Math 20C: Multivariable Calculus,
Fall 09,
(Jacob Sterbenz)
Meetings
Text
Overview
Exams
Review
Practice Exams
Syllabus
Schedule
Homeworks
Grading
ANNOUNCEMENTS:
-
Lecture: MWF
3:00-3:50, in PCYNH 106.
The lecture schedule is available below.
- Recitation sections: Tuesdays (see below for your section).
- Homework: Hand in your homework to your
TA's box on the 6th floor of AP&M. Due at 4p on Wednesdays (I can take them after class).
- Office Hours:
Instructor: Jacob Sterbenz
Office: AP&M 5101
Office Hours: Tue 1:00p - 2:00p.
email: jsterben@math.ucsd.edu
TA: James Berglund
Sections: Tue 2:00p - 2:50p (D01), 3:00p - 3:50p (D02), in U413.
Office: AP&M 6414
Office Hours: Mon 2:00p - 3:00p, Calculus Lab Mon 1:00p - 2:00p.
email: jberglun@math.ucsd.edu
TA: Zezhou Zhang
Sections: Tue 4:00p - 4:50p (D03), 5:00p - 5:50p (D04), in U413.
Office: AP&M 5412
Office Hours: Thu 3:30p - 4:30p, Calculus Lab Thu 12:00p - 1:00p.
email: z9zhang@math.ucsd.edu
TA: Hooman Sherkat
Sections: Tue 6:00p - 6:50p (D05), 7:00p - 7:50p (D06), in U413.
Office: APM 5412
Office Hours: Mon 1:50p - 2:50p, Calculus Lab Thu 12:00p - 1:00p.
email: hsherkat@math.ucsd.edu
- More help:
Tutoring Lab, OASIS, and Private Tutoring
The book store bundles the text with a study guide.
Follow the link above for more study material.
This is a first course in multivariable calculus
which builds on your basic knowledge of one variable calculus.
We will start with a discussion of multidimensional vector spaces,
the multivariable analog of the (x,y) plane. We then move on
to the study of vector-valued functions and real valued functions
of several variables. With this background, we go on to introduce
the fundamental concepts of differentiation and integration
in a multivariable setting. Our focus throughout will be on
concrete calculations as opposed to proofs, and on applications of the material
to problems in the social and physical sciences.
- Midterm I: Monday, October 19th.
- Midterm II: Friday, November 13th.
- Final Exam: Friday December 11th, 3:00p - 5:59p in TBA.
Please bring identification to the exams.
There will be no books or personal notes allowed during exams.
However, you may bring these sheets:
fact-sheet 1,
fact-sheet 2, and fact-sheet 3
to the exams. In general there are no make-up exams.
The exams may have questions about anything covered in homework assignments
due before the exams, as well as lectures
or assigned reading. Further information about
the exams will be given
in the lectures.
- Review for 1st Midterm: Friday October 16th, in class.
- Review for 2nd Midterm: Thursday November 12th, from 5:00-5:50pm in Center 105.
- Review for Final: TBA.
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,
mid1s08,
mid2s08,
fins08,
Note: Some are for a slightly different text and syllabus.
Basically, our goal is to cover Chs. 11-15 of the text. In particular
we will discuss (at least) the following:
12.1-2 Vectors.
12.3 Dot product.
12.4 Cross product.
12.5 Planes in 3D.
11.1 & 13.1: Parametric equations & Vector-valued functions.
13.2: Calculus of vector-valued functions.
11.2 & 13.3: Arclength and speed.
13.5: Motion in three-space.
14.1: Functions of two or more variables.
14.2: Limits and continuity in several variables.
14.3: Partial derivatives.
14.4: Differentiability, linear approximation and tangent plane.
14.5: The gradient and directional derivatives.
14.6: The chain rule.
14.7: Optimization in several variables.
14.8: Lagrange multipliers.
15.1: Integration in several variables.
15.2: Double integrals.
15.3: Triple integrals.
12.7: Cylindrical and spherical coordinates.
15.4: Integration in polar, cylindrical and spherical coordinates.
It is important that you have a look at the material before it is covered
in the lectures.
| Week |
Date (Monday) |
Monday |
Wednesday |
Friday |
| 0 |
9/21 |
|
|
12.1 |
| 1 |
9/28 |
12.2 |
12.3 |
12.4 |
| 2 |
10/5 |
12.5 |
11.1, 13.1 |
13.2 |
| 3 |
10/12 |
11.2, 13.3 |
13.5 |
Review |
| 4 |
10/19 |
Exam 1 |
14.1 |
14.2 (W drop) |
| 5 |
10/26 |
14.3 |
14.4 |
14.5 |
| 6 |
11/2 |
14.6 |
14.7 |
14.7, 14.8 |
| 7 |
11/9 |
14.8 |
Holiday |
Exam 2 |
| 8 |
11/16 |
15.1 |
15.1 |
15.2 |
| 9 |
11/23 |
15.3 |
12.7 |
Holiday |
| 10 |
11/30 |
15.4 (F drop) |
15.4 |
Review |
| 11 |
12/07 |
|
|
Final: 3:00p - 5:59p in TBA |
For old lecture notes on a similar course,
go
here.
Homeworks are due to the TA's box on the 6th floor
of AP&M at 4p on Wednesdays.
Please write your name and section number
on each page.
Late homeworks
will not be accepted.
All homeworks problems be handed in, but we do not have resources to grade them all.
Therefore, a select number of problems from each set will be graded randomly.
However, you will also be graded for attempting each problem.
HW #1: Due 9/30.
12.1: 8, 26, 28, 38, 40, 42, 56, 58.
12.2: 14, 24, 28, 36, 42, 50.
HW #2: Due 10/7.
12.3: 14, 28, 44, 48, 52, 54, 60, 70.
12.4: 4, 6, 14, 20, 32, 34, 42, 48.
12.5: 22, 24, 26, 30, 46, 54, 60.
HW #3: Due 10/14.
11.1: 12, 14, 26, 38.
13.1: 6, 18, 26, 32.
11.2: 12, 18, 20.
13.2: 10, 12, 20, 22, 26, 28, 32, 40, 45, 50.
13.3: 6, 10, 18.
HW #4: Due 10/21.
13.5: 5, 12, 16, 20, 26.
HW #5: Due 10/28.
14.1: 8, 16, 18, 20, 24, 28, 32, 44.
14.2: 4, 8, 14, 16, 18, 26.
14.3: 4, 8, 30, 34, 40, 44, 46, 48, 56, 58, 59, 74, 76.
HW #6: Due 11/04.
14.4: 4, 6, 10, 14, 18, 20, 22.
14.5: 2, 4, 22, 24, 28, 30, 38, 40, 42, 50, 60.
14.6: 2, 4, 10, 12, 16, 28, 30.
HW #7: Due 11/12.
14.7: 2, 8, 14, 20, 24, 38, 40.
14.8: 2, 4, 8, 12, 16, 26, 30.
HW #6: Due 11/25.
15.1: 2, 10, 16, 18, 26, 30, 36, 38, 42, 44.
15.2: 1, 4, 8, 10, 12, 18, 24, 30, 38, 42, 52, 58, 64.
15.3: 6, 10, 14, 16, 18, 24, 26.
Your grade will be calculated as follows:
- 20% HW,
- 20% each Midterm,
- 40% Final.
At the end of the course, there will be a curve. I will also attempt
to give you a clear indication as to where you stand gradewise after
each midterm.