１．Let ａ be an arbitrary real number and ｂ a positive real number. Evaluate the integral ∫[0,∞） cos(ax)/cosh(bx) dx. （Recall that cosh(x) = (1/2)(e^x + e^-x) is the hyperbolic cosine.) {Wed., 2010/Jan/20 (Day 2)}
２．Let ｆ be a holomorphic function on a domain containing the closed disc {z : |z|≦3}, and suppose that f(1) = f(i) = f(-1) = f(-i) = 0. Show that |f(0)| ≦ (1/80)･max{|f(z)| : |z|=3}, and find all such functions for which equality holds in this inequality. {Thu., 2010/Jan/21 (Day 3)}
