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Number derivatives: A treasure trove of student research projects. Mike Krebs, Cal State LA. Based on joint work with:. Caleb Emmons, Pacific University. Anthony Shaheen , Cal State LA. (Product Rule). Number derivative : . Number derivative : . Questions:. Number derivative : .

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slide1

Number derivatives:

A treasure trove of

student research projects

Mike Krebs, Cal State LA

Based on joint work with:

Caleb Emmons, Pacific University

Anthony Shaheen, Cal State LA

slide6

Number derivative:

Questions:

(A) Do they exist?

slide7

Number derivative:

Questions:

(A) Do they exist?

(2) What neat-o properties do they have?

slide8

Number derivative:

Questions:

(A) Do they exist?

(2) What neat-o properties do they have?

(iii) Can we classify all of them?

slide9

Number derivative:

(A) Do they exist?

slide10

Number derivative:

(A) Do they exist?

slide11

Number derivative:

(A) Do they exist?

BAWWWW

slide12

Number derivative:

(A) Do they exist?

BAWWWW-RING

slide13

Number derivative:

(A’)Do any non-trivial number derivatives exist?

slide14

Number derivative:

(A’)Do any non-trivial number derivatives exist?

Stay tuned . . .

slide16

Number derivative:

(2) What neat-o properties do they have?

slide17

Number derivative:

(2) What neat-o properties do they have?

slide18

Number derivative:

(2) What neat-o properties do they have?

slide19

Number derivative:

(2) What neat-o properties do they have?

slide20

Number derivative:

(2) What neat-o properties do they have?

slide21

Number derivative:

(2) What neat-o properties do they have?

slide22

Number derivative:

(2) What neat-o properties do they have?

slide23

Number derivative:

(2) What neat-o properties do they have?

slide24

Number derivative:

(2) What neat-o properties do they have?

slide25

Number derivative:

(2) What neat-o properties do they have?

slide26

Number derivative:

(2) What neat-o properties do they have?

(Power Rule)

slide27

Number derivative:

(2) What neat-o properties do they have?

(Power Rule)

slide28

Number derivative:

(2) What neat-o properties do they have?

slide29

Number derivative:

(2) What neat-o properties do they have?

slide30

Number derivative:

(2) What neat-o properties do they have?

(by Fermat’s

)

theorem

slide31

Number derivative:

(2) What neat-o properties do they have?

(by Fermat’s

)

theorem

(by the Power Rule)

slide32

Number derivative:

(2) What neat-o properties do they have?

(by Fermat’s

)

theorem

(by the Power Rule)

slide33

Number derivative:

(A’)Do any non-trivial number derivatives exist?

slide34

Number derivative:

(A’)Do any non-trivial number derivatives exist?

slide35

Number derivative:

(A’)Do any non-trivial number derivatives exist?

slide36

Number derivative:

(A’)Do any non-trivial number derivatives exist?

slide37

Number derivative:

(A’)Do any non-trivial number derivatives exist?

Yes! For example,

here’s one.

slide38

Number derivative:

(A’)Do any non-trivial number derivatives exist?

Yes! For example,

here’s one.

slide39

Number derivative:

(A’)Do any non-trivial number derivatives exist?

Yes! For example,

here’s one.

slide40

Number derivative:

(A’)Do any non-trivial number derivatives exist?

Yes! For example,

here’s one.

and so on . . .

slide41

Number derivative:

(A’)Do any non-trivial number derivatives exist?

Yes! For example,

here’s an infinite

family.

slide42

Number derivative:

(A’)Do any non-trivial number derivatives exist?

slide43

Number derivative:

(A’)Do any non-trivial number derivatives exist?

slide44

Number derivative:

(A’)Do any non-trivial number derivatives exist?

slide45

Number derivative:

(A’)Do any non-trivial number derivatives exist?

slide46

Number derivative:

(A’)Do any non-trivial number derivatives exist?

slide47

Number derivative:

(A’)Do any non-trivial number derivatives exist?

Yes! For example,

here’s an infinite

family.

slide48

Number derivative:

(A’)Do any non-trivial number derivatives exist?

Yes! For example,

here’s an infinite

family.

slide49

Number derivative:

(A’)Do any non-trivial number derivatives exist?

Yes! For example,

here’s an infinite

family.

slide50

Number derivative:

(A’)Do any non-trivial number derivatives exist?

Yes! For example,

here’s an infinite

family.

slide51

Number derivative:

(A’)Do any non-trivial number derivatives exist?

Yes! For example,

here’s an infinite

family.

slide52

Number derivative:

(A’)Do any non-trivial number derivatives exist?

Yes! For example,

here’s an infinite

family.

slide53

Number derivative:

(A’)Do any non-trivial number derivatives exist?

Yes! For example,

here’s an infinite

family.

slide54

Number derivative:

(A’)Do any non-trivial number derivatives exist?

Yes! For example,

here’s an infinite

family.

slide55

Number derivative:

(A’)Do any non-trivial number derivatives exist?

Yes! For example,

here’s an infinite

family.

slide56

Number derivative:

Now that we have some number derivatives, what

questions can we ask about them?

slide57

Number derivative:

Now that we have some number derivatives, what

questions can we ask about them?

Extend the analogy.

slide58

Number derivative:

Now that we have some number derivatives, what

questions can we ask about them?

Extend the analogy.

 What are the “constants”?

slide59

Number derivative:

Now that we have some number derivatives, what

questions can we ask about them?

Extend the analogy.

 What are the “constants”?

 How do you “integrate”?

slide60

Number derivative:

Now that we have some number derivatives, what

questions can we ask about them?

Extend the analogy.

 What are the “constants”?

 How do you “integrate”?

 Solve ODE.

slide61

Number derivative:

Now that we have some number derivatives, what

questions can we ask about them?

Extend the analogy.

 What are the “constants”?

 How do you “integrate”?

 Solve ODE.

slide62

Number derivative:

Now that we have some number derivatives, what

questions can we ask about them?

Extend the analogy.

 What are the “constants”?

 How do you “integrate”?

 Solve ODE.

slide65

Number derivative:

(iii) Can we classify all of them?

For more details, see:

slide66

Number derivative:

Other papers on number derivatives:

slide67

Number derivative:

Other papers on number derivatives:

slide68

Number derivative:

Other papers on number derivatives:

slide69

Number derivative:

Other papers on number derivatives:

slide70

Number derivative:

Other papers on number derivatives: