ﺏﻼﺗﺎﻣﻟﺍ ﻲﻓ ﺔﺻﺎﺧﻟﺍ ﺔﻳﺿﺎﻳﺭﻟﺍ ﻊﺑﺍﻭﺗﻟﺍ

١٫٤ ﺔﻣﺩﻘﻣ

ﻌﺗﻟﺍ ﻡﺗﻳ ﺏﻼﺗﺎﻣﻟﺍ ﻲﻓ ﺩﻭﺩﺣﻟﺍ ﺕﺍﺭﻳﺛﻛ ﻊﻣ ﻝﻣﺎ ﻥﻣﺿ ﺩﻭﺩﺣﻟﺍ ﺕﺍﺭﻳﺛﻛ ﻝﺣﻟ ﺕﺩﻋﺃ ﺔﺻﺎﺧ ﻊﺑﺍﻭﺗ ﻝﻼﺧ ﻥﻣ

ﻕﺳﻧﻟﺍ ﺍﺫﻫ ﻥﻣﺿ ﺩﺍﺩﻋﻷﺍ ﻝﺛﻣﺗﻭ ، ﻱﺭﻁﺳ ﻉﺎﻌﺷ ﻰﻟﺇ ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ ﻝﻳﻭﺣﺗ ﻡﺗﻳ ﺙﻳﺣ ، ﺞﻣﺎﻧﺭﺑﻟﺍ ﺍﺫﻫ ًﺍءﺩﺑ ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ ﻲﻓ ﻝﻭﺣﺗﻣﻟﺍ ﻯﻭﻗ ﻕﻓﺍﻭﻳ ﻲﻟﺯﺎﻧﺗ ﻝﻛﺷﺑ ﻕﺳﻧﻟﺍ ﻥﻣﺿ ﺏﺗﺭﺗﻭ ، ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ ﺕﻼﻣﺎﻌﻣ ) ﺓﻭﻘﻟﺍ ﻥﻣ ) ﺓﻭﻘﻟﺍ ﻰﺗﺣﻭ (n

ﻲﻓ ﺎﻣﺑ (0 ) ﺙﻳﺣ ، ﻝﻭﺣﺗﻣﻠﻟ ﺔﻣﻭﺩﻌﻣﻟﺍ ﺕﻼﻣﺎﻌﻣﻟﺍ ﻙﻟﺫ

ﺔﺑﺗﺭ ﻰﻠﻋﺃ (n

ﻝﺣ ﻲﻓ ﺏﻼﺗﺎﻣﻟﺍ ﺞﻣﺎﻧﺭﺑ ﻪﻌﻣ ﻝﻣﺎﻌﺗﻳ ﻱﺫﻟﺍ ﺏﻭﻠﺳﻷﺍ ﺎﻣ ﻕﻓﺍﻭﺗﻠﻟ ﻙﻟﺫﻭ ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ ﻲﻓ ﻝﻭﺣﺗﻣﻠﻟ .ﺩﻭﺩﺣﻟﺍ ﺕﺍﺭﻳﺛﻛ : ﻁﻳﺳﺑ ﻝﺎﺛﻣ f(t) = 7ݐ^ସ+6ݐ^ଷ+3ݐ^ଶ+ݐ^ଵ+5

: ﺔﻓﻭﻔﺻﻣﻟﺎﺑ ﺍﺫﻫ ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ ﻝﻳﺛﻣﺗ ﻡﺗﻳ ܣ ൌ ሾ͹ ͸ ͵ ͳ ͷሿ

٢٫٤ ﻠﻣﻌﻟﺍ

ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ ﻰﻠﻋ ﺔﻳﺑﺎﺳﺣﻟﺍ ﺕﺎﻳ

١٫٢٫٤ ﺫﺟ ﺩﺎﺟﻳﺇ

ﺩﻭﺩﺣ ﺭﻳﺛﻛ ﺭﻭ

ﻊﺑﺎﺗﻟﺍ ﻥﺇ roots

، ﺩﻭﺩﺣ ﺭﻳﺛﻛ ﺭﻭﺫﺟ ﺩﺎﺟﻳﺇ ﻪﻘﻳﺭﻁ ﻥﻋ ﻥﻛﻣﻳ ﻱﺫﻟﺍ ﺏﻼﺗﺎﻣﻟﺍ ﻲﻓ ﺹﺎﺧﻟﺍ ﻊﺑﺎﺗﻟﺍ ﻭﻫ

ﺭﻭﺫﺟ ﻲﻫ ﻉﺎﻌﺷﻟﺍ ﺍﺫﻫ ﺭﺻﺎﻧﻋﻭ ﺩﻭﻣﻋ ﻉﺎﻌﺷ ﻝﻛﺷ ﻰﻠﻋ ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ ﺭﻭﺫﺟ ﻊﺑﺎﺗﻟﺍ ﺍﺫﻫ ﻲﻁﻌﻳ ﺙﻳﺣ .ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ

25

ƒ ) ﻝﺎﺛﻣ ١ : (

%f(t) = 7*t^4+6*t^3+3*t^2+t^1+5;

A = [7 6 3 1 5];

A_roots = roots(A)

െͲǤͺ͵Ͳͳ ൅ ͲǤ͸͸͵͸݅

െͲǤͺ͵Ͳͳ െ ͲǤ͸͸͵͸݅

ͲǤͶͲͳͷ ൅ ͲǤ͸ͺ͸Ͷ݅

ͲǤͶͲͳͷ െ ͲǤ͸ͺ͸Ͷ݅

ƒ ) ﻝﺎﺛﻣ ٢ : (

%f(t) = 7t^3+5t^2-3t^1+10 A = [7 5 -3 10];

A_roots = roots(A)

െͳǤͷ͸ͺ͵

ͲǤͶʹ͹Ͳ ൅ ͲǤͺͷ͵ͷ݅

ͲǤͶʹ͹Ͳ െ ͲǤͺͷ͵ͷ݅

٢٫٢٫٤ ﺩﻭﺩﺣ ﺭﻳﺛﻛ ﺩﺎﺟﻳﺇ

ﻩﺭﻭﺫﺟ ﻥﻣ ًﺎﻗﻼﻁﻧﺍ

ﺹﺎﺧﻟﺍ ﻊﺑﺎﺗﻟﺍ ﻡﺍﺩﺧﺗﺳﺎﺑ ﻊﺑﺎﺗﻟﺍ ﺍﺫﻫ ﺔﻔﻳﻅﻭ ﻥﺃ ﻱﺃ ، ﻩﺭﻭﺫﺟ ﻥﻣ ًﺎﻗﻼﻁﻧﺇ ﺩﻭﺩﺣ ﺭﻳﺛﻛ ﺩﺎﺟﻳﺇ ﻥﻛﻣﻳ poly

.ﺭﻛﺫﻟﺍ ﻕﺑﺎﺳ ﻊﺑﺎﺗﻠﻟ ًﺎﻣﺎﻣﺗ ﺔﺳﻛﺎﻌﻣ

ƒ ) ﻝﺎﺛﻣ ١ : (

A = [1 3 4 5 6];

roots(A)

െͳǤ͸͸͸ͷ ൅ ͲǤ͹ͳͲͶ݅

െͳǤ͸͸͸ͷ െ ͲǤ͹ͳͲͶ݅

ͲǤͳ͸͸ͷ ൅ ͳǤ͵Ͷͳͺ݅

ͲǤͳ͸͸ͷ െ ͳǤ͵Ͷͳͺ݅

poly(ans)

ܽ݊ݏ ൌ ሾͳ ͵ Ͷ ͷ ͸ሿ

26

ƒ ) ﻝﺎﺛﻣ : (2

A = [3 5 6 7 8 9];

roots(A)

ͲǤͷʹ͹ͷ ൅ ͳǤͲ͸͹ͻ݅

ͲǤͷʹ͹ͷ െ ͳǤͲ͸͹ͻ݅

െͳǤ͵ͳͻ͹

െͲǤ͹ͲͲͻ ൅ ͳǤͲͷͶͳ݅

െͲǤ͹ͲͲͻ െ ͳǤͲͷͶͳ݅

poly(ans)

ܽ݊ݏ ൌ ሾͳ ͳǤ͸͸͸͹ ʹ ʹǤ͵͵͵ ʹǤ͸͸͸͹ ͵ሿ

ﺭﻳﻏ ﺩﻭﺩﺣ ﺭﻳﺛﻛ ﻙﺎﻧﻫ ﻥﺃ ﻲﻧﺎﺛﻟﺍ ﻝﺎﺛﻣﻟﺍ ﻥﻣ ﻅﺣﻼﻧ ، ﺭﻭﺫﺟﻟﺍ ﺱﻔﻧ ﻪﻟ ًﻻﻭﺃ ﻩﺎﻧﻠﺧﺩﺍ ﻱﺫﻟﺍ ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ

ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ (ﺩﻳﻟﻭﺗ ﺓﺩﺎﻋﺇ) ءﺎﻋﺩﺗﺳﺍ ﺩﻧﻋ ًﺎﻘﺑﺳﻣ ﻝﺧﺩﻣﻟﺍ ﻊﺑﺎﺗﻟﺍ ﻰﻠﻋ ﻝﻭﺻﺣﻟﺍ ﺓﺭﻭﺭﺿﻟﺎﺑ ﺱﻳﻟ ﻲﻟﺎﺗﻟﺎﺑﻭ ) ﻊﺑﺎﺗﻟﺍ ﻥﻣ ﺩﻳﺩﺟﻟﺍ ﺯﻭﺎﺟﺗﺗ ﻻ ﺄﻁﺧ ﺔﺑﺳﻧ ﻪﻳﻓ ﻊﺑﺎﺗ ﺍﺫﻫ ﻪﻧﺃ ﺭﻛﺫﻟﺎﺑ ﺭﻳﺩﺟ ﻭﻫ ﻝﺎﻣﻛ ، (poly

) 1/1000000 .ﺕﻻﺎﺣﻟﺍ ﺽﻌﺑ ﻲﻓ ﺭﻬﻅﺗ ﺩﻗ (

٣٫٢٫٤ ﺏﺎﺳﺣ

ﺔﻧﻳﻌﻣ ﺔﻣﻳﻗ ﺩﻧﻋ ﺩﻭﺩﺣ ﺭﻳﺛﻛ ﺔﻣﻳﻗ

ﺹﺎﺧﻟﺍ ﻊﺑﺎﺗﻟﺍ ﻡﺍﺩﺧﺗﺳﺎﺑ ﺏﻼﺗﺎﻣﻟﺍ ﻲﻓ ﺔﻳﻠﻣﻌﻟﺍ ﻩﺫﻫ ﻡﺗﺗ polyval(p,x)

ﺭﺑﻌﻳ ﺙﻳﺣ ﻕﺳﻧﻟﺍ p

ﺯﻣﺭﻟﺍﻭ ، ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛﻟ ﻝﺛﻣﻣﻟﺍ (ﺔﻓﻭﻔﺻﻣﻟﺍ) ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ ﺏﺎﺳﺣ ﺩﺍﺭﻣﻟﺍ ﻝﻭﺣﺗﻣﻟﺍ ﺔﻣﻳﻗ ﻥﻋ ﺭﺑﻌﻳ x

.ﻩﺩﻧﻋ

ƒ ) ﻝﺎﺛﻣ ١ : ( G(x) = ݔ^ଶ+ݔ^ଵ+1

p = [1 1 1];

x = 3;

gx = polyval(p,x)

gx= 13

ﺹﺎﺧﻟﺍ ﻊﺑﺎﺗﻟﺍ ﻡﺍﺩﺧﺗﺳﺎﺑ ﺔﻧﻳﻌﻣ ﺔﻣﻳﻗ ﻝﺟﻷ ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ ﺔﻣﻳﻗ ﺩﺎﺟﻳﺇ ﺔﻳﻧﺎﺛ ﺔﻘﻳﺭﻁﺑ ﻥﻛﻣﻳ ﺎﻣﻛ subs

ﺔﻣﻳﻠﻌﺗﻟﺎﺑ ﺔﻧﺎﻌﺗﺳﻻﺎﺑﻭ ﻝﻭﺣﺗﻣﻟﺍ ﺔﻣﻳﻗ ﻝﻳﻭﺣﺗﺑ ﺭﻳﺧﻷﺍ ﺍﺫﻫ ﻡﻭﻘﻳ ﺙﻳﺣ syms

ﻝﻣﺎﻌﺗﻟﺍ ﻥﻛﻣﻳ ﺯﻣﺭ ﻰﻟﺇ x

27

ﺭﻣﻷﺍﻭ ، ﻪﻳﻠﻋ ﻑﺭﻌﺗﻟﺍﻭ ﺞﻣﺎﻧﺭﺑﻟﺍ ﻝﺑﻗ ﻥﻣ ﻪﻌﻣ ﺔﻣﻳﻗ ﺩﻧﻋ ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛﻟ ﺔﻣﻳﻘﻟﺍ ﺏﺎﺳﺣﺑ ﻡﻭﻘﻳ ﻱﺫﻟﺍ subs

ﺔﻣﻳﻠﻌﺗﻟﺍ ﻥﺃ ﻱﺃ) ﺔﺑﻭﻠﻁﻣﻟﺍ ﻝﻭﺣﺗﻣﻟﺍ ﺭﻳﻐﺗﻣﻟﺍ ﻑﻳﺭﻌﺗ ﺎﻬﺗﻔﻳﻅﻭ syms

(x

ƒ ) ﻝﺎﺛﻣ : (2

syms x

gx = x^2 + x + 1;

subs(gx,3)

ans = 13

ƒ ) ﻝﺎﺛﻣ : (3

syms x y

gx = y*x^2 + x*y + 1;

subs(gx,x,3)

ans = 12*y + 1

subs(gx,y,3)

ans = 3*x^2 + 3*x + 1

ƒ ) ﻝﺎﺛﻣ : (4

ﺔﻓﻭﻔﺻﻣﻟﺍ ﺭﺻﺎﻧﻋ ﻝﺟﺃ ﻥﻣ ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ ﻡﻳﻗ ﺏﺎﺳﺣ ﺏﻭﻠﻁﻣﻟﺍ x

p=[1 1 1]

x = [2 4 6]

gx = polyval(p,x)

݃ݔ ൌ ሾ͹ ʹͳ Ͷ͵ሿ

٤٫٢٫٣ ﺩﻭﺩﺣﻟﺍ ﺕﺍﺭﻳﺛﻛ ﻕﺎﻘﺗﺷﺍ

ﺭﻳﺛﻛ ﻕﺗﺷﻣ ﺩﺎﺟﻳﺇ ﻥﻛﻣﻳ ﻊﺑﺎﺗﻟﺍ ﻡﺍﺩﺧﺗﺳﺎﺑ ﺩﻭﺩﺣ

polyder ﻝﺛﻣﻳ ﺩﻭﺩﺣ ﺭﻳﺛﻛ ﻥﻋ ﺓﺭﺎﺑﻋ ﺔﺟﻳﺗﻧﻟﺍ ﻥﻭﻛﺗﻭ

.ﻝﺻﻷﺍ ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ ﻕﺗﺷﻣ

ƒ ) ﻝﺎﺛﻣ ١ : (

gx = [2 5 -6 -5];

a = polyder(gx)

a = ሾ͸ ͳͲ െ͸ሿ

(ﺕﺎﻳﺛﺍﺩﺣﻻﺍ ﺭﻭﺎﺣﻣ) ﺭﻭﺎﺣﻣﻟﺍ ﺱﻔﻧ ﻰﻠﻋ ًﺎﻌﻣ ﺎﻣﻬﻣﺳﺭ ﻥﻛﻣﻳ ، ًﺎﻳﻧﺎﻳﺑ ﻪﻘﺗﺷﻣ ﻊﻣ ﻊﺑﺎﺗﻟﺍ ﺔﻧﺭﺎﻘﻣﻟ : ﺔﻳﻟﺎﺗﻟﺍ ﺕﺎﻣﻳﻠﻌﺗﻟﺎﺑ

28

x=-10:0.5:10;

gx=[2 5 -6 -5];

a = polyder(gx)

plot(x,polyval(gx,x),'-*r',x,polyval(a,x),'-og')

ﺭﻣﻷﺍ ﻡﺍﺩﺧﺗﺳﺎﺑ ﻙﻟﺫﻭ ﻯﺭﺧﺃ ﺔﻘﻳﺭﻁﺑ ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ ﻕﺗﺷﻣ ﻡﺍﺩﺧﺗﺳﺍ ﻥﻛﻣﻳ ﺎﻣﻛ syms

ﺭﻣﻷﺍﻭ

diff(function name) ...

ƒ ) ﻝﺎﺛﻣ ٢ : (

syms x

gx = 2*x^3 + 5*x^2 - 6*x - 5;

diff(gx)

ans = 6*x^2 + 10*x -6

ƒ ) ﻝﺎﺛﻣ : (3

syms x

gx = 2*sin(2*x)*exp(x)

29 diff(gx)

ans = 4*cos(2*x)*exp(x) + 2*sin(2*x)*exp(x)

ƒ ) ﻝﺎﺛﻣ : (4

syms x y gx = 2*sin(x*y) diff(gx,x)

ans = 2*cos(x*y)*y

ﻊﺑﺎﺗﻟﺍ ﻥﺃ ﻅﺣﻼﻧ ﻝﺎﺛﻣﻟﺍ ﺍﺫﻫ ﻲﻓ diff

ﻝﺎﺣ ﻲﻓ) ﺕﻻﻭﺣﺗﻣﻟﺍ ﺩﺣﻷ ﺔﺑﺳﻧﻟﺎﺑ ﻕﺗﺷﻣﻟﺍ ﺏﺎﺳﺣ ًﺎﺿﻳﺃ ﻪﻧﻛﻣﻳ

) ﻝﻭﺣﺗﻣﻠﻟ ﺔﺑﺳﻧﻟﺎﺑ ﻊﺑﺎﺗﻟﺍ ﻕﺗﺷﻣ ﺩﺎﺟﻳﺈﺑ ﺎﻧﻣﻗ ﺍﺫﻫ ﺎﻧﻟﺎﺛﻣ ﻲﻓ ، ﻊﺑﺎﺗﻟﺍ ﻲﻓ ﻝﻭﺣﺗﻣ ﻥﻣ ﺭﺛﻛﺃ ﺩﻭﺟﻭ x

.(

ﻲﻠﻳ ﺎﻣﻛ ﻙﻟﺫﻭ ﻕﻭﻓﺎﻣﻭ ﺔﺛﻟﺎﺛﻟﺍﻭ ﺔﻳﻧﺎﺛﻟﺍ ﺔﺑﺗﺭﻣﻟﺍ ﻥﻣ ﺕﺎﻘﺗﺷﻣﻟﺍ ﺩﺎﺟﻳﺇ ﻊﺑﺎﺗﻟﺍ ﺍﺫﻫ ﻝﻼﺧ ﻥﻣ ًﺎﺿﻳﺃ ﻥﻛﻣﻳ ﺎﻣﻛ

diff(gx,x,2) diff(gx,x,3)

ﻝﻭﺣﺗﻣﻠﻟ ﺔﺑﺳﻧﻟﺎﺑ (ﺙﻟﺎﺛﻟﺍ ﻭﺃ ﻲﻧﺎﺛﻟﺍ) ﻕﺗﺷﻣﻟﺍ ﺩﺎﺟﻳﺇ ﻱﺃ x

....

٥٫٢٫٤ ﺩﻭﺩﺣﻟﺍ ﺕﺍﺭﻳﺛﻛ ﻝﻣﺎﻛﺗ

ﻊﺑﺎﺗﻟﺍ ﺎﻧﻧﻛﻣﻳﻭ ، ﻕﺎﻘﺗﺷﻼﻟ ﺔﺳﻛﺎﻌﻣ ﺔﻳﻠﻣﻋ ﻭﻫ ﻕﺎﻘﺗﺷﻻﺍ ﻥﺃ ﻑﻭﺭﻌﻣﻟﺍ ﻥﻣ polyint

ﺔﺑﺗﻛﻣﻟﺍ ﻲﻓ ﺩﻭﺟﻭﻣﻟﺍ

ﺭﻳﺛﻛ ﺕﻼﻣﺎﻌﻣ ﻝﺎﺧﺩﺇ ﻝﻼﺧ ﻥﻣ ﻊﺑﺎﺗ ﻝﻣﺎﻛﺗ ﺩﺎﺟﻳﺇ ﻥﻣ ﺏﻼﺗﺎﻣﻟﺍ ﻲﻓ ﺔﻳﺿﺎﻳﺭﻟﺍ ﻝﻛﺷﺑ ﺩﻭﺩﺣﻟﺍ

. ﺔﻘﺑﺎﺳﻟﺍ ﺔﻠﺛﻣﻷﺍ ﻲﻓ ﻕﺑﺳ ﺎﻣﻛ (ﺔﻓﻭﻔﺻﻣ)ﻕﺳﻧ

ƒ ﻝﺎﺛﻣ :

) ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ ﻝﻣﺎﻛﺗ ﺩﺎﺟﻳﺇ ﺏﻭﻁﻣﻟﺍ 6x²+10x-6

ﻝﻣﺎﻛﺗ ﺕﺑﺎﺛ ﻝﺟﺃ ﻥﻣ ( k = -5

p =[6 10 -6];

k = -5;

gx = polyint(p,k)

gx = ሾʹ ͷ െ͸ െͷሿ

ﻡﺍﺩﺧﺗﺳﺎﺑ ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ ﻝﻣﺎﻛﺗ ﺩﺎﺟﻳﺇ ﻥﻛﻣﻳ ﺎﻣﻛ syms

ﻊﺑﺎﺗﻟﺍﻭ int ﻊﺑﺎﺗﻟﺍ ﻝﺛﺎﻣﻳ ﻝﻛﺷﺑ ﻙﻟﺫﻭ diff

.... ﻕﺗﺷﻣﻟﺍ ﺩﺎﺟﻳﻹ int(gx)

30

٦٫٢٫٤ ﺟﻳﺇ

ﻡﺋﻼﻣﻟﺍ ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ ﺔﻟﺩﺎﻌﻣ ﺩﺎ

، ﻲﻧﺣﻧﻣﻟﺍ ﺍﺫﻬﻟ ﺔﻟﺩﺎﻌﻣ ﻝﻛﺷﺗ ﻥﺍ ﺩﻳﺭﺗﻭ ﻪﺗﻟﺩﺎﻌﻣ ﻑﺭﻌﺗ ﻻ ﻲﻧﺣﻧﻣ ﻥﻣ ﻁﺎﻘﻧ ﺔﻋﻭﻣﺟﻣ ﻙﻳﺩﻟ ﻥﺎﻛ ﺍﺫﺇ ﻊﺑﺎﺗﻟﺎﺑ ﺔﻧﺎﻌﺗﺳﻻﺍ ﻥﻛﻣﻳﻓ polyfit

ﻛ ﺔﻟﺩﺎﻌﻣ ﻙﻳﻁﻌﻳ ﻪﻧﺃ ﺙﻳﺣ ، ﺔﻳﻠﻣﻌﻟﺍ ﻩﺫﻬﺑ ﻡﺎﻳﻘﻠﻟ ﻡﺋﻼﻣﻟﺍ ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛ

.ﻪﻳﻠﻋ ﻝﻭﺻﺣﻟﺍ ﺩﻳﺭﺗ ﻱﺫﻟﺍ ﺩﻭﺩﺣﻟﺍ ﺭﻳﺛﻛ ﺔﺟﺭﺩ ﺭﺎﺗﺧﺗ ﻙﻧﺃ ﺙﻳﺣﺑ ﻲﻧﺣﻧﻣﻠﻟ

ƒ ﻝﺎﺛﻣ :

x=[0:0.2:1.2];

y=[1 2 4 7 8 5 2];

u=polyfit(x,y,3)

u = ሾെʹͲǤͺ͵͵ ʹʹǤͻͳ͸͹ ͵ǤͳͷͶͺ ͲǤͺ͵͵͵ሿ

t=polyval(u,x) plot(x,y,'-or',x,t,'-*')

٧٫٢٫٤ ﻠﻣﻌﻟﺍ

ﺩﻭﺩﺣﻟﺍ ﺕﺍﺭﻳﺛﻛ ﻰﻠﻋ ﺔﻳﺿﺎﻳﺭﻟﺍ ﺕﺎﻳ

ﻥﻛﻣﻳ ﻥﻭﻛﺗ ﻥﺍ ﺔﻅﺣﻼﻣ ﻊﻣ ﺎﻬﻟ ﺔﻠﺛﻣﻣﻟﺍ ﺕﺎﻓﻭﻔﺻﻣﻟﺍ ﻊﻣ ﻝﻣﺎﻌﺗﻟﺍ ﻝﻼﺧ ﻥﻣ ﺩﻭﺩﺣﻟﺍ ﺕﺍﺭﻳﺛﻛ ﺡﺭﻁﻭ ﻊﻣﺟ

.... ﻙﻟﺫ ﺢﺿﻭﻳ ﻲﻟﺎﺗﻟﺍ ﻝﺎﺛﻣﻟﺍﻭ ﺔﺟﺭﺩﻟﺍ ﺱﻔﻧ ﻥﻣ ﻥﻳﺗﻓﻭﻔﺻﻣﻟﺍ ﻼﻛ

var_name = input ('text','s') ;

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ƒ ﻝﺎﺛﻣ : A = 2x⁴ + x³ + 3x² + x + 1

B = 4x² - x -1

: ﻝﺣﻟﺍ

A = [2 1 3 1 1];

B = [4 -1 -1];

C = A + [0,0,B]

D = A - [0,0,B]

C = ሾʹ ͳ ͹ Ͳ Ͳሿ D = ሾʹ ͳ െͳ ʹ ʹሿ

، (Convolution) ﺔﻣﻠﻛ ﺭﺻﺗﺧﻣ conv ﻊﺑﺎﺗﻟﺎﺑ ﺔﻧﺎﻌﺗﺳﻻﺎﺑ ﺎﻬﺑ ﻡﺎﻳﻘﻟﺍ ﻥﻛﻣﻳﻓ ءﺍﺩﺟﻟﺍ ﺔﻳﻠﻣﻋ ﺎﻣﺍ ﺩﻭﺩﺣﻟﺍ ﺕﺍﺭﻳﺛﻛ ﻑﺭﻌﺗ ﻥﺃ ﻁﺭﺷﺑ ﺩﻭﺩﺣﻟﺍ ﺕﺍﺭﻳﺛﻛ ءﺍﺩﺟ ﻰﻠﻋ ﻝﻭﺻﺣﻟﺍ ﻡﺗﻳ ﻊﺑﺎﺗﻟﺍ ﺍﺫﻫ ﻡﺍﺩﺧﺗﺳﺎﺑ ﺙﻳﺣ

.ﺎﻬﺗﻼﻣﺎﻌﻣ ﻥﻋ ﺓﺭﺑﻌﻣﻭ ﺔﻘﻓﺍﻭﻣ ﻕﺎﺳﻧﺄﺑ

conv(A,B) %conv(B,A)

ans = ሾͺ ʹ ͻ Ͳ Ͳ െʹ െͳሿ

٨٫٢٫٤ ﻯﺭﺧﺍ ﺕﺎﻳﻠﻣﻋ

o ﺩﺎﺟﻳﺇ ﺕﺎﻘﺗﺷﻣﻟﺍ ﺔﻳﺋﺯﺟﻟﺍ

) ﻲﺑﻭﻘﻌﻳﻟﺍ (

ﺙﻼﺛﻟ ﻊﺑﺍﻭﺗ ﺙﻼﺛﺑ ﻝﻳﻫﺎﺟﻣ [x,y,z]

ﻥﻌﺗﺳﺍ ﻊﺑﺎﺗﻟﺎﺑ

.jacobian syms x y z

f = [x*y*z; y; x + z];

v = [x, y, z];

R = jacobian(f, v) b = jacobian(x + z, v) R =

[ y*z, x*z, x*y]

[ 0, 1, 0]

[ 1, 0, 1]

b = [ 1, 0, 1]

o ﻙﻓ ﺱﺍﻭﻗﻷﺍ ﻭ

ﻊﻳﻣﺟﺗ ﺕﻼﻣﺎﻌﻣﻟﺍ

ﻥﻣ ﺱﻔﻧ ﺱﻷﺍ , ﻥﻌﺗﺳﺍ ﻊﺑﺎﺗﻟﺎﺑ

.collect syms x y

32

R1 = collect((exp(x)+x)*(x+2)) R2 = collect((x+y)*(x^2+y^2+1), y) R3 = collect([(x+1)*(y+1),x+y]) return

R1 =

x^2 + (exp(x) + 2)*x + 2*exp(x) R2 =

y^3 + x*y^2 + (x^2 + 1)*y + x*(x^2 + 1) R3 =

[ y + x*(y + 1) + 1, x + y]

o ﻙﻓ ﺱﺍﻭﻗﻷﺍ ﻭ

ﺭﺷﻧ ﺭﻳﺛﻛ ﺩﻭﺩﺣﻟﺍ ﻭﺃ

ﺔﻟﺩﺎﻌﻣﻟﺍ ,

ﻥﻌﺗﺳﺍ ﻊﺑﺎﺗﻟﺎﺑ . expand syms x

expand((x-2)*(x-4))

ﺞﺗﺎﻧﻟﺍ : ans =

x^2 - 6*x + 8 syms a b c

expand(log((a*b/c)^2))

ﺞﺗﺎﻧﻟﺍ : ans =

log((a^2*b^2)/c^2)

o ﻁﻳﺳﺑﺗ ﻊﺑﺍﻭﺗﻟﺍ ﻭ

ﺕﻻﺩﺎﻌﻣﻟﺍ ﻭ

ﺕﺍﺭﻳﺛﻛ ﺩﻭﺩﺣﻟﺍ

, ﻥﻌﺗﺳﺍ ﺏﺎﺗﻟﺎﺑ . simplify 1) syms a b c

simplify(exp(c*log(sqrt(a+b)))) ans =

(a + b)^(c/2) 2) syms x

S = [(x^2 + 5*x + 6)/(x + 2), sqrt(16)];

R = simplify(S) R =

[ x + 3, 4]

33

ﻱﺩﺟﺑﻷﺍ ﺏﻳﺗﺭﺗﻟﺍ ﺏﺳﺣﻭ ﺔﻣﺩﺧﺗﺳﻣﻟﺍ ﻊﺑﺍﻭﺗﻟﺍ ﻡﻫﺃ ﻥﻳﺑﻳ ﻲﻟﺎﺗﻟﺍ ﻝﻭﺩﺟﻟﺍ ﺩﻭﺪﺤﻟﺍ ﺮﻴﺜﻛ ﺏﺮﺿ conv

ﺩﻭﺪﺤﻟﺍ ﺮﻴﺜﻛ ﺔﻤﺴﻗ deconv

ﺔﻣﻮﻠﻌﻣ ﺎﻫﺭﻭﺬﺟ ﺩﻭﺪﺣ ﺮﻴﺜﻛ ﺔﻟﺩﺎﻌﻣ ﻑﺎﺸﺘﻛﺍ poly

ﺩﻭﺪﺣ ﺮﻴﺜﻛ ﻖﺘﺸﻣ polyder

ﺩﺎﺠﻳﺇ ﻢﺋﻼﻤﻟﺍ ﺩﻭﺪﺤﻟﺍ ﺮﻴﺜﻛ polyfit

ﺩﻭﺪﺤﻟﺍ ﺮﻴﺜﻛ ﻞﻣﺎﻜﺗ polyint

ﺏﺎﺴﺣ ﺔﻨﻴﻌﻣ ﺔﻤﻴﻗ ﺪﻨﻋ ﺩﻭﺪﺤﻟﺍ ﺮﻴﺜﻛ ﺔﻤﻴﻗ polyval

ﺩﻭﺪﺤﻟﺍ ﺮﻴﺜﻛ ﺭﻭﺬﺟ ﺩﺎﺠﻳﺇ roots

: ﺔﻣﺎﻫ ﺔﻅﺣﻼﻣ ﺔﻠﻣﺟ ﻝﺣ ﻥﻣ ﺏﻼﺗﺎﻣﻟﺍ ﻲﻓ ﺕﺎﻓﻭﻔﺻﻣﻟﺍ ﺎﻧﻧﻛﻣﺗ n

ﺏ ﺔﻟﺩﺎﻌﻣ n

ﺢﺿﻭﻳ ﺎﻣﻛ ﻙﻟﺫﻭ ﺔﻣﺎﺗ ﺔﻟﻭﻬﺳﺑ ﺭﻳﻐﺗﻣ

.... ﻲﻟﺎﺗﻟﺍ ﻝﺎﺛﻣﻟﺍ 5x₁ – 2x₂ + x₃ = 1

x2 + x3 = 0 x1 + 6x2 – 3x3 = 4

: ﻝﺣﻟﺍ

clear

A = [5 -2 1;0 1 1; 1 6 -1];

B = [1;0;4];

X=inv(A)*B

X = ͲǤͷ ͲǤͷ

െͲǤͷ

... ﺭﺧﺁ ﻝﺎﺛﻣ ﺫﺧﺄﻧﻟ x1 – 5x2 – 8x3 + x4 = 3

3x₁ + x₂ – 3x₃ – 5x₄ = 1 x₁ – 7x₃ + 2x₄ = -5 11x₂ + 20x₃ – 9x₄ = 2

: ﻝﺣﻟﺍ

clear

A = [1 -5 -8 1;3 1 -3 -5;1 0 -7 2;0 11 20 -9];

B = [3;1;-5;2];

det(A)

34

X=inv(A)*B

ﺔﻓﻭﻔﺻﻣﻟﺍ ﺩﺩﺣﻣ ﻥﺃ ﺔﻅﺣﻼﻣﺑ A

ﺔﻓﻭﻔﺻﻣﻟﺍ ﺏﻭﻠﻘﻣ ﺩﺟﻧ ﻥﺃ ﻥﻛﻣﻳ ﻻ ﺎﻧﻧﺃ ﻲﻧﻌﻳ ﺍﺫﻬﻓ ﺭﻔﺻﻟﺍ ﻱﻭﺎﺳﻳ

.ﻝﺣ ﺎﻬﻟ ﺱﻳﻟﻭ ﺔﻘﻓﺍﻭﺗﻣ ﺭﻳﻏ ﺔﻘﺑﺎﺳﻟﺍ ﺕﻻﺩﺎﻌﻣﻟﺍ ﺔﻠﻣﺟ ﻥﻭﻛﺗ ﻲﻟﺎﺗﻟﺎﺑﻭ