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Posted Date: 31 Oct 2009 Posted By:: RoseNinja Member Level: Gold Points: 5 (Rs. 1)
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2008 Hindustan Institute of Technology & Science B.E Computer Science MATHMATICS 3 University Question paper
MATHEMATICS 3
PART A:
1.Form a partial differential equation 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 defined in(-1,1) what are the values of a.
8.What is the basic difference between the solutions of one dimensional wave equation and one dimensional heat equation.
9.In steady state conditions derive the solution of one dimensional heat flow equation.
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 OR
(b)A string is stretched and fastened to two 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 one end at time t.
12.(a)Expand in Fourier series of periodicity 2x of f(x)=x square for 0 OR
(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 equation 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 second 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.
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