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Lecture 7. Solving linear recurrence relations презентация

Содержание

1. Lecture 7. Solving linear 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
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
61. Using generating functions to solve recurrence relations

Linear homogeneous recurrence relations with constant coefficients

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Lecture 7. Solving linear recurrence relations

Слайд 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

Слайд 2Linear homogeneous recurrence relations with constant coefficients

Слайд 3Linear homogeneous recurrence relations with constant coefficients

Слайд 4Linear homogeneous recurrence relations with constant coefficients

Слайд 5Linear homogeneous recurrence relations with constant coefficients

Слайд 6Linear homogeneous recurrence relations with constant coefficients

Слайд 7Linear homogeneous recurrence relations with constant coefficients

Слайд 8Linear homogeneous recurrence relations with constant coefficients

Слайд 9Linear homogeneous recurrence relations with constant coefficients

Слайд 10Solving linear homogeneous recurrence relations with constant coefficients

Слайд 11Solving linear homogeneous recurrence relations with constant coefficients

Слайд 12Solving linear homogeneous recurrence relations with constant coefficients

Слайд 13Solving linear homogeneous recurrence relations with constant coefficients

Слайд 14Solving 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.

Слайд 15Solving linear homogeneous recurrence relations with constant coefficients of degree two

Слайд 16Proof of theorem 1

Слайд 17Proof of theorem 1

Слайд 18Proof of theorem 1

Слайд 19Proof of theorem 1

Слайд 20Proof of theorem 1

Слайд 21Proof of theorem 1

Слайд 22Solving linear homogeneous recurrence relations with constant coefficients of degree two

Слайд 23Solving linear homogeneous recurrence relations with constant coefficients of degree two

Слайд 24Solving linear homogeneous recurrence relations with constant coefficients of degree two

Слайд 25Solving linear homogeneous recurrence relations with constant coefficients of degree two

Слайд 26Solving linear homogeneous recurrence relations with constant coefficients of degree two

Слайд 27Solving linear homogeneous recurrence relations with constant coefficients of degree two

Слайд 28Solving linear homogeneous recurrence relations with constant coefficients of degree two

Слайд 29Solving linear homogeneous recurrence relations with constant coefficients of degree three

Слайд 30Solving linear homogeneous recurrence relations with constant coefficients of degree three

Слайд 31Solving linear homogeneous recurrence relations with constant coefficients of degree three

Слайд 32Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 33Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 34Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 35Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 36Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 37Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 38Proof of theorem 4

Слайд 39Proof of theorem 4

Слайд 40Proof of theorem 4

Слайд 41Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 42Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 43Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 44Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 45Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 46Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 47Generating functions

Слайд 48Generating functions

Слайд 49Generating functions

Слайд 50Generating functions

Слайд 51Generating functions

Слайд 52Generating functions

Слайд 53Generating functions

Слайд 54Generating functions

Слайд 55Generating functions

Слайд 56Using generating functions to solve recurrence relations

Слайд 57

Слайд 58

Слайд 59

Слайд 60

Слайд 61Using generating functions to solve recurrence relations

Слайд 62

Слайд 63

Слайд 64

Слайд 65

Слайд 66

Слайд 67

Слайд 68

Слайд 69

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