The document contains solved math and programming problems from a class. It includes: 1) A MATLAB program to calculate the sum of even numbers from 0 to 100 and the sum of a series until it exceeds 1.995. 2) A program to generate the Fibonacci sequence up to the 12th term. 3) Code to calculate the number of students who got a grade of A or F, and the mean and standard deviation of grades. 4) A script to evaluate terms in a difference equation. 5) A program that plots the magnitude of a circuit's equivalent impedance versus frequency and finds the minimum impedance and its corresponding frequency.

1. Sheet 3
>> a=0:2:100;
>>sum(a)
ans =
2550
>>
k=0;
sum=0;
for i=0:1000
k=k+1;
sum=sum+1/2^i;
if (sum>1.995) break
end
end
k =
9
>>sum
sum =
1.9961
>>
3.1 Write a MATLAB program to add all the even
numbers from 0 to 100.
3.2 Add all the terms in the series
1 +
1
2
+
1
4
+
1
8
+ ⋯
until the sum exceeds 1.995.

2. Sheet 3
x=ones(1,12);
for i=3:12
x(i)=x(i-2)+x(i-1);
end
>>sequance
>>x
x =
1 1 2 3 5 8 13 21 34 55 89 144
>>
x=[70,85,90,97,50,60,71,83,91,86,77,45,67,88,64,
79,75,92,69];
A=0;
F=0;
For i=1: length(x);
if x(i)> 90
A=A+1;
elseif x(i)<= 60
F=F+1;
end
end
>>degres
>> A
A =
3.3 The Fibonacci sequence is given as
1 1 2 3 5 8 13 21 34 …
Write a MATLAB program to generate the Fibonacci
sequence up to the twelfth term.
3.4 The table below shows the final course grade and its
correspondingrelevant letter grade(a) Determine the
number of students who attained the grade of A and F.
(b) What are the mean grade and the standard deviation?

3. Sheet 3
2
>> F
F =
3
>>mean(x)
ans =
75.7368
>>std(x)
ans =
14.3946
>>
clear all
y=ones(1,7);
x=ones(1,7);
y(1)=2;
for i=3:7
y(i)=2*y(i-1)-y(i-2)+x(i);
end
z=y(4:7)
z =
2 4 7 11
3.5 Write a script file to evaluate y[1], y[2], y[3] and y[4]
for the difference equation:y[n]=2y[n−1]−y[n−2]+x[n]for
n ≥0. Assume that x[n]=1 for n ≥0, y[−2]=2 andy[−1]=1.

4. Sheet 3
clear all; close all; clc;
l=4; c=1e-6; w=200:1200;
Z=100+1j*w*l+1./(1j*w*c);
semilogy(w,abs(Z))
xlabel('angular frequency rad/sec');
ylabel('abs(z)');
zmin =
min(abs(Z))
k=find(Z==zmin);
w0 = w(k)
zmin =
100
w0 =
500
>>
3.6 The equivalent impedance of a circuit is given as
𝑍𝑍𝑒𝑒𝑒𝑒(𝑗𝑗 𝑗𝑗) = 100 + 𝑗𝑗 𝑗𝑗𝑗𝑗 +
1
𝑗𝑗 𝑗𝑗𝑗𝑗
If L = 4 H and C = 1 μF,
(a) Plot |Zeq(jw )| versus w. (b) What is the minimum impedance?
(c) With what frequency does the minimum impedance occur?
NAME: Ahmed El-morsy Abdel-hamid
Sec: 1
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THANK YOU 