Grewal ((better)) | Higher Engineering Mathematics B S

Evaluate by Simpson’s 3/8 rule: [ \int_0^6 \fracdx1 + x^2 ] taking ( h = 1 ). (7 marks)

Solve the Laplace equation ( \frac\partial^2 u\partial x^2 + \frac\partial^2 u\partial y^2 = 0 ) for a rectangular plate with boundary conditions: ( u(0,y)=0, u(a,y)=0, u(x,0)=0, u(x,b) = \sin\left(\frac\pi xa\right) ). (7 marks) Unit – D: Laplace Transforms Q7 (a) Find the Laplace transform of: (i) ( t^2 e^-3t \sin 2t ) (ii) ( \frac1 - \cos att ) (7 marks) higher engineering mathematics b s grewal

Solve using Laplace transform: [ y'' + 4y = 8t, \quad y(0) = 0, \quad y'(0) = 2 ] (7 marks) Evaluate by Simpson’s 3/8 rule: [ \int_0^6 \fracdx1

Using convolution theorem, evaluate: [ \mathcalL^-1 \left \frac1s(s^2 + a^2) \right ] (7 marks) Unit – E: Numerical Methods & Complex Variables Q9 (a) Using Newton-Raphson method, find a real root of ( x \log_10 x = 1.2 ) correct to 4 decimal places. (7 marks) (7 marks)