Final Exam:  

December 7th,  Wednesday  8:00-10:00am (check this schedule for any updates). I will try to reschedule the exam to a later time.

Total score for the final exam is 200 points; there will be twice as many problems as in the regular 1-hour exam.

50% of the exam will be on Chapter 11;  50%  will be on the previous material.

• 11.1:  practice finding eigenfunctions and eigenvalues of two-point BVPs; understand the connection with the heat conduction equation;
  
• 11.2:  recall general facts about eigenfunctions and eigenvalues assiciated to Sturm-Liouville BVPs, Theorems 11.2.1,2,3; normalization;
• 11.3:  nonhomogeneous BVPs; for SLBVP see Theorem 11.3.1; for  heat equation the procedure of finding solutions is described on p.686, also see your notes;  remember to write equations in the canonical form so that the force appears on the right side;
  
• 11.4:  singular problems; recall the form of relaxed boundary condition we use in this case; recall Bessel's equation from Ch 5 and the fundumental solutions;
• 11.5:  from this section you have to understand how Bessel's functions are used in place of the usual Sin and Cos to expand functions into Fourier series (see your homework).