1. Stewart, Section 14.5, Exercises 10, 13, 18, 21, 22.

2. Stewart, Section 14.5, Exercises 25, 28, 29, 31.

3. Stewart, Section 14.5, Exercises 39, 43, [Optional 44].

4. Show that if H is an incompressible irrotational vector
field, then Laplacian[H] = 0. Show that following vector
fields satisfy Laplacian[H] = 0.

(i) H = (x^3 - 3 x y^2) i + (-3 x^2 y + y^3) j
                        -                    -

(ii) H = e^x cos(y) i - e^x sin(y) j
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