Unformatted text preview: f ( z ) and z ( t ), applying the chain rule of calculus for functions of two variables, and using the Cauchy-Riemann equations. 3. (20 pts.) Evaluate each one of the following two integrals in two diﬀerent ways: ( a ) Z 2 1 (1 /t-i ) 2 dt and ( b ) Z π/ 6 e 2 it dt. 4. (10 pts.) In view of the properties of the exponential function we have Z π e (1+ i ) x dx = Z π e x cos xdx + i Z π e x sin xdx. Evaluate the two integrals on the right by evaluating the single integral on the left and then identifying the real and imaginary parts of the values found. Verify your answers by computing the two integrals on the right-hand side by means of an alternative procedure. Due at 5pm on Wed. October 28....
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This note was uploaded on 01/14/2010 for the course ACM 1 taught by Professor Prof during the Fall '09 term at Caltech.
- Fall '09