This WEB page is http://jcohen.me/340, and
was last updated: 10/13/08
It can also be found at http://www.math.umd.edu/~jmc//340.
Title:
Multivariable Calculus, Linear Algebra & Differential Equations I:
Honors.
Instructor: Professor Joel
M. Cohen
Office: Math 2313, Telephone: (301)405-5109
Home phone: (202)546-1823.
Class Time:
T-Th, 2:00-3:45
Location: Math B0421
E-mail address: jcohen@umd.edu
Books: Susan J.
Colley, Vector
Calculus, 3rd edition, ISBN 978-0-1-3185874-9.
Charles G. Cullen, Matrices and Linear Transformations, 2nd edition,
ISBN
978-0-4-8666328-9
Recommended: Susan J. Colley, Vector Calculus Student Solutions
Manual,
ISBN 978-0-1-3193627-0
Prerequisite: MATH 141
Office Hours: T-Th
1-2. Occasionally, it may
be necessary
to change this time, so let me know if you are planning to see
me. You
can also send me email questions. I will answer queries as quickly as
possible
during office hours, and as time permits
otherwise.
Grader: Wan-Yu Tsai
E-mail address: wanyu@math.umd.edu
Office:
Math 1305
Office Hours: Tu 9-11 am and Th 8-9 am
Course
Description
This class will cover most of the material from MATH 240 (Linear
Algebra) and
MATH 241 (Multivariable Calculus). The remaining material, as well as
the
contents of MATH 246 (Ordinary Differential Equations), will be covered
in MATH
341 next semester. This semester we will cover most Colley’s book,
aside
from Chapter 4, and we will cover Chapters 1-3 in Cullen’s book. This
class will be intensive. The material in this 4 credit course
represents
about 6 credits worth of material in the regular courses, and we will
cover it
in greater depth than those courses do.
Policies
and Procedures
Homework and Quizzes: Homework will be assigned weekly but not
collected. Instead, on the due dates we will have a brief quiz (closed
book,
closed notes, no collaboration) with problems selected from the
assigned
homework. The two lowest quiz scores will be dropped,
Your job each week is to learn how to do the homework
problems.
You are encouraged to consult with each other and any other available
resources
to solve the problems. Homework problems are listed below, but
are
subject to change.
Computer
Assignments. Computer
assignments involving MATLAB will be given on an occasional basis. On
the
computer assignments, you may work in groups of at most 3 people; each
group
will turn in a single printed report and each member of the group will
receive
the same grade for the assignment.
Collaboration of all kinds is allowed and encouraged
on homework from
the text. For computer assignments, you may receive assistance with
MATLAB, but
otherwise no help from people outside your group.
Any student
with a
valid reason to be excused from an exam or quiz must contact me
either
by email or by phone, and present documentation at
the next
class session attended. Any student needing to be excused
for a religious
observance should let me know as soon as possible, but in any case no
later than the end of the schedule adjustment period.
Grading: A
total of 500 points is available in the course:
|
|
Two midterm exams |
200 |
|
|
Quizzes |
75 |
|
|
Computer Projects |
75 |
|
|
Final |
150 |
|
|
Total |
500 |
Quality:
The quality of presentation of solutions will be taken seriously in
this course
in the grading of tests and homework.
The tentative schedule of exams follows:
|
Thursday, October 16 |
Test I |
|
Thursday, November 20 |
Test II |
|
Thursday, Dec. 18, 10:30 -12:30 |
Final |
Sample exams are available at http://db.math.umd.edu/testbank/
A list
of
homework problems follows. The homework to
be covered on each quiz date will be finalized a week in advance.
Colley
1.1: 6, 21a
Colley 1.2: 17, 24, 27, 34, 36
Colley 1.3: 7, 9, 10, 14, 16, 17, 19, 25, 28b
Colley 1.4: 16, 17, 23, 35
Colley 1.5: 4, 5, 6, 16, 18, 25, 27,
33
Colley 1.6: 10, 30, 31, 32, 36, 37
Cullen 1.3: 1, 3, 6, 10, 11, 16
Cullen 1.4: 2, 4, 10
Cullen 1.5: 1, 2, 5, 7
Cullen 1.6: 4a, 6, 7
Cullen 1.8: 2, 3(a,b,d,e,g), 6, 7, 8, 9, 10
Cullen 1.9: 1(A,B), 2, 4, 5, 8, 9, 14
Cullen 1.10: 7
Cullen 1.11: 9
Cullen
2.1: 2, 6, 7, 8, 9, 10, 11
Cullen 2.2: 1, 2, 3, 5, 7, 9, 10
Cullen
2.3: 1, 3, 4, 5, 7, 8, 10
Cullen 2.4: 2, 3, 4, 5, 7, 8
Cullen 3.1: 1, 4
Note: In problem 1.8.3, you can save
time by doing
parts a and g together, and parts b and d
together, as
described in problem 1.8.7.
Colley
2.1: 1, 4, 12, 24, 27, 42
Colley 2.2: 8, 10, 15, 20, 28, 29, 41, 42, 48
Colley 2.3: 3, 6, 9, 15, 22, 25, 29, 31, 34, 50, 51
Colley
2.4: 9, 10, 11, 14, 17, 21a
Colley 2.5: 5, 11, 14, 20, 26, 27, 28
Colley 2.6: 2, 3, 17, 22, 23, 27, 34, 41, 42, 43, 44
Colley 3.1: 1, 2, 4, 7, 8, 15, 18, 21, 22, 26, 32
Colley 3.2: 1, 3, 5, 7, 13, 16, 17, 23, 29
Colley 3.3: 1, 3, 17, 25
Colley 3.4: 1, 3, 4, 7, 8, 16, 17
Notes: Part 1 of Proposition 1.4 (the
product rule
for differentiating a dot product) is helpful for Problems 3.1.32 and
3.2.29.
For Problem 3.1.21, to get the answer in the back of the book, use the
approximate value 32 ft/sec2 for g (32.2 is more
accurate).
For Problems 3.2.13 and 3.2.16, you can skip the computation of the binormal vector B and the torsion.
Colley 5.1: 1,
4, 15
Colley 5.2: 1, 5, 7, 10, 11, 13, 14, 26a, 27
Colley 5.3: 5, 6, 8, 9, 12, 16, 17
Notes: For Problem 5.2.13, the region is
the set
of all points for which x + y ≤ 2 and y2
- 2y - x ≤ 0. For Problem 5.2.14, the region is the set
of
all points for which xy2 ≤ 1, y ≥ x,
x ≥ 0, and y ≤ 3.
Colley
1.7: 9, 11, 14, 18, 24, 27, 42
Colley 5.4: 2, 7, 15, 20, 21
Colley 5.5: 1, 7, 13, 14, 17, 24, 25, 28, 31
Colley 5.6: 3, 7, 10, 11, 18, 19, 20
Colley
6.1: 4, 5, 7, 9, 11, 16, 19, 22,
23, 27
Colley 6.2: 4, 5, 7, 8, 10, 13, 15, 17a, 19, 20
Colley 7.1: 1, 5, 14, 16, 17
Colley 7.1: 19, 21, 25, 26, 28
Colley 7.2: 1, 3, 5, 7, 8, 12, 14, 15, 18, 19, 21
Colley 7.3: 3, 6, 9, 11, 14
Note: The Divergence (Gauss's) Theorem
makes
several of the problems in Section 7.2 easier to do; feel free to use
it.
This homework is not to be turned in; a
quiz drawn
from the assigned problems will be given weekly.
§ Changes in the program are
possible. The
Math 340 WEB PAGE (http://jcohen.me/340) will be kept up-to-date as
changes are
made.
You are responsible for
checking these
updates.
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