Unformatted text preview: Explain. (c) If F ( s ) = log( s ), where are the Cauchy-Riemann conditions valid, or not? Explain. (d) If F ( s ) = √ 1 + s 2 , where are the Cauchy-Riemann conditions valid, or not? Explain. 4. Branch cuts (a) If w ≡ F ( s ) = 1 + s 2 i. What is s = G ( w ) ≡ F-1 ( w ). ii. Map out the range of s = G ( w ) for the two domains of w . Explain. iii. Discuss reasonable places to place the branch cut(s)? (b) Describe the Riemann surface of G ( z ) = ln( z ). 5. Laplace transforms (a) ±ind the Laplace transform of 1, d/dt , i t-∞ δ ( t ) dt , and i t-∞ u ( t ) dt . . (b) If f ( t ) = 1 / √ πt has a Laplace transform F ( s ) = 1 / √ s : i. What is the inverse Laplace transform of √ s ? ii. what is f (-1)? Version 1.2 January 25, 2011 ˜ /493/Assignments/HW #8 – Version 1.2 January 25, 2011...
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- Spring '11
- Laplace, Cauchy-Riemann conditions