Department of Mathematics, Statistics and Physics
College of Arts and Sciences
University of Qatar
Course Syllabus
Components
By
Safeer Hussain Khan
2009/2010 Academic Year
Dr. Safeer Hussain Khan
Mathematics for Computers
Course Information
Course Name: Mathematics for Computer Science
Course Number: 20936-Math 215-L51
Credit Hours: 3
Contact Hours: 4
Class Timings: 11:00-12:15 on Mondays, Wednesdays and
11:00-11:50 Tuesdays
Office Hours: 10:00-11:00 AM Mondays
12:00-1:00 PM Tuesdays
First Day of Classes: Sunday, 21 February 2010
Last Day of Classes: Thursday, 03 June 2010
Pre-requisite:
1051102
Location of Class Room: :
C01-D21
Required Textbooks: 1.Advanced Engineering Mathematics, by Peter
V.O'Neil
2. Calculus 8th edition, by Anton
Faculty Information
Name: Safeer Hussain Khan
Program: Mathematics
Telephone: 4852200
E- Mail: safeer@qu.edu.qa
Office Number: C216 Corridor # 3
2
Dr. Safeer Hussain Khan
Mathematics for Computers
Course Description

First-Order Differential Equations: Preliminary concepts, Separable
equations, Linear differential equations, Exact differential equations, Integrating
Factors, Homogeneous, Bernoulli and Riccati equations, Applications.

Threee Dimensional Spaces;Vectors: Rectangular coordinates in 3-space.
Vectors. Unit vector. Vectors in the plane. Dot product. Direction angles. 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. Notion of differentiability. Differentials. Partial derivatives.
Chain rules. Directional derivatives and gradients. Maxima and Minima. .
Lagrange Multipliers.

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.

Special Functions: Gamma, Beta and Error functions. Derive and use
properties of the Gamma and Beta functions, Evaluate Gamma and Beta
functions for given arguments, Recognize and evaluate integrals that can be
reduced to a the Gamma and Beta functions.
3
Dr. Safeer Hussain Khan
Mathematics for Computers
Course Objectives






To introduce different fundamental methods to solve first order
differential equations.
To develop the notion of vectors and their properties in the plane
and in the 3-dimensional space.
To develop the ability to differentiate functions of several
variables and to deal with limit, continuity, and finding extrema.
To provide the students with the skills of double and triple
integrals for functions of several variables.
To introduce Gamma, Beta and Error function.
To make use of software like Mathematica to show some graphs
in 3-D.
4
Dr. Safeer Hussain Khan
Mathematics for Computers
Learning Outcomes
The students are expected to be able to:
Objective 1:
 Solve first order differential equations using different methods.
.
Objective 2:
 Recognize the 3-space and describe surfaces for a given
equation.
 Do operations on vectors in the plane and the 3- space
 Evaluate dot and cross product of vectors.
 Find parametric equations of lines in 3-space.
 Find equation of planes in 3-space.
 Find all types of intersections between planes and lines
 Recognize the cylindrical and spherical coordinate systems.
 Identify and sketch different types of quadric surfaces
Objective 3:
 Define functions of several variables and recognize its basic
properties.
 Evaluate limits and continuity for functions of several variables.
 Find partial derivatives for functions of several variables.
 Find directional derivatives for functions of several variables.
 Find gradients for functions of several variables.
 Evaluate Maxima and Minima for functions of two variables,
 Using Lagrange Multipliers to find maxima and minima for
functions of 3 variables.
Objective 4:
 Evaluate double and triple integrals over rectangular regions.
 Evaluate double and triple integrals over non-rectangular
regions.
 Using polar coordinates to evaluate double integrals.
 Using cylindrical and spherical coordinate systems to evaluate
triple integrals.
Objective 5:
 Define the Gamma, Beta, and error functions.
 Derive and use properties of the Gamma and Beta functions.
 Evaluate Gamma and Beta functions for given arguments.
 Recognize and evaluate integrals that can be reduced to a
Gamma or Beta function.
5
Dr. Safeer Hussain Khan
Mathematics for Computers
DeliveryMethods
The following teaching methods are followed in the class:
1) Lectures give the basic concepts and examples show how these concepts are
related to each other.
2) Problem solving.
3) Interactive teaching.
4) Thought provoking.
5) I respond to meaningful emails and encourage using discussion board on the
Blackboard.
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
Blackboard will be used frequently: http://mybb.qu.edu.qa/
6
Dr. Safeer Hussain Khan
Mathematics for Computers
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
First Major Exam:
31 -3-10 (Wednesday)
Second Major Exam: 12-5-10 (Wednesday)
Quizzes:
In the class
In the class
In the class
20 Marks
20 Marks
10 Marks
Assignments with presentations:
10 Marks
Final Exam:
40 Marks
07-06-10 (Monday)
Three examinations will be given: First Major Exam, Second Major
Exam and the Final Exam.
Marks are awarded on the basis of both presentation and concept.
Students should show all their work to maximize their grades.
The final exam is comprehensive. Make-up for final examination only under
official permission by the university.
Five quizzes will be given and best three will be chosen for evaluation.
As a matter of principle, no quiz will be repeated. Best three will be
counted toward evaluation.
Five assignments will be given and best three will be chosen for
evaluation. Assignments are to be returned on time. Late submission will
result in loss of marks. A presentation of the assignment problems will
be required in the class and carries marks.
The exam dates and times and the due dates and times for the home works,
that we agree upon cannot be and will not be changed. Exam 1 and Exam2
may be re-taken only if you have a genuine reason like proven illness or
mishap. A certificate of the same is required before the make-up exam.
The place for the final examination will be communicated later.
7
Dr. Safeer Hussain Khan
Mathematics for Computers
Content Distribution
Lectures Schedule
Differential Equations part from Advanced Engineering Mathematics, by Peter
V.O'Neil
Weeks
Section #
1.1
1.2
1 -3
1.3
1.4
1.5
1.6
1.7
Calculus part by Anton
Topic
Preliminary Concepts
Separable Equations
Linear Differential Equations
Exact Differential Equations
Integrating Factors
Homogeneous, Bernoulli, and Riccati Equations
Applications
Week
Sec.
Topics
4
12.1
12.2
12.3
Rectangular Coordinate systems in 3-space
Vectors
Dot product, projections
5
12.4
12.5
12.6
13.1
13.2
13.3
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
7
13.4
13.5
12.7
Unit Tangent, Normal and Binormal vectors
Curvature
Quadric Surfaces
8
14.1
14.2
14.3
14.4
14.5
14.6
Functions of two or more variables
Limits and continuity
Partial derivatives
Differentiability, Local Linearity, and differentials
The Chain rule
Directional derivatives and gradients
14.7
14.8
14.9
15.1
15.2
15.3
15.5
12.8
15.7
Tangent planes and normal vectors
Maxima and minima of functions of two variables
Lagrange multipliers
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
Define the Gamma, Beta, and error functions.
Derive and use properties of the Gamma and Beta functions.
6
9
10
11
12
13
14
Evaluate Gamma and Beta functions for given arguments.
Recognize and evaluate integrals that can be reduced to a
Gamma or Beta function.
8
Dr. Safeer Hussain Khan
Mathematics for Computers
Final Exam
Learning Activities and Tasks
Students are 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.
9
Dr. Safeer Hussain Khan
Mathematics for Computers
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
10
Dr. Safeer Hussain Khan
Mathematics for Computers
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.
Additional Sources:
Printed Sources
1. Calculus, by Swokowski, Sixth Edition 1994,PWS Publishing Company, Boston.
2. Calculus with Analytic Geometry, by H. Edwards and D. E. Penny, 5th Edition,
1998, Prentice Hall.
3. Calculus, by R.T. Smith and R.B. Minton, 2nd Edition, 2002, McGraw-Hill.
4. Calculus: One and Several Variables by S. L. Salas, G. J. Etgen and E. Hille;
10th Edition, 2007, John Wiley & Sons.
5. Calculus, Early Transcendentals by J. Stewart, 6th Edition, 2008, Brooksw/Cole.
6. Differential Equations with boundary problems: Dennis G. Zill and Michael R.
Cullen.
7. Advanced Engineering Mathematics, Kreyszig, 7th ed., 1993, John Wiley.
Non-Printed Sources
Check blackboard site http://mybb.qu.edu.qa for class notes and exams solutions, etc.
Online Sources
Some Useful Resources and Media Address
- http://www.efunda.com
- http://www.sosmath.com/diffeq
- http://www.mathword.wolfram.com
- http://tutorial.math.lamar.edu/
11
Dr. Safeer Hussain Khan
Mathematics for Computers
Course Matrix
Objectives
Objective 1: To introduce
different fundamental methods
to solve first order differential
equations
Objective 2: To develop the
notion of vectors and their
properties in the plane and in
the 3-dimensional space.
Objective 3: To develop the
ability to differentiate
functions of several variables
and to deal with limit,
continuity, and finding
extreme.






















Objective 4: To provide the
students with the skills of
double and triple integrals for
functions of several variables






Objective 5: To introduce
Gamma, Beta and Error
function




Outcomes
Recognize the type of differential equation according to
order, derivative, linearity.
Solve separable equations.
Solve linear Differential equations
Solve exact differential Equations.
Solving differential equations using integrating factors.
Solving some special differential equations.
Recognize the 3-space and describe surfaces for a given
equation.
Do operations on vectors in the plane and the 3- space
Evaluate dot and cross product of vectors.
Find parametric equations of lines in 3-space.
Find equation of planes in 3-space.
Find all types of intersections between planes and lines
Recognize the cylindrical and spherical coordinate systems.
Identify and sketch the basic types of quadric surfaces
Define real-valued functions of several variables and
recognize their basic properties
Draw level curves and level surfaces.
Evaluate limits of functions and discuss their continuity
Find partial derivatives for functions of several variables.
Use the chain rule.
Find directional derivatives and gradients for real-valued
functions and find their rate of change.
Find tangent planes and normal vectors for a given surface.
Evaluate Maxima and Minima for functions of two
variables.
Use Lagrange Multipliers to evaluate Maxima and Minima
Evaluate double and triple integrals over rectangular
regions.
Evaluate double and triple integrals over non-rectangular
regions.
Use polar coordinates to evaluate double integrals.
Evaluate triple integrals.
Evaluate triple integrals in cylindrical and spherical
coordinate systems.
Define the Gamma, Beta, and error functions.
Derive and use properties of the Gamma and Beta
functions.
Evaluate Gamma and Beta functions for given arguments.
Recognize and evaluate integrals that can be reduced to a
Gamma or Beta function.
12
Assessment Tools
Exams
Quizzes
Assignments
Presentations
Exams
Quizzes
Assignments
Presentations
Exams
Quizzes
Assignments
Presentations
Exams
Quizzes
Assignments
Presentations
Exams
Quizzes
Assignments
Presentations
CATEGORY
5
4
3
2
Dr. Safeer Hussain Khan
1
0
Score y/7
Mathematics for Computers
Assignment Rubrics (Written Part 5 Points)
Student name and ID:………………………… Group#
5
Organization
Amount of
Information
Quality of
Information
Sources
Diagrams &
Illustrations
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.
Diagrams and
illustrations are neat,
accurate and add to
the reader's
understanding of the
topic.
3
2
1
Information is
organized
with wellconstructed
paragraphs.
All topics are
addressed
and most
questions
answered
with at least 2
sentences
about each.
Information
clearly relates
to the main
topic. It
provides 1-2
supporting
details and/or
examples.
All sources
(information
and graphics)
are accurately
documented,
but a few are
not in the
desired
format.
Refernces
clearly stated
Diagrams and
illustrations
are accurate
and add to
the reader's
understanding
of the topic.
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.
All sources
(information
and graphics)
are accurately
documented,
but many are
not in the
desired
format. Not all
refernces are
included
Diagrams and
illustrations
are neat and
accurate and
sometimes
add to the
reader's
understanding
of the topic.
Some sources
are not
accurately
documented
or there are
no references
included.
13
0
One or more
topics were
not
addressed.
Information
has little or
nothing to do
with the main
topic.
Diagrams and
illustrations
are not
accurate OR
do not add to
the reader's
understanding
of the topic.
Score= y/5
Dr. Safeer Hussain Khan
Mathematics for Computers
Assignment Rubrics (Oral PresentationPart 5 Points)
Student name and ID:………………………… Group #
5
4
3
2
1
0
 There is a logical
 There is some
 There is little or no
sequence of
logical sequence of
logical sequence of
information.
information.
information.
Organization  Title slide and closing  Title slide and
 Title slide and/ or
slide are included
closing slides are
closing slides are not
appropriately.
included.
included..
Slide Design
(text, colors,
 Presentation is
background,
attractive and
illustrations, size,
appealing to viewers.
titles, subtitles)
Content
Delivery
 Presentation is
somewhat
appealing to
viewers.
 Presentation
includes some
 Presentation covers
essential
topic completely and
information.
in depth.
 Some information
 Information is clear,
is somewhat
appropriate, and
confusing,
accurate.
incorrect, or
flawed.
 There was some
 Ideas were
difficulty
communicated with
communicating
enthusiasm, proper
ideas due to voice
voice projection and
projection, lack of
clear delivery.
preparation,
 There was sufficient
incomplete work,
eye contact with
and/or insufficient
audience.
eye contact.
 There were sufficient  Insufficient use of
use of other nonnon-verbal
verbal
communication
communication skills.
skills.
 Appropriate delivery  Delivery pace is
pace was used.
somewhat
appropriate.
 Little to no attempt has
been made to make
presentation appealing
to viewers.
 Presentation includes
little essential
information.
 Information is
confusing, inaccurate, or
flawed.
 There was great
difficulty
communicating ideas
due to poor voice
projection, lack of
preparation, incomplete
work, and/or little or no
eye contact.
 No use of non verbal
communication skills.
 Inappropriate delivery
pace was used.
14





Score
y/5
Dr. Safeer Hussain Khan
Interaction
with Audience
Mathematics for Computers
 Ideas were
 There was some
communicated with
difficulty
enthusiasm, proper
communicating
voice projection and
ideas due to voice
clear delivery.
projection, lack of
 There was sufficient
preparation,
eye contact with
incomplete work,
audience.
and/or insufficient
 There were sufficient
eye contact.
use of other non Insufficient use of
verbal
non-verbal
communication skills.
communication
 Appropriate delivery
skills.
pace was used.
 Delivery pace is
somewhat
appropriate.
15
 There was great
difficulty
communicating ideas
due to poor voice
projection, lack of
preparation, incomplete
work, and/or little or no
eye contact.
 No use of non verbal
communication skills.
 Inappropriate delivery
pace was used.
Dr. Safeer Hussain Khan
Mathematics for Computers
Practice Problems
"Practice makes a man perfect" is a well-known saying. It is particularly true for
mathematics students. Following are the Recommended Practice Problems from the
text book. It is expected that the students will solve all of them, but shall not restrict
themselves to these problems only.
Practice Problems
(a) Differential Equations
Week
1 -3
Section
#
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Problems #
1-16
1-15
1-15
1-16
4-20
1-14,17,19,21,23
Odd numbered
Recommended Problems for Calculus 3
Chapter 14
Chapter 13
Chapter 12
Text Book: Calculus, Author: Howard Anton 8th edition
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 Section Page
Question Numbers
12.1
794
8,11, 12, 17, 19, 25, 29, 33, 36,37,42
12.2
805
1-19 (odd numbered), 27, 29, 38.(The same as 7th edition)
12.3
814
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
12.7
12.8
841
852
859
13.1
867
13.2
878
13.3
13.4
13.5
14.1
14.2
888
895
901
937
948
14.3
959
14.4
14.5
969
979
3, 11, 14, 15, 17, 19, 21, 23, 26-30, 33, 41, 43, 45.
1, 5, 7, 9, 11-21 (odd), 29, 32, 33, 35. (The same as 7th edition)
1-11 (odd), 15-41 (odd). (The same as 7th edition)
2, 4, 8, 11, 13, 19, 20, 21, 29, 32, 33, 37, 40, 41.(The same as 7th
edition)
2,4, 5, 7, 9, 10,11, 13, 15, 19, 21, 23, 27, 29, 31, 33, 35, 37,39, 42, 51,
54.
1, 4,6, 7,8, 9, 11, 13, 13, 15, 21, 23, 25, 27.
5, 7,9, 15, 16, 17,19.
5,7,9,11,13,15,17,19,21,26,27,29,32.
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.
4,9,15,19,21,23, 37,41, 43,44,45,47,59,60.
1, 3, 5, 17,19,21,23,25,27,29,31,39,40,41,43.
16
Chapter 15
Dr. Safeer Hussain Khan
14.6
14.7
14.8
14.9
15.1
15.2
15.3
15.5
15.7
991
998
1008
1018
1028
1037
1045
1067
1088
Mathematics for Computers
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).
1-15 (odd), 23,24,27-34.
1-11 (odd), 15, 17, 19, 25, 33.
1-19 (odd),24.
Some general instructions for the students
� Feel free to ask any question related to the material presented in the class during the
class time.
� Check blackboard site http://mybb.qu.edu.qa for announcements and some class
material like class notes, assignments, syllabus, assignments and exams solutions, etc.
� Only a limited use of calculators is allowed in the examinations.
� Of course, cell phones must not be used during the class and the
examinations.
� Homework Problems will be assigned by the instructor, and students are strongly
urged to solve much more problems than indicated by the instructor.
� Mathematics Department provides syllabi very close to the ones of the most
international universities. Deducting and cutting short this syllabus is impossible and
the students should understand this in advance.
------One can get only for what (s)he works.---------------------------GOOD LUCK--------------------------
17