MATH 257 Midterm: MATH 257+316 2013 Winter Test 2
Document Summary
To receive full credit, all answers must be supported with clear and correct derivations. No calculators, notes, or other aids are allowed. [15] 1. (a) list all the singular points and test each one for regularity: (cid:0)x2 + 2x(cid:1) y + xy + Determine the exponents of singularity for each regular singular point you nd. A professor plans to show the class how the same function f (x), 0 < x < , can be represented by four di erent eigenfunction series, namely, (a) (c) (cid:19) bn sin(cid:18) n x pn sin(cid:18) (2n 1) x. On the way to class, the wind blows the professor"s notes away. Each page shows a sketch related to the professor"s intended function f . (a) here are the three recovered sketches. Clearly label each one with the letter (a d) for the corresponding eigenfunction series. Write the label in the lower-left corner of each sketch.
