|
ADVANCED MATHEMATICS FOR ENGINEERS
EC 501 (M. Tech. 1st Sem.) May 2k5
Max Marks 100
Note: Attempt any Five questions. All questions carry equal marks.
1. (a) Prove that as the solid figure of revolution for a given surface area the
sphere has maximum volume.
(b) Using Rayleigh-Ritz method, find the potential at a point due to a charged
sphere of radius a.
(c) A mass suspended at the end of a light spring having a spring constant K is
set into vertical motion. Use Lagranges’s equation to find the equation of
motion of the mass. 7,6,6
2. (a) Find the inverse of the matrix
Matrix 1
(b) Solve the following system of equations by Gauss-Siedel Method
X + y + 2z = 4
2X - y + 3z = 9
3X - y - z = 2
3 (a) Draw the flow chart for solution of simultaneous equation using Gauss
Elimination Method.
(b) Write down an algorithm for determination of eigenvalues by iteration.
4 What are the properties of z-f transform? Explain them with examples.
5 List various properties of Fourier transform and explain them with the help of
examples.
6. (a) Describe discrete Fourier series and Fourier transform. Find the Fourier
series of f(x) = ekx in (0,2?) where k >0.
(b) Find circular convolution of the sequence:
Fig. 1
7. What is the relationship between Fourier transform and z-transform? Find
z-transform of given equation:
x(n) = [3(2n) – 4(3n)] u(n)
Find ROC also
8. Write short notes on the following:
(a) Conformal mapping
(b) Schwarz’s Christofel transformations.
(c) Laplace transform.