The homework is due on Wednesday, April 3.
You should Work on it in groups.
For purposes of neatness and simplicity of grading, you should do the homework on an A-4 paper. However, use your exercise book as a scrapbook.
All answers should be written using a pen. Do not use a pencil. If you make an error, strike a line through it and correct it on the next line.
DO NOT PREPARE A COVER PAGE, JUST WRITE THE NAME OF THE MEMBERS ON THE SAME PAGE AS THE ANSWERS
For questions 1-5, find the Laplacian of the function f(x, y, z) in Cartesian coordinates.
f(x, y, z) = x + y + z f(x, y, z) = x7 f(x, y, z) = ex2 + y2 + z2 f(x, y, z) = e − (x2 + y2 + z2) f(x, y) = sin (2x)cos (6y)
For questions 4-6 show the following for the position vector r(x, y, z) = xi + yj + zk
∇(1/r) = − r/r3 Δ(1/r) = 0 ∇(ln r) = r/r3 Δ(fg) = fΔg + gΔf + 2(∇f ⋅ ∇g)