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Posted By: b.thirumaya prabhu Member Level: Gold Posted Date: 22 May 2008
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2007 Anna University B.Tech Chemical engineering MA037 SPECIAL FUNCTIONS, DIFFERENCE EQUATIONS AND Z-TRANSFORMS 2007 Question paper
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B.TECH. CHEMICAL ENGINEERING
SEMESTER V
MA037 SPECIAL FUNCTIONS, DIFFERENCE EQUATIONS AND Z-TRANSFORMS
(Common to Leather and Textile Technology)
Time: 3 Hours Max. Marks: 100
Answer all Questions
PART - A (10 x 2 = 20 marks)
1. Define a regular singular point and an ordinary point of 2nd order differential equation with variable coefficient.
2. Find the series solution of (x-1) y11 + y = 0 at x = 0 by Taylor’s series method.
3. Justify that Exp (t- ) is the Generating function of Jn(x).
4. Show that J0(x) dx = a J1(a)
5. Show that Pn(x) =(-1)n Pn(-x)
6. Prove that (2n+1)x Pn(x) = (n+1) Pn+1(x)+n Pn-1(x).
7. What is the generating function of Hermite polynomial Hn(x). Find the value of H2(x).
8. Show that = 2n Hn-1(x)
9. Solve (E2-5E+6)y=2x
10. Define -Z-transform and verify Z (an fn) = F
PART – B (5 x 16 = 80 marks)
11.i) Find the series solution of x2y11+xy1+(n2-n2) y=0 at a regular singular point.
ii) Prove that J3/2(x) =
12.a)i) Write the Modified Bessel’s differential equation and its solutions.
ii) State & Prove the orthogonal property of ?
OR
12.b)i) Prove that (x) = Cos (n? – x Sin ?) d?, where n is a integer.
ii) Establish x (x) = n Jn (n)-x Jn+1(x) and deduce = -J1
13.a)i) State & Prove Rodrigue’s formula for Legendre’s polynomials.
ii) Show that (x2-1) =
OR
13.b) A thermally conducting solid bounded by 2 concentric spheres of radii a and b: (a
(Hint : Choose Solution as & apply BC)
14.a)i) Show the =
ii) Show that H0(x) = 1; H1(x)=2x; H2(x) = 4x2-2 and H3(x) = 8x3-12x.
OR
14.b)i) Write Rodrigue’s formula for & prove it.
ii) Find the series solution of xy11+(1-x)y1+?y=0, Laguerre’s differential equation.
15.a) Solve the difference equations i) (E2-7E-8)y=2x x(2), ii) (E2+1)y=3x Sin
OR
15.b)i) Show that Z(n2) =
ii) Solve by Z-transform method yn+1 + 6yn +1 + 9yn =2n, with the conditions y0 = 0 = y1
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