(1) Symbolic complex algebra in mathematica and (2) Dsolve

*To*: mathgroup at yoda.ncsa.uiuc.edu*Subject*: (1) Symbolic complex algebra in mathematica and (2) Dsolve*From*: ken yip <yip-ken at CS.YALE.EDU>*Date*: Thu, 22 Nov 90 18:00:16 EST

(1) I hope I am not correct about this. I want to define a complex quantity z = x + I y so that Re[z] ==> x Im[z] ==> y Conjugate[z] ==> x - I y etc. Mathematica doesn't seem to know how to do this even after I define x and y to be real by x/: RealQ[x] = True (Of course, this does not change the head of x which is still Symbol.) Next I tried to define some transformation rules, but then I couldn't find a way to specify the pattern variable to be of type real AND symbol. (2) I want to solve a simple harmonic equation with boundary conditions: DSolve[{x'[t] == y[t], y'[t] == k^2 x[t], y'[-h] == 0},{x[t],y[t]}, t] But mathematica seems to ignore the boundary constraint. Any wisdom? P.S. Originally I plan to use Mathematica to help me solve some linear non-homogenous PDEs, but after a few hours playing witb it, I am becoming increasingly frustrated with many of the simple things it can't do. Is that due to my insufficient knowledge of mathematica or is that due to mathematica itself?