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 poin
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 expre
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
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)
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) li
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
for Engineering - MATH 103
Work Sheet Nr. 3
Types of functions.
1. Find the domain and range of the functions:
f (x) = 2 sin(x3 ).
1
Department of Mathematics
Dr. El-Sharkawy
Winter 2012
Mathematics
for Engineering - MATH 103
Work Sheet Nr. 1
Numbers and Inequalities.
1. Dene the following: N Z Q R.
2. Prove that 3 Q. (Hint: prove
Department of Mathematics
Assoc. Prof. Tarek Emam
Winter 2014
Mathematics
for Engineering Students (MATH-301)
Classwork Nr. 9
Name :
ID:
Group:
Exercise 1
Use the Greens theorem to evaluate:
xy dx + (
Department of Mathematics
Assoc. Prof. Tarek Emam
Winter 2014
Mathematics
for Engineering Students (MATH-301)
Classwork Nr. 7
Name :
ID:
Group:
Exercise 1
Evaluate the following iterated integral:
2 x
Department of Mathematics
Assoc. Prof. Tarek Emam
Winter 2014
Mathematics
for Engineering Students (MATH-301)
Classwork Nr. 6
Name :
ID:
Group:
Exercise 1
Evaluate the following integral:
1 2
(t + 3t
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
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
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
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
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
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
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
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
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)
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) (
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
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,
Department of Mathematics
Assoc. Prof. Tarek Emam
Winter 2014
Mathematics
for Engineering Students (MATH-301)
Classwork Nr. 5
Name :
ID:
Group:
No Submission is Requested !
Exercise 1
Consider a thin
Department of Mathematics
Assoc. Prof. Tarek Emam
Winter 2014
Mathematics
for Engineering Students (MATH-301)
Classwork Nr. 4
Name :
ID:
Exercise 1
Find the Fourier series of the function:
cfw_
1
: x
Math 103 Class Work Sheet (8) Solution
[1] 4 16 dx 4 x (i) 2 x 16 dx 2 x 2 16 ln x 16 x c x x 1 1 (ii) sin(5 x 1) dx sin(5 x 1) 5dx cos(5 x 1) c 5 5 1 1 (iii) cosh(6 x ) dx cosh(6 x ) 6dx sinh(6 x) c
Mathematics for Engineers I (Math103).student-intranet/faculties/math/2009 Fall/math103
Class Work Sheet 81.
1. Evaluate each of the following integrals: i) iv) 2 x+
4 x 2
dx
ii) v) viii) xi)
sin(5x 1
Mathematics for Engineers I (Math103).student-intranet/faculties/math/2008 Fall/math103
Class Work Sheet 71.
1. Graph each of the following functions: (a) f (x) = x3 3x + 3 (b) f (x) = x4 2x2 (c) y =
Mathematics for Engineers I (Math103).student-intranet/faculties/math/2009 Fall/math103
Class Work Sheet 61.
1. Using LHospital rule, evaluate each of the following limits: a) lim x2 1 x 1
x1
9
cos x
Mathematics for Engineers I (Math103).student-intranet/faculties/math/2009 Fall/math103
Class Work Sheet 51.
1. Find y =
dy dx
if: b) y =
ex 1+x
a) y = x2 ex c) y = e3x e) y = g) y =
3
d) y = ex cos