Lecture 10

Learning objectives

After this class, you should be able to:

1. Express a rational function as partial fractions, when the denominator of the rational function has distinct roots, and the degree of the numerator is lower than that of the denominator.
2. Use the above technique to solve recurrence relations using generating functions.

Reading assignment

1. Page 338-340.

Exercises and review questions

• Questions on current lecture's material
  1. Use generating functions to derive the closed for solution to the following recurrence: g0 = 0, g1 = 1/4, gn = (1/2) gn-1 + (1/2) gn-2.
  2. Use generating functions to derive the closed for solution to the following recurrence: g0 = 1/4, g1 = 1/4, gn = (3/2) gn-1 - (1/2) gn-2.
  3. Express the following rational function as partial fractions, and verify that your answer is correct: z/(z2 - 2z + 2).

• Questions on next lecture's material
  1. None