Maria Conceição Leite
MATH 2850 - Elementary Multivariable Calculus, Spring 2014
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  Syllabus  |
  Class Material  |
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Course Description:
The topics in this course include
geometry of functions of several variables, partial differentiation, multiple integrals,
vector algebra and calculus (including Theorems of Green, Gauss and Stokes), and applications.
Learning objectives:
- Differentiate and integrate vector-valued functions.
- Evaluate limits and determine the continuity and differentiability
of functions of several variables.
- Describe graphs, level curves and level surfaces of functions of several variables.
- Find partial derivatives, directional derivatives, and gradients and use them to solve
applied problems.
- Find equations of tangent planes and normal lines to surfaces that are given implicitly
or parametrically.
- Use the chain rule for functions of several variables (including implicit differentiation).
- For functions of several variables, find critical points using first partials and interpret
them as relative extrema/saddle points using the second partials test.
Find absolute extrema on a closed region. Apply these techniques to optimization problems.
- Use Lagrange multipliers to solve constrained optimization problems.
- Evaluate multiple integrals in appropriate coordinate systems such as
rectangular, polar, cylindrical and spherical coordinates and apply them
to solve problems involving volume, surface area, density, moments and centroids.
- Find the curl and divergence of a vector field, the work done on an object moving in a vector field,
and the flux of a field through a surface. Use these ideas to solve applied problems.
- Introduce and use Greens's Theorem, the Divergence (Gauss's) Theorem and Stokes's Theorem.
Textbook: Thomas' Calculus
(12th Edition),
by G.B. Thomas, M.D. Weir and J. Hass
The text is available online at a 30 % discount in electronic form from
www.coursesmart.com. Students should be aware that in purchasing an electronic copy they will be
responsible for printing it or accessing it electronically.
Course Website:
http://www.math.utoledo.edu/~mleite/teaching/math2850-Spring2014.html
Lecture: MTRF 1:00-1:50 pm Palmer Hall 2450
Office Hours: Location: 3017 University Hall (UH)
Time:
M 2:30-5:00 pm; W 1:00-3:30 pm  
E-mail:
Maria.Leite@utoledo.edu
Resources:
Mathematics tutoring is provided by the Mathematics Learning and Resource Center
that is located in Rm B0200 in the basement of Carlson Library - phone ext. 2176.
It operates on a walk-in basis.
MLRC Tutoring Hours can be found at
www.math.utoledo.edu/mlrc/MLRC.pdf .
Grading Policy:
The final course grade will be determined according to the following rules:
  | Homework   | 15 % |
  | Quizzes   | 15 % |
| Midterm exams (two) | 20 % each |
| Final exam | 30 % |
Remarks on Grading Policy:
1. You are expected to review carefully all graded homeworks, quizzes, and exam papers as soon as
they are returned.
All questions and / or perceived descrepancies about grading of papers must be reported to me within
seven calendar days of the date on which the paper was returned to you.
2. I do not give retakes on quizzes / exams, nor I drop any quiz / exam score.
Important dates:
Academic Calendar
Dop/Withdrawal: The last day to drop or add this course is the Friday of the second week of classes
  The las day to withdraw from this class with a grade of "W" is the Friday of the
tenth week of classes.
Important Comments:
Class attendance is expected. Be advised that you are fully responsible for the material covered
in each class, whether or not you attend it.
Before each class, you should both review the material from recent sections and read the section
to be discussed that day. This will allow you to both understand the presentation of new
material and identify questions that you need to resolve during class.
Missed Class Policy:
If circumstances occur in accordance with the
University's missed class policy, result in a student
missing a quiz, test exam, the student must contact me in advance by phone, e-mail or in person,
provide official documentation to back up his/her absence, and arrange to make up the missed item
as soon as possible.
Academic Dishonesty Policy:
Any act of academic as defined by the University of Toledo policy on academic dishonesty (found at
http://www.utoledo.edu/dl/students/dishonesty.html ) will result in an F
on the item in question, if it is
a first time event. If a student commit, for the second time, any act of academic dishonesty
an F in the course
will be assigned.
Academic Adjustments for Students with Disabilities:
The University of Toledo is committed to providing reasonable accommodation
for students with documented
disabilities. Students should contact the Office of Accessibility as soon as possible for more
information and/or
to initiate the process for accessing academic accommodations. The Office of Acessibility
is located in
Rocket Hall, Room 1820, 419.530.4981; officeofaccessibility@toledo.edu,
webpage
http://www.utoledo.edu/utlc/accessibility/faculty.html
Non-Discrimination Policy:
The University of Toledo is committed to a policy of equal opportunity in eduction,
affirms the values and goals of
diversity.
Student Privacy:
Federal law and university policy prohibits instructors from discussing a students's grades or class perfomance
with anyone of university faculty/staff without the student's written andsigned consent. This includes parents and spouses.
For details, see ''Confidentiality of student record (FERPA)'' section of the University Policy Page at
http://www.utoledo.edu/policies/academic/undergraduate/index.html
Class Material
Lecture 7-Level Curves
here
Level curves animation:
http://archives.math.utk.edu/ICTCM/VOL10/C009/lc.gif
http://archives.math.utk.edu/ICTCM/VOL10/C009/lcr.gif
Syllabus
It is your responsibility to stay informed on the progress of the class and important dates.
The following schedule might change. Check this website regularly for updated information.
Lecture |
Date |
Section |
1 |
M, Jan 6 |
13.1 Cancelled
|
2 |
T, Jan 7 |
13.1; 13.2 Cancelled
|
3 |
Th, Jan 9
|
13.1
|
4 |
F, Jan 10
|
13.1; 13.2
|
|
|
|
5 |
M, Jan 13
|
13.3; 14.1
|
6
|
T, Jan 14
|
14.1; 14.2 |
7
|
Th, Jan 16
|
14.2 |
8
|
F, Jan 17
|
14.2; 14.3 |
|
|
|
|
M, Jan 20
|
MLK Holiday
|
9
|
T, Jan 21
|
14.3
|
10
|
Th, Jan 23
|
14.4
|
11
|
F, Jan 24
|
14.4
|
|
|
|
12
|
M, Jan 27
|
14.4; 14.5
|
13
|
T, Jan 28 |
14.5 Cancelled |
14
|
Th, Jan 30
|
14.5
|
15
|
F, Jan 31
|
14.5; 14.6
|
|
|
|
16
|
M, Feb 3
|
14.6
|
17
|
T, Feb 4
|
14.7
|
18
|
Th, Feb 6
|
14.7
|
19
|
F, Feb 7
|
14.7
|
|
|
|
20
|
M, Feb 10
|
14.8
|
21
|
T, Feb 11
|
14.8
|
22
|
Th, Feb 13
|
14.8
|
23
|
F, Feb 14
|
Catching-up
|
|
|
|
24
|
M, Feb 17
|
Exam 1 (Chap. 13, 14- see Exam 1 below)
|
25
|
T, Feb 18
|
15.1
|
26
|
Th, Feb 20
|
15.2 |
27
|
F, Feb 21
|
15.2 |
|
|
|
28
|
M, Feb 24
|
15.3
|
29
|
T, Feb 25
|
15.3; 15.4
|
30
|
Th, Feb 27
|
15.4
|
31
|
F, Feb 28
|
15.4; 15.5
|
|
|
|
|
March 3-7
|
Spring Break
|
|
|
|
32
|
M, March 10
|
15.5
|
33
|
T, March 11
|
15.5
|
34
|
Th, March 13
|
15.5; 15.6
|
35
|
F, March 14
|
15.6
|
|
|
|
36
|
M, March 17
|
15.7
|
37
|
T, March 18
|
15.7
|
38
|
Th, March 20
|
15.7
|
39
|
F, March 21
|
16.1
|
|
|
|
40
|
M, March 24
|
16.1
|
41
|
T, March 25
|
16.1
|
42
|
Th, March 27
|
16.2
|
43
|
F, March 28
|
16.2
|
|
|
|
44
|
M, March 31
|
16.2
|
45
|
T, April 1
|
16.4
|
46
|
Th, April 3
|
16.4
|
47
|
F, April 4
|
16.4
|
|
|
|
48
|
M, April 7
|
Exam 2 ( Chap. 15, 16 )
|
49
|
T, April 8
|
16.5
|
50
|
Th, April 10
|
16.5
|
51
|
F, April 11
|
16.5; 16.6
|
|
|
|
52
|
M, April 14
|
16.6
|
53
|
T, April 15
|
16.6
|
54
|
Th, April 17
|
16.7
|
55
|
F, April 18
|
16.7
|
|
|
|
56
|
M, April 21
|
16.7; 16.8 |
57
|
T, April 22
|
16.8
|
58
|
Th, April 24
|
16.8
|
59
|
F, April 25
|
Review/catch-up
|
Homework Problems
There will be weekly homework assignments. The assignments are due usually on Monday in class,
but ocasionnally the due date may change. The homework due dates will be posted in the
table below
HW # |
Sections/Problems |
Date |
1 | 13.1 (1,3,9,11,13,15,17,19,21) | Jan 14, 2014 |
2 | 13.2 (3,5,7,9,13,15,17,19,21,23); 13.3 (1,3,5,7,9) | Jan 21, 2014 |
3 | 14.1 (5,7,9,11,15,17abc,19abc,31-36,49,61,63) | Jan 27, 2014 |
4 | 14.2 (7,9,11,13,15,17,19,33,39,41,43,45,47,57); 14.3 (7,11,13,15,17,25,29,33) |
Feb 3, 2014 |
5 | 14.3 (43,51,55,61); 14.4 (1,3,5,7,9,11,15,21,23) | Feb 10, 2014 |
| No Homework | Feb 17, 2014 |
6 | 14.7 (7,9,11,21,23,25,27,29,31,33,37,41,61,63) | Feb 24, 2014 |
7 | 14.7 (49,51,53,55,57,59); 14.8 (3,5,7,11,13,15,21,23,25,27,29,31,33,35,37,39) | March 10, 2014 |
8 | 15.1 (7,9,11,15,17,19,25,27) | March 17, 2014 |
| 15.2 (3,5;Evaluate the integral only for 15,19,21,23,29,31;
33,35,39-53 (odd numbers),57,59,61 | |
9 | 15.4 (1,3,5,7,9,13,17,19,21,23,25,27,29) | March 24, 2014 |
10 | 15.5 (3,5,9,11,13,15,23,27,33,41,43) | March 31, 2014 |
11 | 15.7 (7,9,11,15,27,29,31,37,43,49,51,53) | April 14, 2014 |
Quizzes
There will be weekly quizzes usually on Tuesdays during the last 15 minutes of the class,
but ocasionnally the day may change.
The changes will be posted on this website and announced in class.
All quizzes are closed book and closed notes.
Neither graphic calculators nor formula sheet are allowed.
Quiz # |
Date |
Section | Quiz sol. |
1 |
Jan 16, 2014 |
13.1
| Sol.
|
2 |
Jan 23, 2014 |
13.2,13.3 | Sol.
|
3 |
Jan 30, 2014 |
14.1,14.2 | Sol. |
4 |
Feb 4, 2014 |
14.2,14.3 | Sol. |
5 |
Feb 11, 2014 |
14.3, 14.4 | Sol. |
6
|
Feb 25, 2012 |
14.7 Cancelled
|
7
|
March 11, 2014 |
14.7, 14.8
| Sol. |
8
|
March 18, 2014 |
15.2
| Sol. |
9
|
March 25, 2014 |
15.4 | Sol. |
10
|
April 1, 2014
|
15.5 | Sol. |
11
|
April 15, 2014
|
15.7 | Sol. |
Examinations
The midtem examinations will be in class.
All tests are closed book and closed notes.
Neither graphic calculators nor formula sheet are allowed.
Exam I:
Monday, February 17, 2014; In class
(Covering Sections 13.1-13.3 and 14.1-14.5)
Exam I Solutions here:
Practice problems here
Set 1;
Set 2;
Set 3, skip problem 2b;
Sec 14.4, problems 25,27,29,31,33,35,51
Sec 14.5, problems 1,3,5,7,9,13,15,17,19,21,25,27,29,31,33
Exam II: Monday, April 7, 2014; In class
(Covering Sections 14.6 to 14.8; 15.1 to 15.6, inclusive)
Exam II Solutions here
Practice problems for Sec 15.6 here: 24a,25a,29,30
Final Exam: Comprehensive
Wednesday, April 30, 2014; 12:30pm to 2:30 pm; Room: PH 2450
(Covering Sections 13.1-13.3; 14.1-14.8; 15.1-15.7; and 16.1-16.4)
Practice problems for:
- Sec 16.1: 9,11,13,15,19,23,25
Sec 16.2: 7,9,11,13,15,17,19,21,23,25,27,29,31,35
Sec 16.3: 1-6,25
Sec 16.4: 5,7,9,11,15,17,21,23,25,27
Set of practice problems with solutions
If you have any question please contact me by
email