Math 20E: Vector Calculus,
Spring 03,
(Hans Lindblad)
Meetings
Texts
Exams
Review
Practice Exams
Syllabus
Schedule
Lecture Summary
Homeworks
ANNOUNCEMENTS:
It is important that you have a look at the material
before it is covered in the lectures, see schedule
where you also find lecture notes.
Please ask questions in lectures,
sections and office hours.
If you don't quite understand something others may not
understand either.
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 if you have time.
Also please let us know if you have any
complaints and suggestions for improvements.
It can be helpful with a different perspective.
Many multivariable calculus texts e.g.
Stewart Calculus early transcendentals,
contain an easy introduction to vector calculus.
Some books are on reserve in the library.
Colley, Vector Calculus,
Marsden & Tromba, Vector Calculus,
Barr,Vector Calculus
use linear transformations to explain derivatives and surface area.
Shey, Div, grad, curl and all that
is a popular introduction from a physics perspective.
For further study,
of the geometry of curves and surfaces and vector calculus on manifolds
Math 150,
of partial differential eqns
132
or physics classes in fluid mechanics or electromagnetism.
For analysis proofs 140,142 or
Hubbard & Hubbard,
Vector Calculus, Linear Algebra, and Differential Forms
- 1st Midterm Test will be given on 4/28 during class time.
It covers HW #1-4.
- 2nd Midterm Test will be given on 5/19 during class time. It covers HW #5-7.
- Final Examination will be given 6/9, 3-6pm. It covers HW #1-10.
Bring identification to exams.
No calculators, books or notes are allowed in exams.
No make-up exams.
The exams can have questions about anything covered in homeworks
due before the exams, lectures
or assigned 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.
Review - going over questions from the practice exams.
- Review for 1st Midterm Test: Sunday 4/27, 5-6pm in York 2722
- Review for 2nd Midterm Test: Sunday 5/18, 5-6pm in York 2722
mid1w03,
mid1s00,
mid1w99,
mid1f98,
mid2s00,
mid2w99,
mid2f98,
fins00,
finw99,
finf98,
mid1w03s,
mid1s00s,
mid1w99s,
mid1f98s,
mid2s00s,
mid2w99s,
mid2f98s,
finw99s,
finf98s.
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.
Week 1: 1.1-1.6, 1.8-1.13 :
Scalar and vector product, equations of lines and planes,
determinants.
Week 2: 2.1-2.2, 3.1-3.2 :
Curves, velocity, tangents and arclength.
Level surfaces and gradients.
Week 3: 3.3-3.5, 3.7 :
Flow lines, divergence and curl. Taylors formula.
Week 4: 4.1-4.4,(4.5):
Line integrals, simply connected domains, conservative and irrotational fields
Week 5: 15.1, 15.6
Double and triple integrals, change of variables,
cylindrical and spherical coord.
Week 6: 4.6-4.8:
Surface area, surface integrals and flux.
Week 7: 4.9:
Introduction to Divergence Theorem and Stokes' Theorem.
Week 8: 4.9, 5.1 :
Divergence Theorem.
Week 9: 5.4-5.5 , 5.2, (5.3):
Greens and Stokes Theorems, Laplace Equation.
Week 10: (5.7)-5.8:
Orthogonal transformations. Electromagnetism or Differential forms
or Review.
Sections 15.1, 15.6 refers to the handout.
Sections 1.1-1.13, 2.1-2.2 and 3.1-3.2 are review from 20C.
The change of variable theorem in the handout was not in 20C
but is in the book, see syllabus for
20C.
Solutions to homeworks will be available for download below after they are due.
All homeworks should be handed in in section
but we do not have resources to grade all problems.
We will grade 3-4 problems on most
assignments but some might be returned ungraded.
No late homeworks. The lowest homework score will be discarded.
(TBA=to be announced i.e. more to come, x*=problem x will not be graded)
HW #1 Due 4/3
1.5: 10,
1.7: 1,
1.8: 1, 8,
1.9: 4, 7, 21,
1.10: 1f, 6,
1.12: 1a, 2, 6, 13, 22,
1.13: 3, 7, 8.
HW #2 Due 4/10
2.1: 1, 3,
2.2: 2, 5, 8,
2.3: 3, 5,
3.1: 1, 4, 5, 10a, 13, 16, 32-34
HW #3 Due 4/17
3.2: 2, 4,
3.3: 3, 10-12,
3.4: 3, 4, 6, 10, 13,
3.5: 4, 9, 10,
4.1: 1, 2, 3, 7, 8.
HW #4 Due 4/24
4.3: 1, 2ac, 3ac, 4, 5, 6,
4.4: 1ade, 6, 7, 10,
HW #5 Due 5/1
4.5: 2, 8, 9,
3.7: 2,
Handout:
15.1: 6, 7,
Review: 16,
Misc.: 22,
HW #6 Due 5/8
Handout:
15.6: 3, 6, 7, 14, 18, 23,
Review: 23, 26, 29, 31,
Misc.: 26,
Book:
4.6: 1, 3, 5, 6, 10.
HW #7 Due 5/15
4.7: 3, 4, 6, 10, 11, 12, 15, 16, 18, 19,
4.8: 1, 4, 5, 6.
HW #8 Due 5/22
4.9: 3, 5, 7, 11, 13, 15, 16, 17, 20.
HW #9 Due 5/29
4.9: 21, 26, 34,
5.1: 6, 9, 10,
5.4: 4, 5, 7, 8, 9, 12,
5.5: 1, 2, 5, 6.
HW #10 Due 6/5
5.2: 1, 3, 5, 6, 9,
5.8: 1, 2a, 4, 5, 8, 23,
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 approximately a B.
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.