COURSE SYLLABUS
ENGL 202
AMERICAN LITERATURE II
COURSE DESCRIPTION
A survey of American literature following the American Renaissance. Two critical papers are
required.
RATIONALE
The study of literature helps to fulfill the university aims of fostering co
GUC
MATH-101
For Management
Winter 2016
Lecture # 7
Chapter 3
Differentiation of functions
1
Main objectives
Chapter 3
Differentiation of functions
Introduce the formal definition of the derivative
of a function.
Study geometric meaning of the derivative
Robotics
Islam S. M. Khalil
German University in Cairo
Islam S. M. Khalil
Hill Climbing using Newton-Raphson Method
Outline
Hill climbing
Newton-Raphson method
Newton-Raphson in optimization
Islam S. M. Khalil
Hill Climbing using Newton-Raphson Method
Hil
Robotics
Islam S. M. Khalil
German University in Cairo
October 1, 2016
Islam S. M. Khalil
Kinematics
Position and Orientation of Rigid Bodies
Position: A pAB R31 in A.
Orientation: A RB R33 in A.
RT = R1 A RB B RA = I | R |= +1
A B
R = A xB A yB A zB
xA y
1
Modeling of a Pantograph Haptic Device
Islam S. M. Khalil and Mohamed Abu Seif
Kinematics of the Pantograph Haptic Device
The pantograph haptic device consists of 5 links with lengths li for i = 1, . . . , 5. First, we assign frames
of reference to each
Robotics
Islam S. M. Khalil
German University in Cairo
September 18, 2016
Islam S. M. Khalil
Kinematics
Vector Functions
A vector v in a reference frame A depends on a scalar verifiable q.
We can say that v is a vector function of q in A. Otherwise, v is
Robotics
Islam S. M. Khalil
German University in Cairo
September 19, 2016
Islam S. M. Khalil
Kinematics
Angular Velocity
Let bl , b2 , and b3 form a right-handed set of mutually
perpendicular unit vectors fixed in a rigid body B moving in a
reference fram
Robotics
Islam S. M. Khalil
German University in Cairo
Islam S. M. Khalil
Homogeneous Transformations
ZX 0 Z 00 Euler angles
Rotation around Z -axis
cos sin 0
Rz () = sin cos 0
0
0
1
Rotation around X 0 -axis
1
0
0
Rx 0 () = 0 cos sin
0 sin cos
Rotation
Robotics
Islam S. M. Khalil
German University in Cairo
September 6, 2016
Islam S. M. Khalil
Kinematics
Outline
Motivation
Agenda
Generalized pseudoinverse
Over- and under-determined systems
Islam S. M. Khalil
Kinematics
Motivation
Autonomous Robotic Syste
Petersen 1
Kylie Petersen
Professor Williams
THEO 104
April 15, 2016
Biblical Worldview Essay
As a Christian, it is important to always keep in mind the teachings within the Bible. One
of the major components is that God created mankind in his own image.
GUC
MATH103
For Engineering
Winter 2015
Lecture # 1
1
Instructor and Textbooks
Lecturer: Dr. Hany El-Sharkawy
Office:
C3.106
E- mail: [email protected]
Textbooks:
Lecture notes your main source
I- Available on the INTRAnet via:
V:\Faculties\Basic
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
For Engineering - Math 103
Solution for Work Sheet Nr. 8
Continue: Some Applications on Differentiation.
VI- Extrema & Inflection points, Optimization & curve sketching
[1] (i) f ( x ) 3 x
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
For Engineering - Math 103
Solution for Work Sheet Nr. 9
Integration
3
x2
x 1
2
1
x dx
c x2 c
3
3
1
x
2
4
1
4
x 2
8
3
(b) 3 dx 8 x dx 4 dx 8
4 ln | x | c 2 4 ln | x | c
x
x
2
x
x
1
[1
Mathematics Department
Dr. Hany El Sharkawy
Winter 2012
Math103 - Engineering 1st semester
Solution of Inequalities
(I) Some Rules:
Rule 1: If x
y Then
(a) k x
ky
If k
0
(b) k x
ky
If k
0
Rule 2: If x
1
x
y
1
y
If x and y have the same sign,
i.e. +ve toge
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
For Engineering - Math 103
Solution for Work Sheet Nr. 3
Types of functions
[1] (i) f ( x ) 2 sin( x )
3
Df R
1 sin( x 3 ) 1
2 2 sin( x 3 ) 2
2 y 2
R f [2,2]
1
1 sin x
D g cfw_x : 1 sin
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
For Engineering - Math 103
Solution for Work Sheet Nr. 7
Continue: Some Applications on Differentiation.
III Linear approximation & IV- Differential
[1] The linear approximation of the func
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
For Engineering - Math 103
Solution for Work Sheet Nr. 5
Differentiation.
[1] (i) f ( x ) x , f ( x h) ( x h)
3
3
f ( x h) f ( x )
( x h) 3 x 3
[( x h) x][( x h) 2 x( x h) x 2 ]
lim
lim
h
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
For Engineering - Math 103
Solution for Work Sheet Nr. 6
Continue: Differentiation.
[1] (a) f ( x) cos x, f ( x h) cos( x h)
f ( x h) f ( x )
cos( x h) cos( x)
cos( x). cos(h) sin( x). sin(
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
For Engineering - Math 103
Solution for Work Sheet Nr. 4
Some Techniques for limits of functions
[1] (i) lim 3 x 2 x x 1 3( 2) 2( 2) ( 2) 1 59
x 2
(ii) lim
x2
4
2
4
2
2x 2 1
2(2) 2 1
9
2
2
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
For Engineering - Math 103
Solution for Work Sheet Nr. 2
Functions
4 x2
9
2
For each one input value we have two output values, x 9 y 2 4 is NOT a function.
[1] x 9 y 4
2
[2]
y2
2
2 y 6x
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
For Engineering - Math 103
Solution for Work Sheet Nr. 1
Numbers and Inequalities
[1]
N cfw_1, 2, 3, 4, 5, .
Z cfw_. , 3, 2, 1, 0, 1, 2, 3, .
Natural numbers
Integers
Rational numbers Q x
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
for Engineering - MATH 103
Work Sheet Nr. 8
Continue: Some Applications on Dierentiation.
VI- Extrema & Inection points, Optimization & curve sketching
Denition: Critical numbers of a funct
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
for Engineering - MATH 103
Work Sheet Nr. 9
Not so short introduction to Integration.
1. Find the following indenite integrals
(
(
8
1)
4)
(a)
x + 2 dx.
(b)
+
dx.
x
x3 x
x
1
2 3x2
2x
e
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
for Engineering - MATH 103
Work Sheet Nr. 7
Continue: Some Applications on Dierentiation.
III- Linear approximation & IV- Dierential
1. Find the linear approximation of the function f (x) =
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
for Engineering - MATH 103
Work Sheet Nr. 2
Functions.
1. Does the relation x2 + 9y 2 = 4 dene y as a function of x?
2. Does the expression 2y 6x = 2 denes y as a function of x?
3. Find the
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
for Engineering - MATH 103
Work Sheet Nr. 6
Continue: Dierentiation.
1. Use the denition of the derivative to nd f (x):
i) f (x) = cos x
ii) f (x) = sinh x
2. Find the equation of the tange
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
for Engineering - MATH 103
Work Sheet Nr. 5
Dierentiation.
1. Use the denition of the derivative to nd f (x):
i) f (x) = x3
ii) f (x) =
x+1
1
iv)f (x) =
x
2. (i) Show that the function f (
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
for Engineering - MATH 103
Work Sheet Nr. 4
Some techniques for limits of functions.
1. Evaluate each of the following limits:
2
i) lim (3x4 + 2x2 x + 1)
2x +1
ii) lim x2 +6x4
x2
iii) lim
x