Third Semester B. Tech Engineering Mathematics –III SHORT QUESTION Verify Euler’s Theorem when U = x3+y3+x3+3xyz. Expand f(x,y) = ex cos y in powers of x and y upto the second degree terms. Solve z = px + qy + pq Find the Laplace transform of convolution sin t* cos by its own methods. Write a short note on Runge Kutta Methods. – Solve: 2u = 0, subject to the conditions u (x, 0) = 0, uy (x,0) = sin nx ,where n is positive integer. Solve the integral equation and find f(t), if f(t) = t + + dx LONG QUESTION Eliminate the arbitrary functions f and from z = xf ( )+ y (x) and form the PDE Solve (y+z)p + (z+x)q = x+y Solve (D2+2DD'+D'2-2D-2D')Z = ex-y + x2y Find the Laplace transform of | sint| |cost| The temperature at the ends' x = 0 and x = 100 of a rod 100 cm in length are held at 0°C and 100°C respectively until steady state conditions prevail. Then at t = 0, the two ends are suddenly insulated. Find the resultant distribution in the rod.
Third Semester B. Tech Engineering Mathematics –III SHORT QUESTION Verify Euler’s Theorem when U = x3+y3+x3+3xyz. Expand f(x,y) = ex cos y in powers of x and y upto the second degree terms. Solve z = px + qy + pq Find the Laplace transform of convolution sin t* cos by its own methods. Write a short note on Runge – Kutta Methods. Solve: 2u = 0, subject to the conditions u (x, 0) = 0, uy (x,0) = sin nx ,where n is positive integer. Solve the integral equation and find f(t), if f(t) = t + + dx LONG QUESTION Eliminate the arbitrary functions f and from z = xf ( )+ y (x) and form the PDE Solve (y+z)p + (z+x)q = x+y Solve (D2+2DD'+D'2-2D-2D')Z = ex-y + x2y Find the Laplace transform of | sint| |cost| The temperature at the ends' x = 0 and x = 100 of a rod 100 cm in length are held at 0°C and 100°C respectively until steady state conditions prevail. Then at t = 0, the two ends are suddenly insulated. Find the resultant distribution in the rod.
BTEE-3%20SEM%20(ELECTRICAL).docx