Higher Engineering Mathematics B S Grewal | 2026 Update |

Solve the wave equation ( \frac\partial^2 y\partial t^2 = 4 \frac\partial^2 y\partial x^2 ) with boundary conditions ( y(0,t)=0, y(3,t)=0, y(x,0)=0, \frac\partial y\partial t(x,0) = 5 \sin 2\pi x ). (7 marks)

Solve using Laplace transform: [ y'' + 4y = 8t, \quad y(0) = 0, \quad y'(0) = 2 ] (7 marks) higher engineering mathematics b s grewal

Verify Green’s theorem for ( \oint_C (xy , dx + x^2 , dy) ), where ( C ) is the triangle with vertices (0,0), (1,0), and (0,1). (7 marks) Solve the wave equation ( \frac\partial^2 y\partial t^2

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

If ( u = \log(x^3 + y^3 + z^3 - 3xyz) ), prove that: [ \left(\frac\partial\partial x + \frac\partial\partial y + \frac\partial\partial z\right)^2 u = -\frac9(x+y+z)^2 ] (7 marks)

Verify Cauchy-Riemann equations for ( f(z) = e^z ) and find ( f'(z) ). (7 marks)

Find the volume of the sphere ( x^2 + y^2 + z^2 = a^2 ) using triple integration in spherical coordinates. (7 marks)