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Sample Midterm Exam (Max. Duration: 50 minutes)
Disclaimer
1. The Questions are only sample. Actual exam question could be considerably different from these
samples questions in content and level of difficulty
2. The format of the exam is not
Final Exam Preparatory
1.
Determine
2 x +1
dx
3
Let u=2 x +1
du
=2 , also du=2 dx
dx
du
Thus, dx= 2
2 x +1
1
dx = (2 x+1)dx
3
3
1
du
u
3
2
1
u du
6
2
1u
+C
6 2
1 2
u +C
12
Now substituting, u=2 x +1 , we get
2 x +1
1
dx = ( 2 x +1 )2+C
3
12
Try also:
3 x
Midterm Exam 2 Preparatory Material
Exam content and format is NOT guaranteed
1.
f ( x)
The derivative of a continuous function
is given such that
f ' ( x )=( x+ 4 )( x7 )2
.
Find
i. Find the values (x-values) of all relative extrema for the function (1 m
Midterm Exam 2 Preparatory Material
Exam content and format is NOT guaranteed
1.
f ( x)
The derivative of a continuous function
is given such that
f ' ( x )=( x+ 4 )( x7 )2
.
Find
i. Find the values (x-values) of all relative extrema for the function (1 m
ACG 2071 Exam 2 Review Problems
5-1. On July 1, JKL Corporations packaging department had Work in Process inventory of 6,000 units that
were 75% complete with respect to materials and 30% complete with respect to conversion costs. The
cost of these units
Page 1 of 6
MATH 102 - FINAL EXAM Jan 1 2013
Qatar University, Department of Math, Stat 8; Phys
Math 102 (Cale II), Final Exam, Fall 2012
Name: QU ID Serial _Group L _
Show all your work in order to get full credit. Calculators are not allowed.
1. (7 Poin
Qatar University a "mu
Department of Mathematics, Statistics. and Physics -
Calculus II - Math 102 QATAR umvsns 'r'v
Final Exam - Spring 2016
Name:
Name in Arabic:\_
Instructor: SerialNumber:
Total score : . / 30
Exam Regulations:
1. The exam ti
Qatar University 'igqmm,
Department of Mathematics, Statistics, and Physics 4-.
$215 112.01;
QATAR umveas fv
Math 102- Calculus II
Final Exam - Fall 2015
Name (as appears in Bllckboud) :
Univ. Id:
K
I
Instructor: 3 Section: L
Exam Regulations: Page 2
Qatar University
Department of Mathematics, Statistics, and Physics
Calculus II - Math 102
Final Exam Fall 2014
Name:_
Univ.Stud.Id:_
Name in Arabic:_
Section: L _
Instructor:_
SerialNumber:_
Total score : -/ 80
Exam Regulations:
1. The exam time limit is
Qatar University
Department of Mathematics, Statistics, and Physics
CalculusIIMath102
FinalExamSpring2015
Name:_
Univ.Stud.Id:_
Name in Arabic:_
Section: L _
Instructor:_
SerialNumber:_
Total score : -/ 80
Exam Regulations:
1. The exam time limit is 120 m
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
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
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
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
Mechanical Vibrations:
The Mass-Spring Oscillator
By
Dr. Mahmoud BOUTEFNOUCHET
Mechanical Vibrations: The Mass-Spring Oscillator
Table of Contents
1
Introductio
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
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
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
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
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
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
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
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
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
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 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