Engineering mathematics-3
Previous year question paper with solutions for Engineering mathematics-3
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- State and prove Second Shifting property for Laplace Transform
- State Rodrigue’s formula for Legendre polynomials
- Find solution of homogeneous partial differential equation 2r – 5s + 2t = 0.
- If f(z) is analytic and Im f(z) is constant then show that f(z) is constant
- Define even and odd functions. Give an example of a function which is neither even nor odd.
- Write the sufficient conditions for the existence of Laplace transform
- Find the Fourier series of the function f(x) = x, – < x < .
- Show that Pn(1) = 1, where Pn(x) denotes the Legendre Polynomial
- Eliminate the arbitrary constants a and b from z = ax + by + a2 b2 , to obtain the partial differential equation.
- Write half range sine series of the function f (x) = x, in 0 < x < 2
- Define analytic function. Give an example of the same
- Form a differential equation from z = (x + a) (y + b)
- State Cauchy’s Theorem
- State any one property of “conformal mapping”.
- Show that Pn(1) = 1, where Pn(x) denotes the Legendre Polynomial
- Write the sufficient conditions for the existence of Laplace transform
- Compute the residue at all singular points of the function f(z) = cot z.