• Read the Notes on Special Functions through section 1.2 (pg. 5).
• Do the following problems.
  1. Section 9.5 (pgs. 447-449): 7, 9
  2. Verify Stokes's Theorem in case F= 2yi + 3xj − z³k and S is the upper hemisphere of x² + y² + z² = 4, which has the circle x² + y² = 4, z = 0, as a boundary. Use the normal with positive z component.
  3. Use the method of Frobenius in the following differential equations to find the indicial equation, the recurrence (recursion) relation, and the the first few terms of the series solution for the largest root of the indicial equation. (You are not being asked to solve the recurrence relation.)
     1. x²y''+xy' +(x² − 1)y = 0
     2. 9x²y'' +(9x²+2)y = 0
     3. 25x²y''+25xy'+(x⁴-1)y=0

Updated 6/28/07 (fjn).