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Презентация на тему Lecture 7. Solving linear recurrence relations

Содержание

Linear homogeneous recurrence relations with constant coefficients
Solving linear recurrence relations Linear homogeneous recurrence relations with constant coefficients Linear homogeneous recurrence relations with constant coefficients Linear homogeneous recurrence relations with constant coefficients Linear homogeneous recurrence relations with constant coefficients Linear homogeneous recurrence relations with constant coefficients Linear homogeneous recurrence relations with constant coefficients Linear homogeneous recurrence relations with constant coefficients Linear homogeneous recurrence relations with constant coefficients Solving linear homogeneous recurrence relations with constant coefficients Solving linear homogeneous recurrence relations with constant coefficients Solving linear homogeneous recurrence relations with constant coefficients Solving linear homogeneous recurrence relations with constant coefficients Solving linear homogeneous recurrence relations with constant coefficientsAs we will see, these Solving linear homogeneous recurrence relations with constant coefficients of degree two Proof of theorem 1 Proof of theorem 1 Proof of theorem 1 Proof of theorem 1 Proof of theorem 1 Proof of theorem 1 Solving linear homogeneous recurrence relations with constant coefficients of degree two Solving linear homogeneous recurrence relations with constant coefficients of degree two Solving linear homogeneous recurrence relations with constant coefficients of degree two Solving linear homogeneous recurrence relations with constant coefficients of degree two Solving linear homogeneous recurrence relations with constant coefficients of degree two Solving linear homogeneous recurrence relations with constant coefficients of degree two Solving linear homogeneous recurrence relations with constant coefficients of degree two Solving linear homogeneous recurrence relations with constant coefficients of degree three Solving linear homogeneous recurrence relations with constant coefficients of degree three Solving linear homogeneous recurrence relations with constant coefficients of degree three Linear nonhomogeneous recurrence relations with constant coefficients Linear nonhomogeneous recurrence relations with constant coefficients Linear nonhomogeneous recurrence relations with constant coefficients Linear nonhomogeneous recurrence relations with constant coefficients Linear nonhomogeneous recurrence relations with constant coefficients Linear nonhomogeneous recurrence relations with constant coefficients Proof of theorem 4 Proof of theorem 4 Proof of theorem 4 Linear nonhomogeneous recurrence relations with constant coefficients Linear nonhomogeneous recurrence relations with constant coefficients Linear nonhomogeneous recurrence relations with constant coefficients Linear nonhomogeneous recurrence relations with constant coefficients Linear nonhomogeneous recurrence relations with constant coefficients Linear nonhomogeneous recurrence relations with constant coefficients Generating functions Generating functions Generating functions Generating functions Generating functions Generating functions Generating functions Generating functions Generating functions Using generating functions to solve recurrence relations Using generating functions to solve recurrence relations
Слайды презентации

Слайд 2 Linear homogeneous recurrence relations with constant coefficients

Linear homogeneous recurrence relations with constant coefficients

Слайд 3 Linear homogeneous recurrence relations with constant coefficients

Linear homogeneous recurrence relations with constant coefficients

Слайд 4 Linear homogeneous recurrence relations with constant coefficients

Linear homogeneous recurrence relations with constant coefficients

Слайд 5 Linear homogeneous recurrence relations with constant coefficients

Linear homogeneous recurrence relations with constant coefficients

Слайд 6 Linear homogeneous recurrence relations with constant coefficients

Linear homogeneous recurrence relations with constant coefficients

Слайд 7 Linear homogeneous recurrence relations with constant coefficients

Linear homogeneous recurrence relations with constant coefficients

Слайд 8 Linear homogeneous recurrence relations with constant coefficients

Linear homogeneous recurrence relations with constant coefficients

Слайд 9 Linear homogeneous recurrence relations with constant coefficients

Linear homogeneous recurrence relations with constant coefficients

Слайд 10 Solving linear homogeneous recurrence relations with constant coefficients

Solving linear homogeneous recurrence relations with constant coefficients

Слайд 11 Solving linear homogeneous recurrence relations with constant coefficients

Solving linear homogeneous recurrence relations with constant coefficients

Слайд 12 Solving linear homogeneous recurrence relations with constant coefficients

Solving linear homogeneous recurrence relations with constant coefficients

Слайд 13 Solving linear homogeneous recurrence relations with constant coefficients

Solving linear homogeneous recurrence relations with constant coefficients

Слайд 14 Solving linear homogeneous recurrence relations with constant coefficients
As we

Solving linear homogeneous recurrence relations with constant coefficientsAs we will see,

will see, these characteristic roots can be used to

give an explicit formula for all the solutions of the recurrence relation.

Слайд 15 Solving linear homogeneous recurrence relations with constant coefficients

Solving linear homogeneous recurrence relations with constant coefficients of degree two

of degree two

Слайд 16 Proof of theorem 1

Proof of theorem 1

Слайд 17 Proof of theorem 1

Proof of theorem 1

Слайд 18 Proof of theorem 1

Proof of theorem 1

Слайд 19 Proof of theorem 1

Proof of theorem 1

Слайд 20 Proof of theorem 1

Proof of theorem 1

Слайд 21 Proof of theorem 1

Proof of theorem 1

Слайд 22 Solving linear homogeneous recurrence relations with constant coefficients

Solving linear homogeneous recurrence relations with constant coefficients of degree two

of degree two

Слайд 23 Solving linear homogeneous recurrence relations with constant coefficients

Solving linear homogeneous recurrence relations with constant coefficients of degree two

of degree two

Слайд 24 Solving linear homogeneous recurrence relations with constant coefficients

Solving linear homogeneous recurrence relations with constant coefficients of degree two

of degree two

Слайд 25 Solving linear homogeneous recurrence relations with constant coefficients

Solving linear homogeneous recurrence relations with constant coefficients of degree two

of degree two

Слайд 26 Solving linear homogeneous recurrence relations with constant coefficients

Solving linear homogeneous recurrence relations with constant coefficients of degree two

of degree two

Слайд 27 Solving linear homogeneous recurrence relations with constant coefficients

Solving linear homogeneous recurrence relations with constant coefficients of degree two

of degree two

Слайд 28 Solving linear homogeneous recurrence relations with constant coefficients

Solving linear homogeneous recurrence relations with constant coefficients of degree two

of degree two

Слайд 29 Solving linear homogeneous recurrence relations with constant coefficients

Solving linear homogeneous recurrence relations with constant coefficients of degree three

of degree three

Слайд 30 Solving linear homogeneous recurrence relations with constant coefficients

Solving linear homogeneous recurrence relations with constant coefficients of degree three

of degree three

Слайд 31 Solving linear homogeneous recurrence relations with constant coefficients

Solving linear homogeneous recurrence relations with constant coefficients of degree three

of degree three

Слайд 32 Linear nonhomogeneous recurrence relations with constant coefficients

Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 33 Linear nonhomogeneous recurrence relations with constant coefficients

Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 34 Linear nonhomogeneous recurrence relations with constant coefficients

Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 35 Linear nonhomogeneous recurrence relations with constant coefficients

Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 36 Linear nonhomogeneous recurrence relations with constant coefficients

Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 37 Linear nonhomogeneous recurrence relations with constant coefficients

Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 38 Proof of theorem 4

Proof of theorem 4

Слайд 39 Proof of theorem 4

Proof of theorem 4

Слайд 40 Proof of theorem 4

Proof of theorem 4

Слайд 41 Linear nonhomogeneous recurrence relations with constant coefficients

Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 42 Linear nonhomogeneous recurrence relations with constant coefficients

Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 43 Linear nonhomogeneous recurrence relations with constant coefficients

Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 44 Linear nonhomogeneous recurrence relations with constant coefficients

Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 45 Linear nonhomogeneous recurrence relations with constant coefficients

Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 46 Linear nonhomogeneous recurrence relations with constant coefficients

Linear nonhomogeneous recurrence relations with constant coefficients

Слайд 47 Generating functions

Generating functions

Слайд 48 Generating functions

Generating functions

Слайд 49 Generating functions

Generating functions

Слайд 50 Generating functions

Generating functions

Слайд 51 Generating functions

Generating functions

Слайд 52 Generating functions

Generating functions

Слайд 53 Generating functions

Generating functions

Слайд 54 Generating functions

Generating functions

Слайд 55 Generating functions

Generating functions

Слайд 56 Using generating functions to solve recurrence relations

Using generating functions to solve recurrence relations

Слайд 57

Слайд 58

Слайд 59

Слайд 60

Слайд 61 Using generating functions to solve recurrence relations

Using generating functions to solve recurrence relations

Слайд 62

Слайд 63

Слайд 64

Слайд 65

Слайд 66

Слайд 67

Слайд 68

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