Hindustan Institute of Technology and Science (HITE) 2008 B.E Computer Science MATHMATICS 3 - Question Paper
Tuesday, 22 January 2013 09:25Web
MATHEMATICS 3
PART A:
1.Form a partial differential formula by eliminating arbitrary constants a and b from z=(x+a)2+(y+b)2.
2.Find the root mean square value of f(x)=x square in the interval(0,8).
3.State the Fourier Integral theorem.
4.State the convolution theorem of the Fourier transform.
5.Find z{n}.
6.Find the PDE of all planes having equal intercepts on the x and y axis.
7.If f(x) is an odd function described in(-1,1) elaborate the values of a.
8.What is the basic difference ranging from the solutions of 1 dimensional wave formula and 1 dimensional heat formula.
9.In steady state conditions derive the solution of 1 dimensional heat flow formula.
10.State the Fourier transform of the derivatives of a function.
PART B:
11.(a)Express f(x)=x sin x as a Fourier Series in 0
(b)A string is stretched and fastened to 2 points x=0 and x=1 apart.Motion is started by displacing the strings into the form y=k(lx=x)from which
it is released at time t=0.Find the displacement of any point on the string at a distance of x from 1 end at time t.
12.(a)Expand in Fourier series of periodicity 2x of f(x)=x square for 0
(b)A rectangular plate is bounded by the lines x=0 and y=0,x=a and y=b.It's surface are insulated.The temperature along x=0 and y=0 are kept at 0 degree and others at 100 degree.Find the steady state temperature at any point of the plate.
13.(a)Solve the difference formula y(n+3)-3y(n+1)+2y(n)=0,given that y(0)=4,y(1)=0 and y(2)=8.
OR
(b)Find the Fourier series for f(x)=|cos x| in the interval(-x,x).
14.(a)Obtain the half range cosine series for f(x)x in (0,x).
OR
(b)State and prove the 2nd shifting theorem in z transform.
15.(a)Find the half range sine series of f(x)=x in(0,x).
OR
(b)Find the complete integral of p+q=x+y.
| Earning: Approval pending. |
