Math 20E. Vector Calculus - Fall 09 - Hans Lindblad

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

Description:

Its essential in Fluid Mechanics, Electromagnetism and Geometry to take derivatives and integrate vector functions.

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

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.

Exams

Bring identification to exams. No calculators, books or notes are allowed in exams, but this page of formulas will be printed on the 1st midterm, this page on the 2nd and this page on the final. No make-up exams. The exams cover material in homeworks due before the exams, and corresponding lectures and reading, see review and practice exams. Questions about the grading should be brought up with your TA. Solutions to midterms will be given in sections.

Review and Practice Exams.

 Practice Exams:   mid1w05  mid1w03  mid1f98  mid2w05  mid2s00  mid2f98  fins00  finw99  finf98
 Some Solutions:   mid1w05s  mid1w03s  mid1f98s  mid2w05s  mid2s00s  mid2f98s  finw99s  finf98s
In the review we go over problems from practice exams and text. Study review questions and concepts in notes/text. Exams before 04 are for an old syllabus. Line integrals, conservative fields and potential 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  3.5 Implicit Function Theorem  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 cover matrix multiplication and linear transformation. In 2.2 an intuitive definition of limit suffices. In 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 the concepts.

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 sectiondate  Homework  Due 10am Friday after section 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,(no need to hand in again),  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 follows a curve with median grade a low B and median plus standard deviation an A-. About 25% get As (i.e. A+, A or A-), 35% get Bs, and 30% get Cs. The exact percentages are adjusted depending on various factors. Typically it ends up that you need about 80% total score for A-, 65% for B- and 40% for C-, depending on the exams.