MATLAB Week-5

MATLAB
Laplace transforms and limits

Week: 5

LAPLACE TRANSFORM

clc
clear all
syms t s
f=input('Enter the function in terms of  t:');
F=laplace(f)




LAPLACE TRANSFORM OF UNIT STEP FUNCTION



clearall
clc
symsx
g1=x*(heaviside(x-0)-heaviside(x-1));
g2=(2-x)*(heaviside(x-1)-heaviside(x-2));
f=g1+g2;
F=laplace(f)
xv=linspace(0,2,100);   
g1v=subs(g1,x,xv);
g2v=subs(g2,x,xv);
fv=subs(f,x,xv);
subplot(3,1,1)
plot(xv,g1v,'r.')
subplot(3,1,2)
plot(xv,g2v,'r.')
subplot(3,1,3)
plot(xv,fv,'r.')










LAPLACE TRANSFORM OF PERIODIC FUNCTION



clc
clearall
symsts
T=input('enter the period of the periodic function : ');
n=input('enter the number of partitions in one full period : ')
fun = 0*t;
for i=1:n
a(i)=input('enter the left end point of the ith sub interval  :  ');
b(i)=input('enter the right end point of the ith sub interval  :  ');
f(i)=input('enter the function f(i) of the ith sub interval :  ');
fun = fun+f(i)*(heaviside(t-a(i))-heaviside(t-b(i)));
end
ezplot(fun,[a(1) b(n)])
sum=0;
for i=1:n
sum=sum+int(f(i)*exp(-s*t),t,a(i),b(i))
end
g = (1/(1-exp(-s*T)))*sum
g1=simplify(g)
figure
ezplot(g1,[0 b(n)])














LIMITS AND CONTINUITY



clear
clc
syms x y m n
f = input('Enter the function f(x,y): ');
Lp = input('Enter limit point [x0 y0] as a row vector: ');
x0=Lp(1); y0=Lp(2);
L1=limit(limit(f,x,x0),y,y0); L1=double(L1);
L2=limit(limit(f,y,y0),x,x0); L2=double(L2);
disp(['L1 = ', num2str(L1),' L2 = ', num2str(L2)])
if (isnan(L1) || isnan(L2) || (L1~=L2))
    disp('Limit does not exist.')
return
elseif (L1==L2)
    L = input('Enter the value of f at (x0,y0): '); L=double(L);
if (L1~=L)
        disp(['Limit exists for the iterated paths, but f(x,y) fails to be '...
'continuous at the limit point.'])
return
else
npaths=input(['Input the number [of paths through (x0,y0)]. '...
'You may try upto 5: ']);
yp = y0+m*(x-x0)^n;
        f = subs(f,y,yp);
for i=1:npaths
            val = input(['Input the value of m and n (as a row vector), '...
'for the trial path y0+m(x-x0)^n: ']);
            m=val(1); n=val(2);
            y=subs(yp);
            fprintf('The path considered is y = '); disp(y);
            fp=subs(f);
L3 = limit(fp,x,x0); L3=double(L3);
            disp(['Limit along this path is L3 = ',num2str(L3)])
if (isnan(L3)||(L3~=L))
                disp(['Limit does not exist. Function f(x,y) fails to '...
'be continuous at the limit point.'])
return
end
            disp('Function may be continuous at the limit point.')           
end
end
end





Comments

Post a Comment

Popular posts from this blog

MATLAB WEEK-2

Image
MATLAB Plotting of curves and surfaces Week: 2 METHOD 1 x=linspace(0,1,101) plot(x,x.^3, 'r+' ,x,sin(x), 'b-' ,x,exp(x), 'g.' ) METHOD 2 using Hold on clear all x=linspace(0,1,101) plot(x,x^3, 'r*' ) hold on plot(x,sin(x), 'g.' ) hold on plot (x,exp(x), 'b+' ) If we remove hold on, only last graph will be displayed. METHOD 3 using subplot x=0:.1:2*pi; subplot(2,2,1); plot (x,sin(x)); subplot(2,2,2); plot(x,cos(x)); subplot(2,2,3); plot(x,exp(-x)); subplot(2,2,4); plot(x,sin(3*x)); Diffrentiation syms x y f=x^2+2*x*y+y*sin(x) diff(f,x) diff(f,y) f =2*x*y + y*sin(x) + x^2 ans = 2*x + 2*y + y*cos(x) ans = 2*x + sin(x) Integration syms x f=x^3 + 3*x^2 + 5*x + 12 int(f,x,0,2) f = x^3 + 3*x^2 + 5*x + 12 ans = 46 Plotting graph syms x f=sin(2*x)+ cos(3*x) ezplot(f) ...
Read more

PRACTICE PROBLEM 8

Image
PRACTICE PROBLEM 8 Verification of 'L' shaped arrangement of Coins on Game Board (Id-2435) Consider a nxn board game with four types of coins red, green, blue and yellow. Given the state of the board with coins in all cells, develop an algorithm and write a C program to check if the same coins are placed in ‘L’ shape on the board. The number of cells in the vertical and horizontal line of ‘L’ shape should be same and should be greater than 1. Red coins are represented by ‘r’, blue coins are represented by ‘b’, green coins are represented by ‘g’ and yellow coins are represented by ‘y’.  For example, given the configuration of a 4 X 4 board with coins as shown below, b r y r r r y b y r b b b r r r the program must print 'Yes'. As there is a 'L' shape as shown in the figure below. Input Format Number of rows, r Number of columns, c Next ‘r x c’ lines contains the elements in the matrix Elements in the matrix given row by row ...
Read more

BONUS PRACTICE PROBLEMS

Bonus Practice Problems(GMT To IST) IST (Indian Standard Time) is 5 hours 30 minutes ahead of GMT(Greenwich Mean Time). Develop an algorithm and write the Python code to find day and IST, given day and time in GMT. For example, if day is Sunday and time in GMT is 23:05 then in IST is Monday (Next day) and time is 04:35. Check boundary conditions and print 'Invalid input' for wrong input. Write appropriate functions for accomplishing the task. Use rstrip() to remove extra spaces while reading strings Input Format Day Hours minutes of time in GMT Output Format Day Hours minutes of time in IST Boundary Condition: All hour > 0 and <24 Minutes > 0 and < 60 Seconds > 0 and <60 Day is Sunday or Monday or Tuesday or Wednesday or Thursday or Friday or Saturday Input: Take the input serially as day,hours and minutes. Processing Involved: days=["Sunday","Monday","Tuesday","Wednesday"...
Read more