Math 20E. Vector Calculus - Fall 09 - 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, 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 used to be the text for 20E, see old syllabus/notes. Shey, Div, grad, curl and all that is a popular introduction from a physics perspective. Colley, Vector Calculus is similar to Marsden-Tromba. For further study: Math 150A. The differential geometry of curves and surfaces, Math 150B. Vector Calculus on Manifolds and Differential Forms, Math 110,132A Partial Differential Equations (see also 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 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 and Practice Exams.

The review consist of going over problems from practice exams and book, e.g. Review questions
 Paractice Exams:   mid1w05,  mid1w03,  mid1f98,  mid2w05,  mid2s00,  mid2f98,  fins00,  finw99,  finf98,
 Some Solutions:   mid1w05s,  mid1w03s,  mid1f98s,  mid2w05s,  mid2s00s,  mid2f98s,  finw99s,  finf98s.
Exams before 04 are for an old syllabus. Line integrals and conservative fields will not be on midterm 1.

Syllabus, Schedule and summary of lectures.

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
  0  9/21  No Class  No Class  1.1-3 Overview, vector operations
  1  9/28  1.3 Cross product, determinants,  1.5 Matrices-linear maps  1.4 Cylindrical, spherical coord.,  2.1 Graphs-surfaces, (2.2 Limit)  2.3 Derivative matrix,
 2.4 curves, 2.5 chainrule
  2  10/5  2.5 Chain rule, 2.6 Gradient  3.2 Taylor's theorem-vector func.  4.1-2 Curves, arc length
  3  10/12  4.3-4 Vector fields-flow lines  4.4 Divergence and curl  5.1-3 Double-, iterated-integrals
  4  10/19  Exam  5.4 Changing order of intergration  5.5 Tripple intergrals  6.1 Change of variables,geometry
of maps in plane(3.5 Inv Func Th)
  5  10/26  6.2 Change variables in integrals  7.1 Path-, 7.2 Line-integrals  7.2-3 Parametrized surface
  6  11/2  7.4 Area of surface  7.5 Integrals over surfaces  7.6 Integrals over surfaces
  7  11/9  7.6 Integrals over surfaces  Holiday  8.1 Green's thereom
  8  11/16  Exam  8.2 Stokes' theorem  8.3 Conservative fields
  9  11/23  8.4 Gauss' theorem  8.5 Electromagnetism, Fluids  Holiday
 10  11/30  8.6 Differential forms  TBA  Review
 11  12/7  No class  Final 3-6pm  No class
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. In 1.5 we only cover matrix multiplication and linear transformation. In 2.2 an intuitive definition of limit suffices. From 3.1 we only recall equality of mixed partials. If time cover 3.5 Inverse Function theorem, 8.5 Electromagnetism, Fluids, 8.6 Differential Forms. Surface integrals is the hardest part. Thinking geometrically and physically helps understanding concepts but is not needed to do problems. One could move 4.2 later with 7.1 since its just a half a lecture. It would also be natural to to also show that the derivative matrix of the inverse is the inverse of the derivative matrix.

Homework Assignments (tentative)

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?
wk  date  Homework (tentative)  Due 8pm in box 6th floor APM. No Late homeworks.   Solutions
  1  10/1  1.1:16,  1.2:8,14,23,  1.3:6,7,12,16a,  1.5:7,18,  review ch 1:29,  1.4:4ab,  2.1:6,11,21,28    
  2  10/8  2.3:6a,8cd,12c,18,20,  2.4:8,18,  2.5:4,5c,15,8,10,14,  2.6:3c,4a,6a,9,12,24b,  3.2:2,6,  
  3  10/15  4.2::2,10,11*,  4.3:3,4,9,14,20,  4.4:4,5,8,18,20,26,    
  4  10/22  5.1:1a,4,  5.2:2d,4,  5.3:2f,6,  5.4:2b,8,  5.5:4,11,    
  5  10/29  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*,    
  6  11/5  7.2:12,15,18,  7.3:2,5,12,14,  7.4:1,4,6,11,  7.5:2,4,8,10,    
  7  11/12  7.5:6,15,  7.6:2,3,5,7,10,18,    
  8  11/19  8.1:1,3d,4,9,12,13,14,20,  8.2:3,6,10,23,    
  9  11/25  Holiday-No homework      
 10  12/2  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.