O’zbekiston respublikasi oliy va o’rta maxsus ta’lim vazirligi urganch davlat universiteti fizika-matematika fakulteti amaliy matematika va informatika yo’nalishi 184-guruh talabasi nazarov orazmyratning

>> m1

a=4

m=6

0.3806

2. n-natural son berilgan bo’lsin. Ildizni hisоblash dasturini tuzing.

function m2()

n=input('n=');

s=0;

for i=1:n

s=sqrt(2+s);

end

disp(s);

end

Natija:

>> m2

n=15

2.0000

3. Bеrilgan n-natural sоn uchun quyidagi yig’indini hisoblash dasturini tuzing.

function m3()

n=input('n=');

s=0;

surat=1;

maxraj=1;

for i=1:n

surat= surat*sin(2*i-1);

maxraj=maxraj*cos(2*i);

s=surat/maxraj;

end;

disp(s);

end

Natija:

>> m3

n=15

-1.8662

4. Bеrilgan n-natural sоn uchun quyidagi yig’indini hisoblash dasturini tuzing.

function m4()

n=input('n=');

s=0;

surat=1;

maxraj=1;

for i=1:n

maxraj=maxraj+cos(2*i);

s=s+surat/maxraj;

end;

disp(s)

end

Natija:

>> m4

n=100

-293.5395

5. Bеrilgan n-natural sоn uchun quyidagi ifodani hisoblash dasturini tuzing.

function m5 ()

n=input('n=');

x=0;

s=0;

for i=1:n

x=x+cos(i);

s=x+(1+cos(i));

end

disp(s);

end

Natija:

>> misol5

n=125

1.1177

6. Quyidagi ifodani hisoblash dasturini tuzing. x-haqiqiy son.

function m6 ()

x=input('x=');

s=1;

for i=1:6

s=s*(x-(2^i-1))/(x-2^i);

end

disp(s);

end

Natija:

>> m6

x=245

1.0274

7. Yig’indini hisоblash dasturini tuzing. n-natural sоn x-haqiqiy son.

function misol7 ()

x=input('x=');

n=input('n=');

s=0;

for i=1:n

x=cos(x^i);

s=s+x;

end

disp(s);

end

Natija:

>> misol7

x=452

n=12

9.3927

8. Ildizni hisоblash dasturini tuzing. n-natural sоn .

function m8()

n=input('n=');

s=1;

for i=1:n;

s=(sqrt(3*n+s))-3*n*n;

end

disp(s);

end

Natija:

>> m8

n=4

-47.4969 + 5.9817i

9. bo’lsa kеtma-kеtlik yig’indini hisоblash dasturini tuzing.

function m9()

x=input('x=');

a=input('a=');

b=input('b=');

c=input('c=');

n=input('n=');

for k=0:n-1;

y(k+1)=x*x-a*b*x+c^k;

end;

for k=1:n

disp(y(k));

end;

end

Natija:

>> m9

x=5

a=1

b=3

c=4

n=3

11

14

2

6-Mavzu: Matlab 2014 dasturda bir o’lchovli massivlar va ular ustida amallar bajarish.

Nazariy qism:

Murakkab hisoblarni bajarish uchun Besic yoki Paskal dasturlash tillarida maxsus dasturlarni tuzish talab qilingan bo’lar edi. Matlab – vektorlar matrissalar va massivlar ustida murakkab hisoblarni bajarish uchun mo’ljallangan maxsus tizimdir. Bundan u har qanday berilgan o’zgaruvchini uning konkret qiymatiga asoslanib vektor matrissa yoki massiv deb qabul qiladi. Masalan , x=1 berilganj bo’lsa demak x qiymati birga teng bo’lgan yagona elementli vektor. Agar uch elementli vektorni berish zarur bo’lsa uning elementlarining qiymatlarini probbellar bilan ajratilib, kvadrat kavs ichida yozib chiqish kerak. Matrissa va vektorlarning ayrim elementlari bilan bir qatorda ularning hamma elementlari (massivlar) ustida amallar bajarish mumkin buning uchun amal belgisining oldiga nuqta qo’yiladi. Masalan , * operatori vektorlari yoki matrissalarini ko’paytirishni anglatadi, Operator esa massivning hamma elementlarini elementlararo ko’paytirishni bildiradi. Matrissa skalyarga ko’paytiriladigan M *2 va M.*2 ifodalar teng kuchlidir. Vektorlarni ko’paytirish M=M1*M2 ifodasida ko’paytirish belgisidan oldin nuqta qo’yilmaganligi uchun tizim hato to’g’risidagi Inner matrix dimensions must agree (matrissalarning o’lchamlari o’zaro moslashishi kerak) degan axborotni berdi. Hato tuzatilgandan keyin to’g’ri natija olindi. Matrissalarni transponerlash, ya’ni ustunlarini satrlari bilan almashtirish uchun .’ Operatoridan foydalaniladi. Ustunlaridagi elementlarning yig’indisi sum operatori yordamida hisoblaniladi. Satrlaridagi elementlarining yig’indisini hisoblash uchun matrissa avval transponerlaniladi va transponerlangan matrissaning ustunlaridagi elementlarining yig’indisi aniqlaniladi. Matrissalarni Matlab 2014 dasturida ishlaganda ullarda for operatoridan foydalanib sikl bajariladi va e’lon qilinadi.

matrix(m, n, [[a11, a12, ...], [a21, a22, ...], ...]) returns an m×n matrix of the domain type Dom::Matrix().

matrix(m, n, [a11, a12, ..., a21, a22, ..., a.m.n]) returns an m×n matrix of the domain type Dom::Matrix().

matrix(m, 1, [a1, a2, ...]) returns an m×1 column vector of the domain type Dom::Matrix().

Amaliy qism:

1.n-natural son berilgan bo’lsin.1 dan n gacha bo’lgan sonlarni ekranga chiqaruvchi dastur tuzing.

function m1()

n=input('n=');

for i=1:n

a(i)=i;

disp(a(i));

end

end

Natija:

>> m1

n=5

1

2

3

4

5

2. n-natural son va x{n} ketma-ketlik berilgan bo’lsin. Ketma – ketlikning juft elementlarini va ularning soni hisoblang.

function m2()

n=input('n=');

k=0;

for i=1:n

fprintf('a(%.d)=',i);

a(i)=input('');

end

for i=1:n

if mod(a(i),2)==0

k=k+1;

disp(a(i));

end

end

fprintf('k=%.d',k);

end

Natija:

>> m2

n=5

a(1)=4

a(2)=9

a(3)=145

a(4)=268

a(5)=458

4

268

458

k=3>>

3. n-natural son va x{n} ketma-ketlik berilgan bo’lsin. Ketma – ketlikning toq elementlarini va ularning soni hisoblang.

function m3()

n=input('n=');

k=0;

for i=1:n

fprintf('a(%.d)=',i);

a(i)=input('');

end

for i=1:n

if mod(a(i),2)==1

k=k+1;

disp(a(i));

end

end

fprintf('k=%.d',k);

end

Natija:

>> m3

n=3

a(1)=579

a(2)=876

a(3)=463

579

463

k=2>>

4. n-natural son va x{n} ketma-ketlik berilgan bo’lsin. Ketma – ketlikning dastlab juft elementlarini keyin toq elementlarini ekranga chiqaruvchi dastur tuzing.

function m4()

n=input('n=');

for i=1:n

fprintf('a(%.d)=',i);

a(i)=input('');

end

for i=1:n

if mod(a(i),2)==0

disp(a(i));

end

end

for i=1:n

if mod(a(i),2)==1

disp(a(i));

end

end

end

Natija:

>> m4

n=5

a(1)=489

a(2)=562

a(3)=325

a(4)=789

a(5)=628

562

628

489

325

789

5. n-natural son va x{n} ketma-ketlik berilgan bo’lsin. Ketma – ketlikdagi barcha tub sonlarni ekranga chiqaring va ularning sonini hisoblang.

function m5()

n=input('n=');

k=0;

for i=1:n

fprintf('a(%.d)=',i);

a(i)=input('');

end

for i=1:n

for j=1:a(i)

m=mod(a(i),j);

if m==0

k=k+1;

end

end

if k==2

fprintf('a(%.d)=%.d',i,a(i));

disp('\n');

end

k=0;

end

end

Natija:

>> m5

n=3

a(1)=2

a(2)=31

a(3)=26

a(1)=2\n

a(2)=31\n

6. n-natural, k-haqiqiy son va x{n} ketma-ketlik berilgan bo’lsin. Ketma – ketlik elementlarini k soniga bo’lib chiqing.(k!=0).

function m6 ()

n=input('n=');

k=input('k=');

for i=1:n

fprintf('a(%.d)=',i);

a(i)=input('');

end

for i=1:n

s=a(i)/k;

disp(s);

end

end

Natija:

>> m6

n=5

k=3

a(1)=3

a(2)=6

a(3)=9

a(4)=21

a(5)=33

1

2

3

7

11

7. n-natural son va x{n} ketma-ketlik berilgan bo’lsin. Ketma – ketlikning eng katta elementini toping.

function m7()

n=input('n=');

max=0;

for i=1:n

fprintf('a(%.d)=',i);

x(i)=input('');

end

for i=1:n

if max

max=x(i);

end

end

disp(max);

end

Natija:

>> m7

n=3

a(1)=458

a(2)=786

a(3)=897

897

8. n-natural son va x{n} ketma-ketlik berilgan bo’lsin. Ketma – ketlikning eng kichik elementini toping.

function misol8()

n=input('n=');

for i=1:n

fprintf('a(%.d)=',i);

a(i)=input('');

end

min=a(1);

for i=2:n

if min>a(i)

min=a(i);

end

end

disp(min);

end

Natija:

>> misol8

n=5

a(1)=25

a(2)=43

a(3)=78

a(4)=14

a(5)=89

14

7-Mavzu: Matlab 2014 dasturda ikki o’lchovli massivlar va ular ustida amallar bajarish.

Nazariy qism:

Matlab 2014 dasturida ikki o’lchovli massivlar va ular ustida amallar bajarish. Quyidagi ko’rinishida belgilangan asosda aniqlaniladi va dasturga kiritiladi. matlabda ma'lumotlar faqat matritsa shaklida tashkil qilinadi. Buning esa 3ta usuli bor:

• 
  ma'lumotlarni klaviaturadan to’qridan-to’qri kiritish;
  
• 
  ma'lumotlarni faylli disklardan kiritish;
  
• 
  ma'lumotlarni matlab komandalari yordamida xosil qilish.
  

Klaviaturadan to’g’ridan-to’g’ri kiritishga misollar ko’raylik:

>> х= [ 5 4 -3]yoki >> х= [ 5, 4, -3]

tеrilsa, x – vеktor-qator dеb qabul qilinib х(1) =5, х(2)=4, х(3)= -3 bo’ladi.

>> у= [ 0 2 2 3

5 -3 6 2 ] yoki у= [ 0 2 2 3; 5 -3 6 2 ]

у-(2х4) o’lchovli matritsa bo’ladi vа у(1.1)=0, у(1.2)=2, у(1.3)=2, у(1.4)=3, у(2.1)=5, у(2.2)=3, у(2.3)= 6, у(2.4)=2 bo’ladi. Matritsada (;) qatorlar orasini ajratish uchun kеrak.

Matritsa elеmеntlari ifoda bo’lishi mumkin:

Z= [sin(0) sqrt(4) 2^3+1 5/2 3^2].

U holda quyidagi vеktor aniqlanadi:

Z= [0 4.000 9.000 2.500 9.000]

Bеrilgan matritsani kеngaytirish orqali ham matritsa qolishi mumkin. Masalan, x1q [x 1 2] dеb olsak,

х₁= [5 4 -3 1 2] xosil bo’ladi.

Agar х(5)= 7 dеsak, avvalgi x vеktor х= [5 4 -3 0 8] kabi kеngaytiriladi, bunda ko’rinib turibdiki, x(4) ga “0” qiymat bеrildi.

Endi u matritsadan foydalanib,

c= [1 2 3 4]

y₁= [y; c]

bеlgilash natijasida

y₁= [0 2 2 3

5 -3 6 2

1 2 3 4]

matritsani xosil qilamiz.

Amaliy qism:

1. 
   O’lchamlari nxm bo’lgan matritsa elementlari yig’indisini toping. n,m-natural son.
   

function m1()

n=input('n=');

m=input('m=');

for i=1:n

for j=1:m

fprintf('a(%.d,%.d)=',i,j);

a(i,j)=input('');

end

end

a

end

Natija:

>> m1

n=2

m=2

a(1,1)=1

a(1,2)=4`

a(2,1)=3

a(2,2)=5
a = 1 4

3 5

2. 
   O’lchamlari nxm bo’lgan matritsa hosil qiling.n,m-natural son.
   

function m2()

n=input('n=');

m=input('m=');

s=0;

for i=1:n

for j=1:m

fprintf('a(%.d,%.d)=',i,j);

a(i,j)=input('');

end

end

for i=1:n

for j=1:m

s=s+a(i,j);

end

end

disp(s);

end

Natija: >> m2

n=3

m=3

a(1,1)=4

a(1,2)=6

a(1,3)=8

a(2,1)=9

a(2,2)=5

a(2,3)=3

a(3,1)=4

a(3,2)=8

a(3,3)=9

56
3.O’lchamlari nxm bo’lgan matritsaning eng kichik elementlari yig’indisini toping. n,m-natural son

function m3()

n=input('n=');

m=input('m=');

s=0;

for i=1:n

for j=1:m

fprintf('a(%.d,%.d)=',i,j);

a(i,j)=input('');

end

end

k=a(1,1);

for i=1:n

for j=1:m

if k>a(i,j);

k=a(i,j);

end

end

end

for i=1:n

for j=1:m

if k==a(i,j);

s=s+a(i,j);

end

end

end

disp(s);

end

Natija:

>> m3

n=2

m=2

a(1,1)=4

a(1,2)=8

a(2,1)=9

a(2,2)=12

4
4.O’lchamlari nxm bo’lgan matritsaning eng katta elementlari yig’indisini toping.

function m4()

n=input('n=');

m=input('m=');

s=0;

for i=1:n

for j=1:m

fprintf('a(%.d,%.d)=',i,j);

a(i,j)=input('');

end

end

k=a(1,1);

for i=1:n

for j=1:m

if k

k=a(i,j);

end

end

end

for i=1:n

for j=1:m

if k==a(i,j);

s=s+a(i,j);

end

end

end

disp(s);

end

Natija:

>> m4

n=2

m=2

a(1,1)=12

a(1,2)=25

a(2,1)=78

a(2,2)=68

78

6.O’lchamlari nxm bo’lgan matritsani toq satridagi elementlarini chiqaring. n,m-natural son.

function m6()

n=input('n=');

m=input('m=');

for i=1:n

for j=1:m

fprintf('a(%.d,%.d)=',i,j);

a(i,j)=input('');

end

end

for i=1:2:n

for j=1:m

disp(a(i,j))

end

end

end

Natija:

>> m6

n=2

m=2

a(1,1)=4

a(1,2)=15

a(2,1)=36

a(2,2)=76

4

15

7.O’lchamlari nxm bo’lgan matritsaning juft satrdagi elementlarini chiqaring. n,m-natural son.

function m7()

n=input('n=');

m=input('m=');

for i=1:n

for j=1:m

fprintf('a(%.d,%.d)=',i,j);

a(i,j)=input('');

end

end

for i=2:2:n

for j=1:m

disp(a(i,j))

end

end

end

Natija:

>> m7

n=2

m=2

a(1,1)=16

a(1,2)=18

a(2,1)=25

a(2,2)=34

25

34

8.A matrisaga B matrisa ko`paytirilsin. Hosil bo`lgan C matrisani n dan katta elementlarini o`rtacha kiymati hisoblansin.

function m8()

n=input('n=');

n1=input('n1=');

m1=input('m1=');

for i=1:n1

for j=1:m1

fprintf('a(%.d,%.d)=',i,j);

a(i,j)=input('');

end

end

for i=1:n1

for j=1:m1

fprintf('b(%.d,%.d)=',i,j);

b(i,j)=input('');

end

end

c=a*b;

disp(c);

s=0;

k=0;

for i=1:n1

for j=1:m1

if n

k=k+1;

s=s+c(i,j);

end

end

end

s=s/k;

disp(s);

end

Natija:

>> m8

n=2

n1=2

m1=2

a(1,1)=23

a(1,2)=45

a(2,1)=29

a(2,2)=89

b(1,1)=1

b(1,2)=27

b(2,1)=87

b(2,2)=99

3938 5076

7772 9594

6595

9.O’lchamlari nxm bo’lgan matrisa ustida quyidagi amallar bajarilsin: matrisani eng kichik elementi joylashgan qator va ustun elementlarini o’rni almashtirilsin. n,m-natural son.

function m9()

n=input('n=');

m=input('m=');

c=1;

b=1;

p=0;

for i=1:n

for j=1:m

fprintf('a(%.d,%.d)=',i,j);

a(i,j)=input('');

end

end

k=a(1,1);

for i=1:n

for j=1:m

if k>a(i,j)

k=a(i,j);

b=i;

c=j;

end

end

end

k=1;

for i=1:n

for j=1:m

if j==c

for q=1:m

p=a(q,c);

a(q,c)=a(b,q);

a(b,q)=p;

end

end

end

break;

end

disp(a)

end

Natija:

>> m9

n=2

m=2

a(1,1)=13

a(1,2)=64

a(2,1)=59

a(2,2)=79

13 59

64 79

10. 
    O’lchamlari nxm bo’lgan matrisa ustida quyidagi amallar bajarilsin: matrisani eng katta elementi joylashgan qator va ustun elementlarini o’rni almashtirilsin. n,m-natural son.
    

function m10()

n=input('n=');

m=input('m=');

c=1;

b=1;

p=0;

for i=1:n

for j=1:m

fprintf ('a(%.d,%.d)=',i,j);

a(i,j)=input('');

end

end

disp(a);

k=a(1,1);

for i=1:n

for j=1:m

if k

k=a(i,j);

b=i;

c=j;

end

end

end

k=1;

for j=1:m

if j==c

for q=1:m

p=a(q,c);

a(q,c)=a(b,q);

a(b,q)=p;

end

end

end

disp(a);

end

Natija:

>> m10

n=2

m=2

a(1,1)=44

a(1,2)=56

a(2,1)=150

a(2,2)=256

44 56

150 256
44 150

56 256