Math 340, Joel M. Cohen (Fall, 2008)

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

Web Posting:  If you have emailed me your permission to post your grades under an alias, you may check the grades by clicking here.

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.

 

Homework

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 1.7: 2, 6, 9
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, yx, 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.

 

Note: For Problems 6.2.10 and 6.2.13, I recommend that you don't follow the method of Examples 2 and 3 in Section 6.2. Instead, use one of the formulas from Problem 6.2.15.


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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