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Lecture 7. Solving linear recurrence relations

1.

Solving linear recurrence
relations
Irina
Prosvirnina
Linear homogeneous
recurrence relations
with constant coefficients
Solving linear homogeneous recurrence relations
with constant coefficients
Solving linear homogeneous recurrence relations
with constant coefficients of degree two and of
degree three
Linear nonhomogeneous recurrence relations
with constant coefficients
Generating functions
Using generating functions to solve recurrence
relations

2.

Linear homogeneous recurrence relations
with constant coefficients

3.

Linear homogeneous recurrence relations
with constant coefficients

4.

Linear homogeneous recurrence relations
with constant coefficients

5.

Linear homogeneous recurrence relations
with constant coefficients

6.

Linear homogeneous recurrence relations
with constant coefficients

7.

Linear homogeneous recurrence relations
with constant coefficients

8.

Linear homogeneous recurrence relations
with constant coefficients

9.

Linear homogeneous recurrence relations
with constant coefficients

10.

Solving linear homogeneous recurrence relations
with constant coefficients

11.

Solving linear homogeneous recurrence relations
with constant coefficients

12.

Solving linear homogeneous recurrence relations
with constant coefficients

13.

Solving linear homogeneous recurrence relations
with constant coefficients

14.

Solving linear homogeneous recurrence relations
with constant coefficients
As we will see, these characteristic roots can be used to
give an explicit formula for all the solutions of the
recurrence relation.

15.

Solving linear homogeneous recurrence relations with
constant coefficients of degree two

16.

Proof of theorem 1

17.

Proof of theorem 1

18.

Proof of theorem 1

19.

Proof of theorem 1

20.

Proof of theorem 1

21.

Proof of theorem 1

22.

Solving linear homogeneous recurrence relations with
constant coefficients of degree two

23.

Solving linear homogeneous recurrence relations with
constant coefficients of degree two

24.

Solving linear homogeneous recurrence relations with
constant coefficients of degree two

25.

Solving linear homogeneous recurrence relations with
constant coefficients of degree two

26.

Solving linear homogeneous recurrence relations with
constant coefficients of degree two

27.

Solving linear homogeneous recurrence relations with
constant coefficients of degree two

28.

Solving linear homogeneous recurrence relations with
constant coefficients of degree two

29.

Solving linear homogeneous recurrence relations with
constant coefficients of degree three

30.

Solving linear homogeneous recurrence relations with
constant coefficients of degree three

31.

Solving linear homogeneous recurrence relations with
constant coefficients of degree three

32.

Linear nonhomogeneous recurrence relations
with constant coefficients

33.

Linear nonhomogeneous recurrence relations
with constant coefficients

34.

Linear nonhomogeneous recurrence relations
with constant coefficients

35.

Linear nonhomogeneous recurrence relations
with constant coefficients

36.

Linear nonhomogeneous recurrence relations
with constant coefficients

37.

Linear nonhomogeneous recurrence relations
with constant coefficients

38.

Proof of theorem 4

39.

Proof of theorem 4

40.

Proof of theorem 4

41.

Linear nonhomogeneous recurrence relations
with constant coefficients

42.

Linear nonhomogeneous recurrence relations
with constant coefficients

43.

Linear nonhomogeneous recurrence relations
with constant coefficients

44.

Linear nonhomogeneous recurrence relations
with constant coefficients

45.

Linear nonhomogeneous recurrence relations
with constant coefficients

46.

Linear nonhomogeneous recurrence relations
with constant coefficients

47.

Generating functions

48.

Generating functions

49.

Generating functions

50.

Generating functions

51.

Generating functions

52.

Generating functions

53.

Generating functions

54.

Generating functions

55.

Generating functions

56.

Using generating functions to solve recurrence relations

57.

58.

59.

60.

61.

Using generating functions to solve recurrence relations
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