MTH632 Assignment no 2 solution by taleemi markaz
MTH632 Assignment No.2 solution Due Date February 16, 2022.
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Questions:
Test whether the function 𝒘=𝟐𝒙𝒚+𝒊(𝒙^𝟐−𝒚^𝟐 ) is analytic or not.
Prove that 𝒖=𝟏/𝟐 𝒍𝒐𝒈(𝒙^𝟐+𝒚^𝟐 ) is harmonic.
Prove that 𝒖=𝒙^𝟑−𝟑𝒙𝒚^𝟐+𝟑𝒙^𝟐−𝟑𝒚^𝟐+𝟏 satisfies Laplace’s equation.