Lecture 12
Learning objectives
After this class, you should be able to:
- Prove the theorem on page 341.
- Apply the above theorem to express a rational function as partial fractions, and to solve a recurrence using generating functions.
- Solve mututally recursive sequences.
Reading assignment
- Page 341-344.
Exercises and review questions
- Questions on current lecture's material
- Express the following fraction as partial fractions:
z/((1-z)2 (1+2z)2)
.
- Express the following fraction as partial fractions:
(3z+1)/((1+z) (1-z)2 (1+2z)3)
.
- Solve the following recurrence:
u0 = v0 = 0
, u1 = v1 = 1
, un = un-1 + 3 vn-1, n > 1
, vn = un-1 - vn-1, n > 1
.
- Questions on next lecture's material
- None.
Last modified: 27 Nov 2017