Math 20C: Multivariable Calculus, Fall 02, (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

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.

Review - going over questions from the practice exams.

Practice Exams and Solutions to some of the exams.

 mid1f02,  mid1s02,  mid1w02,  mid1w01,   mid2f02,  mid2s02,  mid2w96,   finf02,  fins02a,  finw02a,  
mid1f02s,  mid1s02s,  mid1w02s,  mid1w01s,   mid2f02s,  mid2s02s,  mid2w96s,   finf02s,  finw02as,  
No more solutions or exams will be posted. Why? You can ask about solutions to problems in reviews.

Schedule and summary of lectures (tentative)

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

 wk  date  Monday  Wednesday  Friday
  0  9/23  ------  -------  10.1
  1  9/30  10.2  10.3  10.4,10.5*
  2  10/7  12.1, 12.2  12.3#  12.4#
  3  10/14  12.5  12.6#  12.7, review
  4  10/21  Exam  to 12.6  13.1, 13.2  13.3#
  5  10/28  14.1  14.2  14.3
  6  11/4  14.4#  14.5  14.6
  7  11/11  Holiday  14.7  14.7,14.8
  8  11/18  14.8, review#  15.1, 15.2  15.2, 15.3
  9  11/25  Exam   to 14.8  15.4  Holiday
 10  12/2  15.6  15.7  review
* Most of this was in 20B. # Some material may be omitted.

Syllabus (tentative)

Lec. 1: Sec 10.1: Curves defined by parametric equations.
Lec. 2: Sec 10.2: Tangents and areas for parametric curves.
Lec. 3: Sec 10.3: Arc length and surface area (of revolution).
Lec. 4: Sec 10.4-5: Polar coordinates; areas and lengths in polar coordinates
Lec. 5: Sec 12.1-2: Three-dimensional coordinate systems; vectors.
Lec. 6: Sec 12.3: The dot product, projections and components.
Lec. 7: Sec 12.4: The cross product.
Lec. 8: Sec 12.5: Equations of lines and planes.
Lec. 9: Sec 12.6: Cylinders and quadric surfaces.
Lec. 10: Sec 12.7: Cylindrical and spherical coordinates. Review.
Lec. 11: Sec 13.1-2: Vector functions and space curves and derivatives of those.
Lec. 12: Sec 13.3: Arc length and curvature.
Lec. 13: Sec 14.1: Functions of several variables; level curves.
Lec. 14: Sec 14.2: Limit and continuity.
Lec. 15: Sec 14.3: Partial derivatives.
Lec. 16: Sec 14.4: Tangent planes and linear approximations.
Lec. 17: Sec 14.5: Chain rule (without implicit differentiation).
Lec. 18: Sec 14.6: Directional derivatives and the gradient vector.
Lec. 19: Sec 14.7: Maximum and minimum values.
Lec. 20: Sec 14.8: Lagrange multipliers.
Lec. 21: Sec 15.1: Double integrals over rectangles.
Lec. 22: Sec 15.2: Iterated integrals.
Lec. 23: Sec 15.3: Double integrals over general regions.
Lec. 24: Sec 15.4: Double integrals in polar coordinates.
Lec. 25: Sec 15.6: Surface area.
Lec. 26: Sec 15.7: Triple integrals.

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 10/3
10.1: 4,6, 9, 18, 22,      10.2: 2, 6, 14, 20, 28, 32,      10.3: 4, 8, 18, 22, 24.

HW #2 Due 10/10
10.4: 58, 60, 64, 66,  10.5: 46, 48,  12.1: 6ab, 16, 22, 24,  12.2: 4, 14, 18,  12.3: 2, 8, 22, 26, 30, 40, 42

HW #3 Due 10/17
12.4: 3, 5, 15, 23, 26, 29,      12.5: 3, 9, 19, 25, 28, 31, 35, 47, 55, 62,      12.6: 5, 9, 19, 22, 23, 27, 33

HW #4 Due 10/24
12.7: 14, 21, 34, 36, 38, 40, 52, 56, 58,      13.1: 5, 8, 10, 12, 16, 22, 32.

HW #5 Due 10/31
13.2: 2, 4, 6, 14, 18, 24, 25, 34, 40,      13.3: 1, 4, 7, 11, 14, 21, 30,      14.1: 7, 11, 15, 23, 28, 30ace,

HW #6 Due 11/7
14.2: 7, 12, 24, 28, 30,      14.3: 8, 14, 18, 26, 36, 52, 64ab, 67, 69,      14.4: 2, 6, 12, 14, 17, 23, 29.

HW #7 Due 11/14
14.5: 3, 8, 11, 13, 19, 26, 33      14.6: 7, 13, 25, 29, 39, 45, 51, 53.

HW #8 Due 11/21
14.7: 1a, 3, 5, 11, 28, 29, 40, 42,      14.8: 4, 10, 18, 38, 39,      15.1: 5, 12.

HW #9 Due 12/5
15.2: 3, 9, 22, 26,   15.3: 12, 18, 22, 24, 40, 48,   15.4: 8, 11, 20, 24, 28,   15.6: 2, 3, 9,   15.7: 7, 9, 17

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 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.