1. Decide whether the following operators L are formally self adjoint, and whether they are self adjoint on M. Decide whether the equation L(y) = f on M is in the first or second alternative.

(a) L(y) = y'', M = {y: y(0) = y'(0) = 0 }. ans: yes, no, 1st.

(b) L(y) = y'', M= {y: y(0) = y(1) = 0 }. ans: yes, yes, 1st.

ans: yes, yes, 2nd.

(d) L(y) = y'' + 3y' + 2y, M = {y: y(0) = y(1) = 0}. ans: no, no, 1st.

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