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QATAR UNIVERS’TY
Department of Mathematics, Statistics & Physics
First Exam
Math-Engineer, MATH 217
March 16th, 2013 Time: 2 hrs
Student Name: QU-ID #:
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OAIAR leVERS TY
Department of Mathematics, Statistics & Physics
First Exam
Math for Engineers, MATH 217
November 2", 2013 Time: 2 hrs
Student Name: QU-lD #:
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QATAR UNIVERSETY
Department of Mathematics, Statistics & Physics
Second Exam
Math-Engineer, MATH 217
April 27‘“, 2013 Time: 2 hrs
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Higher Order Linear Differential Equations
6 Higher-Order Equations
The theoretical structure and methods of solutions developed for second order
differential equations is extended, in this section, to linear higher order differential
equation.
We briefly

The Laplace Transform
5 Solving Initial Value Problems
The Laplace transform can be used to solve initial-value problems for linear
differential equations with constant coefficients.
The previous methods, namely, the method of undetermined coefficients an

The Laplace Transform
7 Special Functions
In previous sections, we outlined the general procedure involved in solving initial
value problems by means of the Laplace transform.
Some of the most interesting elementary applications of the transform method oc

Higher Order Linear Differential Equations
7 Cauchy-Euler Equations
In this section, we will introduce one type of differential equations with variable
coefficients and, present its method of solutions.
More precisely, we will discuss the method of soluti

Department of Mathematics, Statistics and Physics
College of Arts and Science
Qatar University
Some Mathematical Models
Involving First Order
Differential Equations
By
Dr. Mahmoud BOUTEFNOUCHET
Some Mathematical Models Involving First Order Differential E

Department of Mathematics, Statistics and Physics
College of Arts and Science
Qatar University
The Laplace Transform
By
Dr. Mahmoud BOUTEFNOUCHET
The Laplace Transform
Table of Contents
1
Introduction . 3
2
Definitions. 4
3
Properties . 7
4
Inverse Laplac

Systems of Linear Differential Equations
4 Homogeneous Linear Systems
In this section, we shall be concerned only with linear systems with constant
coefficients and we shall discuss a procedure for obtaining a general solution for the
homogeneous system:

Department of Mathematics, Statistics and Physics
College of Arts and Science
Qatar University
Mechanical Vibrations:
The Mass-Spring Oscillator
By
Dr. Mahmoud BOUTEFNOUCHET
Mechanical Vibrations: The Mass-Spring Oscillator
Table of Contents
1
Introductio

Department of Mathematics, Statistics and Physics
College of Arts and Science
Qatar University
First Order Differential
Equations
By
Dr. Mahmoud BOUTEFNOUCHET
First Order Differential Equations
Table of Contents
1
Introduction . 3
2
Initial-Value Problem

Department of Mathematics, Statistics and Physics
College of Arts and Science
Qatar University
Systems of Linear
Differential Equations
By
Dr. Mahmoud BOUTEFNOUCHET
Systems of Linear Differential Equations
Table of Contents
1
Introduction . 3
2
Definition

Partial Differential Equations
4 Heat Flow in a Wire
Consider the one-dimensional heat flow boundary-value problem:
U xx U t =
0
(4.1)
( 0, t ) U=
( L, t ) 0
U=
=
U ( x,0 ) f ( x )
;
;
0< x <L, t >0, >0
0<x<L
The first equation governs the flow of heat

Partial Differential Equations
5 Vibrating String
Consider the one-dimensional wave boundary-value problem:
a 2 U xx U tt =
0
0, t ) U ( L,
t) 0
=
U (=
(5.1)
=
U ( x,0 ) f ( x )
U ( x,0 ) g ( x )
=
t
0<x<L, t >0
;
;
0<x<L
;
0<x<L
The first equation g

2 Fourier Series
Partial Differential Equations
Fourier series are infinite series designed to represent general periodic functions in
terms of simple ones, namely, cosines and sines. They constitute a very important tool,
in particular in solving problem

Department of Mathematics, Statistics and Physics
College of Arts and Science
Qatar University
Basic Definitions
and Terminology
By
Dr. Mahmoud BOUTEFNOUCHET
Basic Definitions and Terminology
Table of Contents
1
Introduction . 3
2
Definitions. 4
3
Classif

Coilege of Arts & Sciences .
Department of Mathematics, Statistics 8- Physics
Mathematics Program
7 Find the most general function M(x, y) so that the differential equation below is exact: (Do not solve
the differential equation).
2y X—l
M(x,y)dx + ﬁ

College of Arts 8. Sciences
Department of Mathematics, Statistics 8. Physics
Mathematics Pro ram
W
i
‘ 1. Bacteria in a certain culture increase at a rate proportional to the-number present. I
If the number N increases from 1000 to 2000 Mona hour, how m

OAIAR UNIVERSiTY
Department of Mathematics, Statistics & Physics
First Exam
Math-Engineer, MATH 217
November 10‘", 2012 Time: 2 hrs
Student Name: QU-ID #:
Show all of your work to receive credit. No credit will be given to answers for non requested ques

College of Arts 8. Sciences
Department of Mathematics, Statistics 8: Physics
Mathematics Program
A 2 Kg mass is attached to a spring with stiffness k — 32me. The mass is [spi‘éiéedﬁ .2 me er
to the right of the equilibrium point and given a velocity of 2.

College of Arts 8. Sciences
Department of Mathematics, Statistics & Physics
Mathematics Program
Hadlemaﬁcs for Engineers (Ill'l'l'l Ill)
Instructor : Dr Mahmoud BOU'IEFNOUCHET
Exam Duration: 1 M 5
Monday ,1 6" of November 2009 -
1 1:00 - 12:15 PM

,hé (idol;
QATAR UNIVERSETY
Department of Mathematics, Statistics & Physics
Second Exam
Math-Engineer, MATH 217
December 15‘", 2012 Time: 2 hrs
Student Name: QU-ID #:
Show all of your work to receive credit. No credit will be given to answers for non re

Math 217- Summer -2016
Homework I
Group L02
Department of Mathematics, Statistics, and Physics
Show all your work in order to get full credit,
Every student has to submit the answers by Monday, 18-July -2016
Q1:(20 pts) Solve the initial value problems
a)

College of Arts & Sciences
Department of Mathematics, Statistics & Physics
Mathematics Program
Mathematics for Engineers (MATH 217)
Instructor : Dr Mahmoud BOUTEFNOUCHET
COLLEGE OF ARTS & SCIENCES
Department of Mathematics & Physics
HOMEWORK 2-8
Questions

3 Classification
Partial Differential Equations
As we know, ordinary differential equations arise naturally when modeling physical
phenomena, such as mechanical and electrical oscillations. If a phenomena involves
functions of more than one variable, then

College of Arts & Sciences
Department of Math, Statistics & Physics
Mathematics Program
Mathematics for Engineers (MATH 217)
Instructor : Dr Mahmoud BOUTEFNOUCHET
COLLEGE OF ARTS & SCIENCES
Department of Mathematics & Physics
ASSIGNMENT 1
Question 1
State

Department of Mathematics, Statistics and Physics
College of Arts and Science
Qatar University
Higher Order Linear
Differential Equations
By
Dr. Mahmoud BOUTEFNOUCHET
Higher Order Linear Differential Equations
Table of Contents
1
Introduction . 3
2
Initia