Exercise 2.1. For the following functions u(x, y) with domain D C C, check that u...
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Exercise 2.1. For the following functions u(x, y) with domain D C C, check that u is harmonic on D, and find a "harmonic conjugate" v(x, y) on D, 1. u = e" sin(y) 2. u = 2x3 – 3x?y – 6xy +y° | Зд2 + 8у — Зу? (x2 + y?)2 gebra might help on this one) 3. и 3 domain D = {(x, y) # (0,0)}. (some computer al- 4. u = tan (2) Domain D = {x> 0} Exercise 2.1. For the following functions u(x, y) with domain D C C, check that u is harmonic on D, and find a "harmonic conjugate" v(x, y) on D, 1. u = e" sin(y) 2. u = 2x3 – 3x?y – 6xy +y° | Зд2 + 8у — Зу? (x2 + y?)2 gebra might help on this one) 3. и 3 domain D = {(x, y) # (0,0)}. (some computer al- 4. u = tan (2) Domain D = {x> 0}
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