Consider the laplace equation for a ball of radius r described in spherical coordinates (r, 0) 2 1 cot 72 0= n where is the zenith angle and assume u is independent on the azirnuth angle d. a) by separation of variables, derive two ordinary differential equations of r and w: = cos e given by 2 f" (r) +2rf (r) - n(n + 1) f, (r) = 0, (1 w2)g (w) - 2wg", (w) +n(n +1)g, (w) 0. (n 0,1,2,. .) b) find fn (r) and gn (w) satisfying g(1) = 1 for n = 1,3. c) show that for n m, gn (w)gm (w)dw = 0. d) assume the boundary condition is given by u(r, o) = cos 0. then determine u(r, ) inside the ball.

You need to be more specific.  i really don't know what a "motion map" is.you can draw a graph of an object's position, distance, displacement, speed,velocity, or acceleration versus time, or you can draw a graph of the object's x-position versus its y-position and not give any information about time at all.if the graph presents position or displacement against time,  then constant velocity is a straight line . . i.e. a line that has  constant slope.if the graph shows speed against time, then constant velocityis a horizontal piece of line.if the graph shows acceleration against time, then constant  velocity is a piece of line that lies on the x-axis . . it's value is zero. 

connectedness in handwriting analysis is a useful tool in establishing the writer’s method of thinking and its perception in where he/she fits in to the environment around him in the social sense. in addition, the more connected the writing of an individual, the more he/she is flexible and single minded.