Applied mathematics-3
Previous year question paper with solutions for Applied mathematics-3
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- Write half range sine series of the function f (x) = x, in 0 < x < 2.
- Find Laplace transform of the function t2 cos 2t.
- Define analytic function. Give an example of the same.
- Form a differential equation from z = (x + a) (y + b).
- An infinitely long metal plate of width 1 with insulated surfaces has its temperature zero along both the long edges y = 0 and y = l at infinity. If the edge x = 0 is kept at fixed temperature T0 and if it is required to find the temperature T at any point (x, y) of the plate in the steady state, then state the boundary conditions for the same.
- State Cauchy’s Theorem.
- Define the Legendre’s equation of order n. What are its particular solutions called?
- State Cauchy Riemann equations in Cartesian and polar coordinates.
- Express 4x3–2x 2 –3x + 8 in terms of Legendre polynomials
- 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.
- Eliminate the arbitrary constants a and b from z = ax + by + a2b2, to obtain the partial differential equation.
- Show that Pn(1) = 1, where Pn(x) denotes the Legendre Polynomial.