Solve using Laplace transform: [ y'' + 4y = 8t, \quad y(0) = 0, \quad y'(0) = 2 ] (7 marks)
Find the half-range cosine series for ( f(x) = x(\pi - x) ) in ( (0,\pi) ). (7 marks) higher engineering mathematics b s grewal
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) Solve using Laplace transform: [ y'' + 4y
The problems are similar in logic and complexity to those found in GATE. Thousands of problems designed to test your grasp
Thousands of problems designed to test your grasp of the concepts.
Prove that ( \nabla \times ( \nabla \times \vecF ) = \nabla(\nabla \cdot \vecF) - \nabla^2 \vecF ). Hence find ( \nabla \times (\nabla \times \vecr) ) where ( \vecr = x\hati + y\hatj + z\hatk ). (7 marks)