MediumCalculusca-032

Laplacian of 2D Polynomial

Problem

Compute the Laplacian of f(x, y) = a * x^3 + b * y^3 + c * x * y^2 at (x, y):

Laplacian = f_xx + f_yy = 6 * a * x + 6 * b * y + 2 * c * x

Hint

Differentiate twice in x, twice in y, then add the two results.

case 1

in: [1,0,1,2,3]

expected: 16

case 2

in: [0,1,0,1,-1]

expected: -6

case 3

in: [2,3,5,1,1]

expected: 40

case 4

in: [0,0,7,5,1]

expected: 70

Starter codePython

def laplacian(a, b, c, x, y):
    # Your code here
    pass

4 test cases · run your code against them in the editor