Solving linear recurrence relations презентация
Содержание
- 2. Linear homogeneous recurrence relations with constant coefficients Definition 1 A linear
- 3. Linear homogeneous recurrence relations with constant coefficients A sequence satisfying the
- 4. Linear homogeneous recurrence relations with constant coefficients Example 1 The recurrence
- 5. Linear homogeneous recurrence relations with constant coefficients Example 2 The recurrence
- 6. Linear homogeneous recurrence relations with constant coefficients Example 3 The recurrence
- 7. Linear homogeneous recurrence relations with constant coefficients Example 4 The recurrence
- 8. Linear homogeneous recurrence relations with constant coefficients Example 5 The recurrence
- 9. Linear homogeneous recurrence relations with constant coefficients Example 6 The recurrence
- 10. Solving linear homogeneous recurrence relations with constant coefficients The basic approach
- 11. Solving linear homogeneous recurrence relations with constant coefficients Note that
- 12. Solving linear homogeneous recurrence relations with constant coefficients When both sides
- 13. Solving linear homogeneous recurrence relations with constant coefficients Consequently, the sequence
- 14. Solving linear homogeneous recurrence relations with constant coefficients As we will
- 15. Solving linear homogeneous recurrence relations with constant coefficients of degree two
- 16. Proof of theorem 1 ? If and are roots of ,
- 17. Proof of theorem 1 ? If the sequence is a solution
- 18. Proof of theorem 1 ? If the sequence is a solution
- 19. Proof of theorem 1 ? If the sequence is a solution
- 20. Proof of theorem 1 ? If the sequence is a solution
- 21. Proof of theorem 1 ? If the sequence is a solution
- 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 Definition 2 A linear
- 33. Linear nonhomogeneous recurrence relations with constant coefficients Example 11 The recurrence
- 34. Linear nonhomogeneous recurrence relations with constant coefficients Example 12 The recurrence
- 35. Linear nonhomogeneous recurrence relations with constant coefficients Example 13 The recurrence
- 36. Linear nonhomogeneous recurrence relations with constant coefficients Example 14 The recurrence
- 37. Linear nonhomogeneous recurrence relations with constant coefficients Theorem 4 If is
- 38. Proof of theorem 4 Because is a particular solution of the
- 39. Proof of theorem 4 Now suppose that is a second solution
- 40. Proof of theorem 4 So, , . Subtracting the first of
- 41. Linear nonhomogeneous recurrence relations with constant coefficients Example 15 Find all
- 42. Linear nonhomogeneous recurrence relations with constant coefficients Example 15 Find all
- 43. Linear nonhomogeneous recurrence relations with constant coefficients Example 15 Find all
- 44. Linear nonhomogeneous recurrence relations with constant coefficients Example 16 Find all
- 45. Linear nonhomogeneous recurrence relations with constant coefficients Example 16 Find all
- 46. Linear nonhomogeneous recurrence relations with constant coefficients Example 16 Find all
- 47. Generating functions Definition 3 The generating function for the sequence
- 48. Generating functions Example 17 The generating function for the sequence is
- 49. Generating functions Example 18 The generating function for the sequence
- 50. Generating functions Example 19 The generating function for the sequence
- 51. Generating functions We can define generating functions for finite sequences of
- 52. Generating functions Example 20 The generating function of is We
- 53. Generating functions Example 21 Let be a positive integer. The generating
- 54. Generating functions Example 22 The function is the generating function
- 55. Generating functions Example 23 The function is the generating function
- 56. Using generating functions to solve recurrence relations Example 24 Solve the
- 57. Solution of example 24 Let be the generating function for the
- 58. Solution of example 24
- 59. Solution of example 24
- 60. Solution of example 24
- 61. Using generating functions to solve recurrence relations Example 25 Solve the
- 62. Solution of example 25 To make our work with generating functions
- 63. Solution of example 25 Let be the generating function
- 64. Solution of example 25 We sum both sides of the last
- 65. Solution of example 25
- 66. Solution of example 25
- 67. Solution of example 25 Expanding the right-hand side of this
- 68. Solution of example 25
- 69. Solution of example 25
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