UNIVERSITY OF QATAR / COLLEGE OF ARTS AND SCIENCE
DEPARTMENT OF MATH, STAT. AND PHYSICS
MATH PROGRAM
Course Syllabus
Math 211 (Calculus III) Section L51
Spring Semester 2010
Course Information
Course Number: Math 211
Course Title: Calculus III Section: L51
Credit Hours: 3
Contact hours: 4
Course Status: major compulsory
Time: Sunday: 14:00 – 15:15, Tuesday: 14:00 – 15:15, Thursday: 14:00 – 14:50.
Location: College of Arts and Science Building/Female campus, Room: B230
Required Text: Calculus, by H. Anton, I. Bivens, and S. Davis, 8th Edition, 2005, Wiley.
Faculty Information
Name: Mahmoud Alrefaei
Academic Title: Associate Professor
Office Location: Corridor 2; B212
Telephone Number: 485-2202
Email Address: malrefaei@qu.edu.qa
Office Hours: Sunday: 13:00 – 14:00, Thursday: 13:00 – 14:00 or by appointment
OH room: SA210
Course Description




Vectors:
Cartesian space coordinate. Distance formula. Vectors. Unit vector. Vectors in the
plane. Dot product. Direction angle. Cross product. Lines. Vector parameterization.
Intersecting lines. Parallel lines. Planes.
Vector Calculus:
Vector functions. Differentiation formulas. Curves. Tangent vector. Intersecting
curves. Unit tangent. Arc length. Curvilinear Motion. Curvature.
Functions of Several Variables:
Elementary examples. Quadric surfaces. Limits and Continuity. Direction angle.
Differentials and Applications:
Notion of differentiability. Differentials. Directional derivatives. Mean value
theorem. Chain rules. Maximum and Minimum values. Lagrange’s method.
Math 211(Calculus III) Syllabus
Section L51 Spring 2010
Dr. M. Alrefaei
Page 1
UNIVERSITY OF QATAR / COLLEGE OF ARTS AND SCIENCE
DEPARTMENT OF MATH, STAT AND PHYSICS/MATH PROGRAM

Double and Triple Integrals:
Double integrals. Properties. Evaluation by repeated integrals. Polar coordinates.
Triple integrals. Properties. Evaluation by repeated integrals. Cylindrical and
spherical coordinates. Applications.
Course Objectives
The course aims at:
1. Developing the notion of vectors and their properties in the three-dimensional
space and the plane.
2. Presenting the calculus of vector functions and curves.
3. Developing the ability to differentiate functions of several variables to solve
practical problems.
4. Providing students with the skills of multiple integration for function of several
variables and its application to practical problems
Learning Outcomes
By the end of the course, the students should be able to:
1. Recognize the 3-space in different types of coordinates systems.
2. Do operations on vectors.
3. Identify different types of equations of lines, planes and surfaces.
4. Recognize different types of calculus operations of vector-valued functions.
5. Find arc length, unit tangent and normal vectors.
6. Identify the basic properties of the real-valued functions of several variables.
7. Evaluate limits of functions, and discuss their continuity and partial derivatives.
8. Find directional derivatives and gradients and their properties.
9. Solve optimization problems involving two or three variables.
10. Evaluate multiple integrals in different types of coordinates systems.
Delivery Methods
We will use different types of teaching methods including:
 Presentation explaining material.
 Problem solving.
 Discussion - actively involving students in learning by asking questions that
provoke thinking and verbal response.
 Using Math packages explaining some material including Autograph.
 The lecture will be posted on the e-learning tool Blackboard, so pay you attention
to the class and try to understand everything.
Math 211(Calculus III) Syllabus
Section L51 Spring 2010
Dr. M. Alrefaei
Page 2
UNIVERSITY OF QATAR / COLLEGE OF ARTS AND SCIENCE
DEPARTMENT OF MATH, STAT AND PHYSICS/MATH PROGRAM
Learning Resources & Media






In class we will use Digital Camera to explain mathematical formulas
Data show will be used also to visualize some important graphs in the three
dimension space
We will use Autograph 3.2 software that help students understand some graphs.
WeBWork will be used for assignments:
http://hosted2.webwork.rochester.edu/webwork2/QAT_102_3/
Blackboard will be used frequently: http://mybb.qu.edu.qa/
The Student companion site for the text: http://bcs.wiley.com/hebcs/Books?action=index&itemId=0471482730&bcsId=2252
Assessment Policy and Tools
Grades for the course will be assigned as follows:
Percent grade
Letter grade
Earned Points
90 -100 85 - 89
A
B+
4.0
3.5
80 - 84 75 -79 70 - 74
B
C+
C
3.0
2.5
2.0
65 - 69
D+
1.5
60 - 64
D
1.0
below 60
F
0.0
Description of Exams:
1. Exams: There will be three major exams:
1. First Exam: 20%, Tuesday March 30th, Time: 14:00 – 15:30 PM
2. Second Exam: 25%, Tuesday May 11th, Time: 14:00 – 15:30 PM
3. Final Exam: 40%, Wednesday June 9th , 8:00 – 10:00
Each exam will consist of comprehensive questions, there will be partial credits, so
students are required to show all their work to maximize their grades.
2. Quizzes (7.5%)

Approximately a total of 3-4 quizzes during the course. Quizzes will be announced
in advance. Each quiz will normally consist of 2 - 3 questions.
3. Assignments (7.5%)
 Approximately 5-6 webwork assignments, students are required to answer all
problems, they will get feedback immediately after posting their answers, if the
answer is incorrect, they will be allowed to redo the problem and resubmit the
answer and no grades will be deducted.
Math 211(Calculus III) Syllabus
Section L51 Spring 2010
Dr. M. Alrefaei
Page 3
UNIVERSITY OF QATAR / COLLEGE OF ARTS AND SCIENCE
DEPARTMENT OF MATH, STAT AND PHYSICS/MATH PROGRAM
Content Distribution
Lectures schedule
Week
1
Date
Fe. 21- Feb. 25
2
Feb. 28 – Mar. 4
3
Mar. 7 – Mar 11
4
Mar. 14 – Mar 18
5
Mar. 21 – Mar. 25
6
Mar. 28 – Apr. 1
Sec.
12.1
12.2
12.3
12.4
12.5
12.6
13.1
13.2
13.3
13.4
13.5
Topics
Rectangular Coordinate systems in 3-space
Vectors
Dot product, projections
Cross product
Parametric equations of line
Planes in 3-space
Introduction to vector-valued functions
Calculus of vector-valued functions
Change of parameters , Arc Length
Unit Tangent, Normal and Binormal vectors
Curvature
First Exam; Tuesday March 30th, Time: 14:00 – 15:30 PM
7
Apr. 4 – Apr. 8
Apr. 9 - Apr. 18
8
Apr. 18 – Apr. 22
9
Apr. 26 – Apr. 29
10
May 2– May 6
11
May 9 – May 13
12.7
14.1
Quadric Surfaces
Functions of two or more variables
Spring Brake
14.2
14.3
14.4
14.5
14.6
14.7
14.8
14.9
Limits and continuity
Partial derivatives
Differentiability, Local Linearity, and differentials
The Chain rule
Directional derivatives and gradients
Tangent planes and normal vectors
Maxima and minima of functions of two variables
Lagrange multipliers
Second Exam; Tuesday May 11th, Time: 14:00 – 15:30 PM
12
May 16 – May 20
13
May 23– May 27
14
May 30– June 3
15.1
15.2
15.3
15.5
12.8
15.7
Double integrals
Double integrals over non rectangular regions
Double integrals in polar coordinates
Triple integrals
Cylindrical and spherical coordinates, Triple integrals in
cylindrical and Spherical coordinates
Final Exam, Wednesday June 9th , 8:00 – 10:00
Math 211(Calculus III) Syllabus
Section L51 Spring 2010
Dr. M. Alrefaei
Page 4
UNIVERSITY OF QATAR / COLLEGE OF ARTS AND SCIENCE
DEPARTMENT OF MATH, STAT AND PHYSICS/MATH PROGRAM
Learning Activities and Tasks
Students should be held responsible for their own ongoing learning process. They need to
do their assignments independently unless they are allowed to work in groups.
Course Regulations
Student Responsibilities and Attendance Policies and Procedures


Class attendance is compulsory. In accordance with University regulations, a
student’s absence cannot exceed 25% of the total number (entire semester) of
class meetings. If your absence rate exceeds 25%, including both excused and
unexcused absences, you will NOT be allowed to take the final examination
and will receive an ‘F barred’ grade for the course.
Students are expected to be punctual (every 3 late class arrivals will be counted as 1
class absence) in class attendance and to conduct themselves in an adult and
professional manner.

Homework assignments and library assignment should be worked
independently. Exchanging ideas are permitted orally but don't require any kind
of copying.

Homework assignment should be submitted in organized way and any late
assignments may be assessed and corrected but the grade will be zero.
Plagiarism (Academic Dishonesty)

All students are expected to turn in work that is their own. Any attempt to pass
off another's work as your own will constitute an "F" in the entire course.
 Using part of, or the entire work, prepared by another or turning in a homework
assignment prepared by another student or party are examples of plagiarism.
 You may discuss assignments and projects with each other, but you should do
the work yourself. In the case of group projects, you will be expected to do your
share of the work. If you use someone else's words or ideas, you must cite your
sources.
Plagiarism is considered a serious academic offence and can result in your work losing marks or
being failed. QU expects its students to adopt and abide by the highest standards of conduct in their
interaction with their professors, peers, and the wider University community. As such, a student is
expected not to engage in behaviours that compromise his/her own integrity as well as that of QU.
You may discuss assignments and projects with each other, but you should do the work yourself. In
the case of group projects, you will be expected to do your share of the work. If you use someone
else's words or ideas, you must cite your sources.
Math 211(Calculus III) Syllabus
Section L51 Spring 2010
Dr. M. Alrefaei
Page 5
UNIVERSITY OF QATAR / COLLEGE OF ARTS AND SCIENCE
DEPARTMENT OF MATH, STAT AND PHYSICS/MATH PROGRAM
Plagiarism includes the following examples and it applies to all student assignments or submitted
work:




Use of the work, ideas, images or words of someone else without his/her permission.
Use of someone else's wording, name, phrase, sentence, paragraph or essay without
using quotation marks.
Misrepresentation of the sources that were used.
For further information see: http://www.plagiarism.org/
The instructor has the right to fail the coursework or deduct marks where plagiarism is
detected
Classroom Discipline
 The use of mobile telephones inside the classroom is NOT allowed.
 Any student disciplinary issues, which may arise, will be referred to the head of
the Department.
References:




Calculus with Analytic Geometry, by H. Edwards and D. E. Penny, 5th Edition, 1998,
Prentice Hall.
Calculus, by R.T. Smith and R.B. Minton, 2nd Edition, 2002, McGraw-Hill.
Calculus: One and Several Variables by S. L. Salas, G. J. Etgen and E. Hille; 10th
Edition, 2007, John Wiley & Sons.
Calculus, Early Transcendentals by J. Stewart, 6th Edition, 2008, Brooksw/Cole.
Additional Sources
Online Sources
 The Student companion site for the text: http://bcs.wiley.com/hebcs/Books?action=index&itemId=0471482730&bcsId=2252
 Course notes will be posted on the blackboard system: http://mybb.qu.edu.qa/
Math 211(Calculus III) Syllabus
Section L51 Spring 2010
Dr. M. Alrefaei
Page 6
UNIVERSITY OF QATAR / COLLEGE OF ARTS AND SCIENCE
DEPARTMENT OF MATHEMATICS AND PHYSICS/MATH PROGRAM
Matrix of Objectives and Outcomes
OBJECTIVES
LEARNING OUTCOMES
1.
To develop the notion of
vectors and their
properties in the threedimensional space and
the plane.
Assessment
Tools
Recognize the 3-space in different types of
coordinates systems.
2. Do operations on vectors.
3. Identify different types of equations of lines,
planes and surfaces.
To present the calculus of
vector functions and
curves.
4. Recognize different types of calculus operations of
vector-valued functions.
To develop the ability to
differentiate functions of
several variables to solve
practical problems.
6. Identify the basic properties of the real-valued
functions of several variables.
5. Find arc length, unit tangent and normal vectors.
Exams
Quizzes
Assignments
Exams
Quizzes
Assignments
7. Evaluate limits of functions, and discuss their
continuity and partial derivatives.
8. Find directional derivatives and gradients and
their properties.
Exams
Quizzes
Assignments
9. Solve optimization problems involving two or
three variables.
To provide students with
the skills of multiple
integration for function of
several variables and its
application to practical
problems
Math 211(Calculus III) Syllabus
10. Evaluate multiple integrals in different types of
coordinates systems.
Section L51 Spring 2010
Dr. M. Alrefaei
Exams
Quizzes
Assignments
Page 7
UNIVERSITY OF QATAR / COLLEGE OF ARTS AND SCIENCE
DEPARTMENT OF MATHEMATICS AND PHYSICS/MATH PROGRAM
Assignment Rubrics
Student name:……………………………
Instructor name: ………………………….
CATEGORY
Organization
Amount of
Information
Quality of
Information
Sources
Mechanics
4
Information is very
organized with wellconstructed
paragraphs and
subheadings.
All topics are
addressed and all
questions answered
with at least 2
sentences about
each.
Information clearly
relates to the main
topic. It includes
several supporting
details and/or
examples.
All sources
(information and
graphics) are
accurately
documented in the
desired format.
References clearly
stated.
No grammatical,
spelling or
punctuation errors.
Diagrams &
Illustrations
Diagrams and
illustrations are neat,
accurate and add to
the reader's
understanding of the
topic.
Paragraph
Construction
All paragraphs
include introductory
sentence,
explanations or
details, and
concluding sentence.
3
2
Information is
organized with wellconstructed
paragraphs.
Information is
organized, but
paragraphs are
not wellconstructed.
All topics are
addressed, and
most questions
answered with 1
sentence about
each.
Information clearly
relates to the main
topic. No details
and/or examples
are given.
The information
appears to be
disorganized. 8)
All sources
(information and
graphics) are
accurately
documented, but
many are not in
the desired format.
Not all references
are included
A few grammatical
spelling, or
punctuation errors.
Some sources are
not accurately
documented or
there are no
references
included.
All topics are
addressed and
most questions
answered with at
least 2 sentences
about each.
Information clearly
relates to the main
topic. It provides 12 supporting details
and/or examples.
All sources
(information and
graphics) are
accurately
documented, but a
few are not in the
desired format.
References clearly
stated
Almost no
grammatical,
spelling or
punctuation errors
Diagrams and
illustrations are
accurate and add
to the reader's
understanding of
the topic.
Most paragraphs
include introductory
sentence,
explanations or
details, and
concluding
sentence.
Diagrams and
illustrations are
neat and accurate
and sometimes
add to the reader's
understanding of
the topic.
1
One or more
topics were not
addressed.
Information has
little or nothing to
do with the main
topic.
Many
grammatical,
spelling, or
punctuation errors.
Diagrams and
illustrations are
not accurate OR
do not add to the
reader's
understanding of
the topic.
Paragraphing
structure was not
clear and
sentences were
not typically
related within the
paragraphs.
Score
Math 211(Calculus III) Syllabus
Section L51 Spring 2010
Dr. M. Alrefaei
Page 8
Score
UNIVERSITY OF QATAR / COLLEGE OF ARTS AND SCIENCE
DEPARTMENT OF MATHEMATICS AND PHYSICS/MATH PROGRAM
Recommended Problems for Calculus III
Text Book: Calculus, Author: Howard Anton 8th
Note to the students: The following problems are meant for the least practice. They only show the type of
the problems you will encounter in this course. You are strongly urged to solve much more problems to
get an excellent skill.
Chapter 15
Chapter 14
Chapter 13
Chapter 12
Chapter
Section Page
Question Numbers
12.1
794
8,11, 12, 17, 19, 25, 29, 33, 36,37,42
12.2
12.3
805
814
1-19 (odd numbered), 27, 29, 38.(The same as 7th edition)
1, 3, 7, 9, 11, 12, 13, 15, 24,26.
12.4
825
1, 3, 5, 7, 10, 13, 19, 21, 24, 25, 26, 27.(The same as 7th edition)
12.5
832
3, 5, 7, 9, 12, 13, 15, 18, 19, 20, 21, 23, 25, 27, 29, 31, 33, 39, 48,49.
12.6
841
3, 11, 14, 15, 17, 19, 21, 23, 26-30, 33, 41, 43, 45.
12.7
852
1, 5, 7, 9, 11-21 (odd), 29, 32, 33, 35. (The same as 7th edition)
12.8
859
1-11 (odd), 15-41 (odd). (The same as 7th edition)
13.1
867
2, 4, 8, 11, 13, 19, 20, 21, 29, 32, 33, 37, 40, 41.(The same as 7th edition)
13.2
878
2,4, 5, 7, 9, 10,11, 13, 15, 19, 21, 23, 27, 29, 31, 33, 35, 37,39, 42, 51, 54.
13.3
888
1, 4,6, 7,8, 9, 11, 13, 13, 15, 21, 23, 25, 27.
13.4
895
5, 7,9, 15, 16, 17,19.
13.5
901
5,7,9,11,13,15,17,19,21,26,27,29,32.
13.6
14.1
14.2
914
937
948
14.3
959
14.4
14.5
14.6
14.7
14.8
14.9
15.1
15.2
15.3
15.5
15.7
969
979
991
998
1008
1018
1028
1037
1045
1067
1088
1, 3, 5, 6, 13, 17, 19, 25, 27, 29, 31, 33, 35, 37, 39, 43
1, 3, 5, 13, 15, 19, 21, 23, 25-31, 39, 41, 43, 45, 47, 49, 51, 53, 55.
1-19 (odd), 33, 37, 41, 43.
1, 5, 11, 13, 15,17, 19, 23, 25, 27, 29, 31, 33, 35, 37,43, 43, 45, 57, 59, 61, 63,
65, 68,74, 91,93.
45,47,59,60.
1, 3, 5, 17,19,21,23,25,27,29,31,39,40,41,43.
1-19 (odd), 26, 29, 30, 33, 35, 37, 39, 41, 43, 47-61 (odd), 68.
1-9 (odd), 10-12, 17, 22, 23, 25.
1, 3, 9-19 (odd), 27, 29, 31, 35.
5-13 (odd), 14, 15, 19, 21, 22, 24, 25.
1-15 (odd), 19, 21, 23, 24, 25.
1-9 (odd), 14,17,19,21,23,25,29,31,35,37,38, 45-53 (odd).
1,3,5,13,15, 23,24,27-34.
1-11 (odd), 15, 17, 19, 25, 33.
1-19 (odd),24.
Math 211(Calculus III) Syllabus
Section L51 Spring 2010
Dr. M. Alrefaei
Page 9