Department of Mathematics and Physics
College of Arts and Sciences
University of Qatar
Course Syllabus
Components
By
Dr. Safeer Hussain Khan
2009/2010 Academic Year
Dr. Safeer Hussain Khan
Mathematics for Engineers
Faculty Information
Name: Safeer Hussain Khan
Program: Math & Physics
Telephone: 4852200
E- Mail: safeer@qu.edu.qa
Office Number: C216 Corridor # 3
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Dr. Safeer Hussain Khan
Mathematics for Engineers
Course Information
Course Name: Mathematics for Engineers
Course Number:
20967-MATH 217 – L01
Credit Hours: 3
Class Timings:
Contact Hours: 4
8:00-9:15 on Mondays,Wednesdays and
2:00-3:15 Wednesdays
Office Hours:
Tue 10:00-11:00
Wed 1:00-2:00,
First Day of Classes: Sunday, Feb 21, 2010
Last Day of Classes: Thursday, June 3, 2010
Location of Class Room: BCR-C201
Prerequisites: Calculus 3
Required Textbook: Fundamentals of Differential Equations bound with
IDE CD (5th Edition) by Nagle, Saff and Snider
Reference Books
1. Advanced Engineering Mathematics, by Peter V.O'Neil
2. Differential Equations with boundary problems: Dennis G. Zill and
Michael R. Cullen.
3. Advanced Engineering Mathematics, Kreyszig, 7th ed., 1993, John
Wiley.
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Dr. Safeer Hussain Khan
Mathematics for Engineers
Course Description
Mathematics for Engineers is a course which introduces some
mathematical tools for solving and analyzing the problems arising
in the mathematical modeling in engineering. A specified
differential equation endeavors to match the known features of the
application being modeled, as well as to be able to predict the
systems' behavior in other circumstances. The course integrates
theory and application using a problem-based approach. This course
prepares the students for future learning in relation to problem
solving and decision-making, technical competence, teamwork and
leadership.
First-Order Differential Equations:
Initial-value problem. separable variables. Homogeneous equations.
Exact equations. Linear equations. Integrating factor. Bernoulli equation.
Applications.
 Second-Order Differential Equations:
Initial-value and Boundary-value problems. Linear differential
operators. Reduction of order. Homogeneous equations with constant
coefficients. Nonhomogeneous equations. Method of undetermined
coefficients. method of variation of parameters. some nonlinear equations.
Applications. Higher order Differential Equations.
 Series Solutions:
Cauchy-Euler equation method. Solutions about ordinary points.
Solutions about singular points. Method of Frobenius. Second Solutions and
Logarithm terms.
 System of Linear Differential Equations:
Definitions. Elimination method. Application of Linear Algebra.
Homogeneous linear systems. Nonhomogeneous linear systems. Solving systems
by Laplace transforms.
 Laplace Transforms:
Definitions. Properties. Inverse Laplace transforms. Solving initialvalue problems. Special functions: Heavyside unit step function.
Convolution theorem.
 Partial Differential Equations:
Some mathematical models. Fourier series solutions. Method of
seperation of variables. The D’Alembert solution of the wave equation.
Applications.

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Dr. Safeer Hussain Khan

Mathematics for Engineers
Course Objectives

To acquaint students with the necessary basic theories and methods
both in Ordinary and Partial Differential Equations.

To acquaint students with the Differential Equations and their
applications.

To introduce, among others, the Laplace Transform method which is
an efficient tool for solving Engineering problems in an elegant way.

To present students with some realistic problems.
To equip the students with a number of methods for solving
differential equations, concentrating on those which are of practical
importance.
 To make use of softwares like Mathematica wherever required.

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Dr. Safeer Hussain Khan
Mathematics for Engineers
Content Distribution
The distribution of the textbook units over one semester (14 weeks)
Topics Weeks
Basic Definitions and Terminology: Motivation,
½
Definitions, Classification by type, Classification by order,
Linearity, Solutions.
First-Order Differential Equations: Initial-value problem,
½-3
Separable variables, Homogeneous equations, Exact
equations. Linear equations, Integrating factor, Bernoulli
equation, Applications.
Second-Order Differential Equations: Initial-value and
3-6
Boundary-value problems, Linear differential operators,
Reduction of order, Homogeneous equations with constant
coefficients, Nonhomogeneous equations, Method of
undetermined coefficients, Method of variation of parameters,
Some non-linear equations, Applications, Higher order
Differential Equations.
Series Solutions: Cauchy-Euler equations, Solutions about
6-8
ordinary points, Solutions about singular points. Method of
Frobenius, Second solutions and Logarithm terms.
Systems of Linear Differential Equations: Definitions,
8-9½
Elimination method, Application of Linear Algebra,
Homogeneous linear systems, Nonhomogeneous linear
systems, Solving systems by Laplace transforms.
Laplace Transforms: Definitions, Properties, Inverse
9½-11
Laplace transforms, Solving initial-value problems. Special
functions: Heavyside unit step function, Periodic function,
Dirac delta function, Convolution theorem.
Partial Differential Equations: Some mathematical models,
11-14
Fourier series solutions, Method of separation of variables,
The D’Alembert solution, Applications.
Notice: This schedule is only a rough guideline and changes may occur as and when deemed
necessary by the instructor. These changes will be notified to the students.
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Dr. Safeer Hussain Khan
Mathematics for Engineers
Methods of Teaching
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) Some quizzes and/or assignments will be given.
3) Two major exams will be given.
4) Meaningful emails are responded.
Methods of Students Evaluation:
First Exam:
31-3-09 (Wednesday)
8 AM-9:00 AM
20 Marks
Second Exam: 12-5-10 (Wednesday)
8 AM-9:00 AM
20Marks
Final Exam:
8 -6-10 (Tuesday)
Quizzes
In the class.
11:00 PM-1:00 PM 40 Marks
10 Marks
Assignments
10 Marks
Marks are awarded on the basis of both
presentation and concept.
The place for the final examination will be
communicated later on.
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Dr. Safeer Hussain Khan
Mathematics for Engineers
Instructions for the students
� Attendance: According to the University of Qatar policy, a student has to
attend more than 75 % of the lectures; otherwise the student will not be
able to enter the final exam and consequently can not pass this course.
� Only a limited use of calculators is allowed in the examinations.
� Of course, cell phones must not be used during the classes and the
examinations.
� The final exam is comprehensive.
� Possibly three quizzes and assignments will be given.
� Assignments are to be returned on time. Late submission will result in
loss of marks.
� Marks are awarded on the basis of both presentation and concept.
� Homework/Practice Problems will be assigned by the instructor, and
students are strongly urged to solve much more problems than indicated by
the instructor.
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Dr. Safeer Hussain Khan
Mathematics for Engineers
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.
Plagiarism includes the following examples and it applies to all student assignments or
submitted work:
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Dr. Safeer Hussain Khan




Mathematics for Engineers
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
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Dr. Safeer Hussain Khan
Mathematics for Engineers
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. Differential Equations with boundary problems: Dennis G. Zill and Michael R.
Cullen.
2. Advanced Engineering Mathematics, Kreyszig, 7th ed., 1993, John Wiley.
3. Calculus, by Swokowski, Sixth Edition 1994,PWS Publishing Company, Boston.
4. Calculus with Analytic Geometry, by H. Edwards and D. E. Penny, 5th Edition,
1998, Prentice Hall.
5. Calculus, by R.T. Smith and R.B. Minton, 2nd Edition, 2002, McGraw-Hill.
6. Calculus: One and Several Variables by S. L. Salas, G. J. Etgen and E. Hille;
10th Edition, 2007, John Wiley & Sons.
7. Calculus, Early Transcendentals by J. Stewart, 6th Edition, 2008, Brooksw/Cole.
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
-Differential Equations, Paul Dawkins, http://tutorial.math.lamar.edu/index.aspx
- http://www.efunda.com
- http://www.sosmath.com/diffeq
- http://www.mathword.wolfram.com
- http://tutorial.math.lamar.edu/
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CATEGORY
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4
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Dr. Safeer Hussain Khan
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1
0
Score y/7
Mathematics for Engineers
Course Matrix
Objectives
Objective 1: To introduce
Outcomes
 Identify and classify differential equations by type, order and linearity.
different fundamental methods to
 Define an initial-value problem and state the theorem of existence and
solve first order differential
uniqueness of its solution.
equations and their applications
 Solve equations by the method of separation of variables.
 Find the general solution of a homogeneous equation
 Solve exact differential equations
 Find integrating factors.
 Solve linear equations and non-exact equations.
 Solve Bernoulli’s equation.
 Solve problems involving rates of growth, decay, and physical reaction.
 Solve equations solvable for y (dependent variable) and equations
solvable for x (independent variable).
 Recognize initial- and boundary-value problems.
Objective 2 To familiarize
students with the fundamental
 Recognize a linear differential operator.
methods in linear differential
 Reduce the order of a differential equation.
equations of the second (and
 Solve equations whose characteristic equation has distinct or repeated
higher) order(s) with constant
real roots or imaginary roots.
coefficients and their
 Solve non-homogeneous differential equations using the method of
applications.
undetermined coefficients.
 Solve non-homogeneous differential equations using the method of
variation of parameters.
 Solve some non-linear differential equations.
 Solve some vibration models.
 Solve higher order equations with constant coefficients.
Objective 3: To acquaint
 Find the general solution of the Cauchy-Euler equations
students with the basic methods in  Identify singular points and ordinary points.
differential equations of the
 Identify regular singular points and irregular singular points.
second order with non-constant
 Solve nonsingular differential equations by the power series method.
coefficients.
 Identify the interval of convergence of a power series solution.
 Find the indicial equation of a differential equation.
 Determine solutions of differential equations for various values of the
roots of the indicial equation
Objective 4: To learn the steps  Set up systems of equations from given situations.
of solving more than one
 Use elementary elimination techniques to solve systems of equations.
differential equation.
 Solve homogeneous linear systems by the Eigenvalues-Eigenvectors
method.
Objective 5: E. To develop the
ability to apply Laplace transforms
method to solve differential
equations and systems of
differential equations
 Find the Laplace transform of elementary functions and their
derivatives.
 Solve differential equations using the Laplace transform.
 Use the convolution integral to find inverse transforms.
 Solve initial-value problems.
 Solve systems of differential equations.
Objective 6: . To develop
basic methods for solving
problems involving partial
differential equations.
 Find a Fourier series solution of a function.
 Recognize Heat, Wave and Laplace operators.
 Find the general solution of second order PDEs by assuming a trial
solution of the form u(x, y) = f (mx + y).
 Use the method of separation of variables to solve boundary value
problems for the wave, heat and Laplace’s equations.
 Determine the D’Alembert solution of the second order PDEs.
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Assessment Tools
Exams
Quizzes
Assignments
Presentations
Exams
Quizzes
Assignments
Presentations
Exams
Quizzes
Assignments
Presentations
Exams
Quizzes
Assignments
Presentations
Exams
Quizzes
Assignments
Presentations
Exams
Quizzes
Assignments
Presentations
Dr. Safeer Hussain Khan
Mathematics for Engineers
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 Engineers
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.
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


Score
y/5
Dr. Safeer Hussain Khan

Interaction
with Audience
Mathematics for Engineers

 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 Engineers
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.
Section
1.1
1.2
2.2
2.3
2.4
2.6
Page 82
3.3
3.5
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.9
4.10
Page 250
6.1
6.2
6.3
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
Page 444
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
9.5
9.6
9.7
10.2
10.6
10.7
Question Numbers
1, 2, 3, 4,5,8,11
3,8,17,18,23,25,28
1-15 odd,19-23 odd,29
7-21 odd, 30*,32*
1-17 odd,23,25
1-15 odd,17-27 odd
1-39 odd
1*,2*,3*,6*,7*
1*,2*,3*
1-9 odd
1-19 odd,34
1-27 odd,34
9-35 odd
3-7 odd,17-21 odd,23-27 odd
1-17 odd
9-17 odd
1-9 odd
1-5 odd,11,13
1-35 odd
1-13 odd
1-13 odd
1-9 odd
1-29 odd
1-27 odd
1-29 odd,33-36
1-23 odd
1-39 odd,51,52
1-21 odd
1-19 odd
1-13 odd
1-31 odd
1-9 odd
1-9 odd
1-23 odd,35*
1-11 odd
1-9 odd
1-9 odd,19-33 odd
1-9 odd
13-18
1-15 odd,31-33
1-7 odd
1-15 odd,33*
1-21 odd
1-8
1-5
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Dr. Safeer Hussain Khan
Mathematics for Engineers
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--------------------------
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