Number derivatives: A treasure trove of student research projects

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# Number derivatives: A treasure trove of student research projects - PowerPoint PPT Presentation

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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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

Number derivative:

Questions:

(A) Do they exist?

Number derivative:

Questions:

(A) Do they exist?

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

Number derivative:

Questions:

(A) Do they exist?

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

(iii) Can we classify all of them?

Number derivative:

(A) Do they exist?

Number derivative:

(A) Do they exist?

Number derivative:

(A) Do they exist?

BAWWWW

Number derivative:

(A) Do they exist?

BAWWWW-RING

Number derivative:

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

Number derivative:

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

Stay tuned . . .

Number derivative:

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

Number derivative:

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

Number derivative:

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

Number derivative:

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

Number derivative:

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

Number derivative:

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

Number derivative:

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

Number derivative:

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

Number derivative:

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

Number derivative:

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

Number derivative:

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

(Power Rule)

Number derivative:

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

(Power Rule)

Number derivative:

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

Number derivative:

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

Number derivative:

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

(by Fermat’s

)

theorem

Number derivative:

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

(by Fermat’s

)

theorem

(by the Power Rule)

Number derivative:

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

(by Fermat’s

)

theorem

(by the Power Rule)

Number derivative:

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

Number derivative:

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

Number derivative:

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

Number derivative:

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

Number derivative:

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

Yes! For example,

here’s one.

Number derivative:

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

Yes! For example,

here’s one.

Number derivative:

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

Yes! For example,

here’s one.

Number derivative:

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

Yes! For example,

here’s one.

and so on . . .

Number derivative:

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

Yes! For example,

here’s an infinite

family.

Number derivative:

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

Number derivative:

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

Number derivative:

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

Number derivative:

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

Number derivative:

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

Number derivative:

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

Yes! For example,

here’s an infinite

family.

Number derivative:

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

Yes! For example,

here’s an infinite

family.

Number derivative:

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

Yes! For example,

here’s an infinite

family.

Number derivative:

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

Yes! For example,

here’s an infinite

family.

Number derivative:

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

Yes! For example,

here’s an infinite

family.

Number derivative:

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

Yes! For example,

here’s an infinite

family.

Number derivative:

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

Yes! For example,

here’s an infinite

family.

Number derivative:

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

Yes! For example,

here’s an infinite

family.

Number derivative:

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

Yes! For example,

here’s an infinite

family.

Number derivative:

Now that we have some number derivatives, what

Number derivative:

Now that we have some number derivatives, what

Extend the analogy.

Number derivative:

Now that we have some number derivatives, what

Extend the analogy.

 What are the “constants”?

Number derivative:

Now that we have some number derivatives, what

Extend the analogy.

 What are the “constants”?

 How do you “integrate”?

Number derivative:

Now that we have some number derivatives, what

Extend the analogy.

 What are the “constants”?

 How do you “integrate”?

 Solve ODE.

Number derivative:

Now that we have some number derivatives, what

Extend the analogy.

 What are the “constants”?

 How do you “integrate”?

 Solve ODE.

Number derivative:

Now that we have some number derivatives, what

Extend the analogy.

 What are the “constants”?

 How do you “integrate”?

 Solve ODE.

Number derivative:

(iii) Can we classify all of them?

For more details, see:

Number derivative:

Other papers on number derivatives:

Number derivative:

Other papers on number derivatives:

Number derivative:

Other papers on number derivatives:

Number derivative:

Other papers on number derivatives:

Number derivative:

Other papers on number derivatives: