The document contains 4 problems: 1) Calculating the isothermal work done on a gas compressed from 23L to 3L. 2) Interpolating viscosity data to find viscosity at 7.5°C. 3) Solving a system of 3 equations. 4) Approximating the solution to a differential equation.

1. 1.- Dados los siguientes datos,encuentre el trabajo isotérmico (𝑤 = ∫ 𝑃𝑑𝑉) Realizado sobreel gas
cuando se comprime de 23L a3l.
clear clc
syms x Y c1 c2 c3 c4 c5 D
X=[3 8 13 18 23] % V,l
f=[12.5 3.5 1.8 1.4 1.2] % P,atm
plot(X, f, 'p')
C=[c1, c2, c3, c4, c5]
y=Y*ones(5,5)
for i=1:5
for j=1:5
s(i, j)=sum(X.^(i-1).*X.^(j-1))
end
end
p=inv(s)
d=D*ones(1,5)
for i=1:5
D(i)=sum(f.*X.^(i-1))
end
c=p*D'
f1=c(1,1)+c(2,1)*x+c(3,1)*x^2+c(4,1)*x^3+c(5,1)*x^4
hold on
fplot(char(f1), [23 3], 'r')
F=f1
syms x
Funcion=vpa(int(F, x, [23, 3]))
POLINOMIO f1 =
F=(132511742741563028118449706779*x^4)/405648192073033408478945025720320 -
(137666855188831736408209924901*x^3)/6338253001141147007483516026880 +
(21140978790370187092321969137*x^2)/39614081257132168796771975168 -
(576967209289482091394341575591*x)/99035203142830421991929937920 +
2548627377380721607314386298391/99035203142830421991929937920
EVALUANDO EN EL RANGO DE [23 A 3]
F, x, [23 3]= - 60.955555383300052355524086801562
EVALUANDO EN EL RANGO DE [3 A 23]
F, x, [3 23]= 60.955555383300052355524086801562

2. 2., LA VISCOSIDAD DINÁMICA DEL AGUA u(10^-3N.S/m^2) SE REALCIONA CON
LA TEMPERATUA T(C), DE LA SIGUIENTE MANERA:
a) Grafique los datos
B)CALCULE LA VISCOSIDAD DINÁMICA POR INTERPOLACIÓN A LA TEMPERATURA
T=7.5 C
u= 1.4068632289341517857142857142857
clear; clc;
syms x
X=[0 5 10 20 30 40]%volumen
f=[1.787 1.519 1.307 1.002 0.7975 0.6529]
plot(X, f, 'p')
n=numel (X)-1;
P=0
for k=1:n+1
I=1
for i=1:n+1

3. if i~=k
I=I*(x-X(i))/(X(k)-X(i));
end
end
P=P+f(k)*I;
end
vpa(subs (P,x,7.5))
pretty (P)
X =
0 5 10 20 30 40
f =
1.7870 1.5190 1.3070 1.0020 0.7975 0.6529
P =
0
I =
1
I =
1
I =
1
I =
1
I =
1
I =
1
ans =

4. 1.4068632289341517857142857142857
6529 x (x - 5) (x - 10) (x - 20) (x - 30)
-----------------------------------------
84000000000
319 x (x - 5) (x - 10) (x - 20) (x - 40)
- ----------------------------------------
600000000
167 x (x - 5) (x - 10) (x - 30) (x - 40)
+ ----------------------------------------
100000000
1307 x (x - 5) (x - 20) (x - 30) (x - 40)
- -----------------------------------------
300000000
217 x (x - 10) (x - 20) (x - 30) (x - 40)
+ -----------------------------------------
46875000
/ x
| - - 1 | (x - 10) (x - 20) (x - 30) (x - 40) 1787
5 /
- --------------------------------------------------
240000000
Published withMATLAB® R2015b
C)USE EL AJUSTE DE CURVAS PARA HACER EL CÁLCULO ANTERIOR
clear clc
syms x Y c1 c2 c3 c4 c5 D
X=[0 5 10 20 30 40]%volumen
f=[1.787 1.519 1.307 1.002 0.7975 0.6529]
plot(X, f, 'p')
C=[c1, c2, c3, c4, c5]
y=Y*ones(5,5)
for i=1:5
for j=1:5
s(i, j)=sum(X.^(i-1).*X.^(j-1))
end
end
p=inv(s)
d=D*ones(1,5)
for i=1:5
D(i)=sum(f.*X.^(i-1))
end
c=p*D'
f1=c(1,1)+c(2,1)*x+c(3,1)*x^2+c(4,1)*x^3+c(5,1)*x^4
hold on
F=f1
syms x
vpa(subs (F,x,7.5))

5. ans =
1.4068564099042179949929734811461
3. RESUELVA EL SIGUIENTE SISTEMA DE ECUACIONES
4X-Y+Z-2=0
-X+6Y-3Z-11=0
X-4Y+5Z+5=0
clear;clc;
A=[4 -1 1;-1 6 -3;1 -4 5];%INGRESO LAS TRES ECUACIONES
B(:,1)=[2 11 -5];
[n m]=size(A)
for i=1:n
for j=1:n
I(i,j)=0
if i==j
I(i,j)=1
end
end
end
M=[A,I]
for i=1:n
M(i,:)=M(i,:)/M(i,i)
for j=1:n
if j~=i
M(j,:)=M(j,:)-M(j,i)*M(i,:)
end
end

6. end
MIA=M(:,4:6)
X=MIA*B
n =
3
m =
3
I =
0
I =
1
I =
1 0
I =
1 0 0
I =
1 0 0
0 0 0
I =
1 0 0
0 0 0
I =
1 0 0
0 1 0

7. I =
1 0 0
0 1 0
I =
1 0 0
0 1 0
0 0 0
I =
1 0 0
0 1 0
0 0 0
I =
1 0 0
0 1 0
0 0 0
I =
1 0 0
0 1 0
0 0 1
M =
4 -1 1 1 0 0
-1 6 -3 0 1 0
1 -4 5 0 0 1
M =
1.0000 -0.2500 0.2500 0.2500 0 0
-1.0000 6.0000 -3.0000 0 1.0000 0
1.0000 -4.0000 5.0000 0 0 1.0000
M =

8. 1.0000 -0.2500 0.2500 0.2500 0 0
0 5.7500 -2.7500 0.2500 1.0000 0
1.0000 -4.0000 5.0000 0 0 1.0000
M =
1.0000 -0.2500 0.2500 0.2500 0 0
0 5.7500 -2.7500 0.2500 1.0000 0
0 -3.7500 4.7500 -0.2500 0 1.0000
M =
1.0000 -0.2500 0.2500 0.2500 0 0
0 1.0000 -0.4783 0.0435 0.1739 0
0 -3.7500 4.7500 -0.2500 0 1.0000
M =
1.0000 0 0.1304 0.2609 0.0435 0
0 1.0000 -0.4783 0.0435 0.1739 0
0 -3.7500 4.7500 -0.2500 0 1.0000
M =
1.0000 0 0.1304 0.2609 0.0435 0
0 1.0000 -0.4783 0.0435 0.1739 0
0 0 2.9565 -0.0870 0.6522 1.0000
M =
1.0000 0 0.1304 0.2609 0.0435 0
0 1.0000 -0.4783 0.0435 0.1739 0
0 0 1.0000 -0.0294 0.2206 0.3382
M =
1.0000 0 0 0.2647 0.0147 -0.0441
0 1.0000 -0.4783 0.0435 0.1739 0
0 0 1.0000 -0.0294 0.2206 0.3382
M =
1.0000 0 0 0.2647 0.0147 -0.0441
0 1.0000 0 0.0294 0.2794 0.1618
0 0 1.0000 -0.0294 0.2206 0.3382

9. MIA =
0.2647 0.0147 -0.0441
0.0294 0.2794 0.1618
-0.0294 0.2206 0.3382
X =
0.9118
2.3235
0.6765
X=0.9118
Y= 2.3235
Z= 0.6765
4. ENCUENTRE LA SOLUCIÓNAPROXIMADA DE LA SIGUIENTEECUACIÓNDIFERENCIAL
clear;clc;
h=0.1
x=0:h:1
syms X
n=numel(x)
for i=1:n
y(i)=sym(['y',num2str(i)])%[genera ya lamtriz y1 y2 y3....yn]
end
y(1)=0
y(end)=0% lo que cambia
for i=1:n-2
f(i,1)=((y(i+2)-2*y(i+1)+y(i))/h^2)+pi^2/4*y(i)-pi^2/16*cos(pi*x(i)/4)
end
R=solve(f)%resuelve el sistema de ecuaciones
V(:,1)=sort(symvar(f))%ordenq los vectores
R=struct2cell(R)
R=cell2num(R)
y=vpa(subs(y,V,R))
plot(x,y)
n=numel (x);
P=0
for k=1:n
I=1
for i=1:n
if i~=k
I=I*(X-x(i))/(x(k)-x(i));
end
end
P=P+y(k)*I;
end
P=expand(P)

10. hold on
fplot(char(P),[0 1],'r')
h =
0.1000
x =
Columns 1 through 7
0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000
Columns 8 through 11
0.7000 0.8000 0.9000 1.0000
n =
11
y =
y1
y =
[ y1, y2]
y =
[ y1, y2, y3]
y =
[ y1, y2, y3, y4]
y =
[ y1, y2, y3, y4, y5]
y =
[ y1, y2, y3, y4, y5, y6]
y =

11. [ y1, y2, y3, y4, y5, y6, y7]
y =
[ y1, y2, y3, y4, y5, y6, y7, y8]
y =
[ y1, y2, y3, y4, y5, y6, y7, y8, y9]
y =
[ y1, y2, y3, y4, y5, y6, y7, y8, y9, y10]
y =
[ y1, y2, y3, y4, y5, y6, y7, y8, y9, y10, y11]
y =
[ 0, y2, y3, y4, y5, y6, y7, y8, y9, y10, y11]
y =
[ 0, y2, y3, y4, y5, y6, y7, y8, y9, y10, 0]
f =
100*y3 - 200*y2 - 2778046668940015/4503599627370496
f =
100*y3 - 200*y2 -
2778046668940015/4503599627370496
(115368037353202415*y2)/1125899906842624 - 200*y3 + 100*y4 -
5538965756371755/9007199254740992
f =
100*y3 - 200*y2 -
2778046668940015/4503599627370496
(115368037353202415*y2)/1125899906842624 - 200*y3 + 100*y4 -
5538965756371755/9007199254740992
(115368037353202415*y3)/1125899906842624 - 200*y4 + 100*y5 -
5487688609082427/9007199254740992
f =

12. 100*y3 - 200*y2 -
2778046668940015/4503599627370496
(115368037353202415*y2)/1125899906842624 - 200*y3 + 100*y4 -
5538965756371755/9007199254740992
(115368037353202415*y3)/1125899906842624 - 200*y4 + 100*y5 -
5487688609082427/9007199254740992
(115368037353202415*y4)/1125899906842624 - 200*y5 + 100*y6 -
2701289018338233/4503599627370496
f =
100*y3 - 200*y2 -
2778046668940015/4503599627370496
(115368037353202415*y2)/1125899906842624 - 200*y3 + 100*y4 -
5538965756371755/9007199254740992
(115368037353202415*y3)/1125899906842624 - 200*y4 + 100*y5 -
5487688609082427/9007199254740992
(115368037353202415*y4)/1125899906842624 - 200*y5 + 100*y6 -
2701289018338233/4503599627370496
(115368037353202415*y5)/1125899906842624 - 200*y6 + 100*y7 -
5284158774134893/9007199254740992
f =
100*y3 - 200*y2 -
2778046668940015/4503599627370496
(115368037353202415*y2)/1125899906842624 - 200*y3 + 100*y4 -
5538965756371755/9007199254740992
(115368037353202415*y3)/1125899906842624 - 200*y4 + 100*y5 -
5487688609082427/9007199254740992
(115368037353202415*y4)/1125899906842624 - 200*y5 + 100*y6 -
2701289018338233/4503599627370496
(115368037353202415*y5)/1125899906842624 - 200*y6 + 100*y7 -
5284158774134893/9007199254740992
(115368037353202415*y6)/1125899906842624 - 200*y7 + 100*y8 -
5133160915589677/9007199254740992
f =
100*y3 - 200*y2 -
2778046668940015/4503599627370496
(115368037353202415*y2)/1125899906842624 - 200*y3 + 100*y4 -
5538965756371755/9007199254740992
(115368037353202415*y3)/1125899906842624 - 200*y4 + 100*y5 -
5487688609082427/9007199254740992
(115368037353202415*y4)/1125899906842624 - 200*y5 + 100*y6 -
2701289018338233/4503599627370496
(115368037353202415*y5)/1125899906842624 - 200*y6 + 100*y7 -
5284158774134893/9007199254740992
(115368037353202415*y6)/1125899906842624 - 200*y7 + 100*y8 -
5133160915589677/9007199254740992
(115368037353202415*y7)/1125899906842624 - 200*y8 + 100*y9 -
4950515413050633/9007199254740992

13. f =
100*y3 - 200*y2 -
2778046668940015/4503599627370496
(115368037353202415*y2)/1125899906842624 - 200*y3 + 100*y4 -
5538965756371755/9007199254740992
(115368037353202415*y3)/1125899906842624 - 200*y4 + 100*y5 -
5487688609082427/9007199254740992
(115368037353202415*y4)/1125899906842624 - 200*y5 + 100*y6 -
2701289018338233/4503599627370496
(115368037353202415*y5)/1125899906842624 - 200*y6 + 100*y7 -
5284158774134893/9007199254740992
(115368037353202415*y6)/1125899906842624 - 200*y7 + 100*y8 -
5133160915589677/9007199254740992
(115368037353202415*y7)/1125899906842624 - 200*y8 + 100*y9 -
4950515413050633/9007199254740992
(115368037353202415*y8)/1125899906842624 - 200*y9 + 100*y10 -
2368674168388353/4503599627370496
f =
100*y3 - 200*y2 -
2778046668940015/4503599627370496
(115368037353202415*y2)/1125899906842624 - 200*y3 + 100*y4 -
5538965756371755/9007199254740992
(115368037353202415*y3)/1125899906842624 - 200*y4 + 100*y5 -
5487688609082427/9007199254740992
(115368037353202415*y4)/1125899906842624 - 200*y5 + 100*y6 -
2701289018338233/4503599627370496
(115368037353202415*y5)/1125899906842624 - 200*y6 + 100*y7 -
5284158774134893/9007199254740992
(115368037353202415*y6)/1125899906842624 - 200*y7 + 100*y8 -
5133160915589677/9007199254740992
(115368037353202415*y7)/1125899906842624 - 200*y8 + 100*y9 -
4950515413050633/9007199254740992
(115368037353202415*y8)/1125899906842624 - 200*y9 + 100*y10 -
2368674168388353/4503599627370496
(115368037353202415*y9)/1125899906842624 - 200*y10 -
4494973932678371/9007199254740992
R =
y2: [1x1 sym]
y3: [1x1 sym]
y4: [1x1 sym]
y5: [1x1 sym]
y6: [1x1 sym]
y7: [1x1 sym]
y8: [1x1 sym]
y9: [1x1 sym]
y10: [1x1 sym]
V =
y2

14. y3
y4
y5
y6
y7
y8
y9
y10
R =
[1x1 sym]
[1x1 sym]
[1x1 sym]
[1x1 sym]
[1x1 sym]
[1x1 sym]
[1x1 sym]
[1x1 sym]
[1x1 sym]
R =
-
5479480335076111974454307016617118247814794623629915525398060954655645196105908691/16652
6140704593586610215588894933189801576823372031615697621472639563198192890675200
-
1241467964144459044791372777739847138082774634969182699644925920740032345062669869/20815
767588074198326276948611866648725197102921503951962202684079945399774111334400
-
2977950296898445163316325462680505042561611028785621032278639896313331451171197419703592
88312689767/3749835326123272314354241130007724453017593764194257367200298172281167449757
485627800856869994496000
-
1717914066534286339595969631322530063972912951137326276150630377474180181505278807593138
54193803979/1874917663061636157177120565003862226508796882097128683600149086140583724878
742813900428434997248000
-
3358608839805541139339632072712832617955056225963513807996684510102544420976820691/35029
604586466190446559122324188521566881025673128934216139862552944888114053120000
-
1942193839611116471941432436481786875894521394144609085871122170184276894456977429136656
726456353715918054836756181/211096962217868644249156937479372940942901952247599873171552
25575615611421862296161608936531431632430698090987520000
-
1522365289391611371765580911012770391270863579825783193029347838455554598899908602047449
87992545704891079147923071205088455366106463/1901392400766873798178740679832603891465408
0351348880043211536172900014069947851641627966312302727628008464002010210714710441984000
00
-
5738449853945654575928682306930829044283860604295000928808751179860006665896084138502514

15. 8213329008784313205769099536721554452947617/95069620038343689908937033991630194573270401
7567444002160576808645000703497392582081398315615136381400423200100510535735522099200000
-
1430901260164460489703022676664353189263928871836348349027461869752071363788993545179389
758378177603551089097496915468760056056995714488495148659011/428155505378939281517418673
9876936007478810260904326163166428642542960608981333008777322299933586233171221230378136
8051925062480552449940652032000000
y =
[ 0, -0.03290462573558555858768644316681, -0.05964074872049026843018229875493, -
0.079415495292620427042006826597999, -0.091626107128834037134502402588291, -
0.095879153631758416843133586417488, -0.092004821822429632713408409267006, -
0.080065813283865425589841603532548, -0.060360500564020454268710267968903, -
0.03342012988710820123494764952464, 0]
P =
0
I =
1
I =
1
I =
1
I =
1
I =
1
I =
1
I =
1

16. I =
1
I =
1
I =
1
I =
1
P =
0.000008377446453390598345464870661955*X^10 - 0.000069602164145921450316337671428029*X^9
- 0.00011698363573581745189686669582295*X^8 + 0.001533299032018222700433745025631*X^7 +
0.0040930901028205732145231521862629*X^6 - 0.024128925374348760378954901216781*X^5 -
0.058257941125119981073034651845014*X^4 + 0.17271940874980220128830367905092*X^3 +
0.26103566669973466448955614575887*X^2 - 0.3568163897314785719369594294633*X