, and corresponding lectures and reading. Further information about the exams will be given in lectures, reviews or on the web, but not on an individual basis. Questions about the grading should be brought up directly with your TA. This page of formulas will be printed on the 1st midterm, this page on the 2nd and this page on the final. Solutions to midterms will be given in sections.

Review. Go over questions from practice exams. Review questions. Review sessions:

Practice Exams and Solutions to Some of the exams.

mid1w05mid1w03mid1f98mid2w05mid2s00mid2f98fins00finw99finf98,
mid1w05smid1w03smid1f98smid2w05smid2s00smid2f98sfinw99sfinf98s.

Exams before 04 are for an old syllabus. Line integrals and conservative fields will not be on midterm 1 but on midterm 2. Instead we might ask about Taylor series, the chain rule or the derivative matrix.

Syllabus

   1.1-2 Vectors, scalar product, 1.3 Cross product, determinants. 1.5 Matrix multiplication, linear maps.
   1.4, 2.1 Cylindrical, spherical coordinates, surfaces, (2.2)-2.3 Derivatives, 2.4-5 Curves, the chain rule.
   2.6 Gradient, (3.1)-3.2 Taylors theorem, (3.5 Implicit and inverse function theorems).
   4.2 Parametrized curves and arclength, 4.3 Vector fields and flow lines, 4.4 Divergence and curl.
   5.1-5.4 Areas and double and iterated integrals, 5.5 Triple integrals, 6.1-6.2 Change of variables.
   7.1.2 Path, line integrals, 7.3 Parametrized surface, 7.4 Area of surface, 7.5-6 Integrals over surfaces.
   8.1 Green's theorem, 8.2 Stokes theorem, 8.3 Conservative Fields, 8.4 Gauss's Theorem.
   (8.5 Maxwell's equations, Fluid mechanics), (8.6 Differential forms.)

1.1-4, 2.1-6, 3.1, 4.2, 5.1-5 are review of 20C, but matrix notation for the derivative is new. 1.5-only cover matrix multiplication and linear transformation. 2.2-an intuitive definition of limit suffices. 3.1-only recall equality of mixed partials. If time cover 3.5/8.5-6. Surface integrals is the hardest part. Thinking geometrically and physically helps understanding concepts but is not needed to do problems.

Schedule and summary of lectures (tentative).

If you click on the day you might find a summary of the lecture, without the important pictures.
It is important that you have a look at the material before it is covered in the lectures. Why?

 wk  date  Monday  Wednesday  Friday
  1  1/7  1.1-1.2  1.3,1.5  1.4,2.1,(2.2)
  2  1/14  2.3-2.5  2.5-2.6  (3.1)-3.2
  3  1/21  Holiday  4.2  4.3-4.4
  4  1/28  4.4  5.1-5.3  5.4-5.5
  5  2/4  Exam  6.1-6.2(3.5)  6.2
  6  2/11  7.1-7.2  7.2-7.3  7.4
  7  2/18  Holiday  7.5  7.6
  8  2/25  7.6  8.1  8.2
  9  3/3  Exam  8.3  8.4
 10  3/10  8.5  8.6  review

In the future I might move 4.2 arc length and do it later with 7.1 path integrals. (its just half a lecture) Perhaps I will also show that the derivative matrix of the inverse is the inverse of the derivative matrix.

Homework Assignments (tentative)

Homeworks due in box on 6th floor of AP&M by 8pm. No late homeworks. 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. Solutions to homeworks will be available for download below after they are due. Attempt to solve all problems yourself to learn it. Why?

HW #1 Due 1/10   
1.1:16,    1.2:8,14,23,    1.3:6,7,12,16a ,    1.5:7,18,    review ch 1:29,

HW #2 Due 1/17   
1.4:4ab,    2.1:6,11,21,28,    2.3:6a,8cd,12c,18,20,    2.4:8,18,    2.5:4,5c,15,

HW #3 Due 1/24   
2.5:8,10,14,    2.6:3c,4a,6a,9,12,24b,    3.2:2,6,

HW #4 Due 1/31   
4.2::2,10,11*,    4.3:3,4,9,14,20,    4.4:4,5,8,18,20,26,

HW #5 Due 2/7   
5.1:1a,4,    5.2:2d,4,    5.3:2f,6,    5.4:2b,8,    5.5:4,11,

HW #6 Due 2/14   
6.1:2,3,4,10,    6.2:1,4a,5,8,9,19,29,    7.1:2a,4a,    7.2:1c,2a,3,12*,15*,18*,

HW #7 Due 2/21   
7.2:12,15,18,    7.3:2,5,12,14,    7.4:1,4,6,11,    7.5:2,4,8,10,

HW #8 Due 2/28   
7.5:6,15,    7.6:2,3,5,7,10,18,

HW #9 Due 3/6   
8.1:1,3d,4,9,12,13,14,20,    

HW #10 Due 3/13   
8.2:3,6,10,23,    8.3:4,7,10,12,13ac,20,24,    8.4:2,3,5a,8,

Grades

The grade is based on a total score calculated from 10% homeworks 20% each midterm and 50% final. The grade distribution will follow a curve with median grade a low B and median plus standard deviation an A-. Usually about 25% of students get As (i.e. A+, A or A-), 35% get Bs, and 30% get Cs. The exact borders are adjusted depending on various factors and typically vary up or down by 5%. Typically it ends up that you need about 80% total score for A-, 65% for B- and 40% for C-, but it varies with the level of the exams. Midterm 1: Max 40, Mean 26, Median 28, StDev 7. Midterm 2: Max 80, Mean 47, Median 47, StDev 14. Final; Max 80, Mean 32, Median 30, StDev 16.