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"Roots of polynomials and parameter spaces"

"Roots of polynomials and parameter spaces"

"Roots of polynomials and parameter spaces"

"Optimal polynomial approximants of reciprocals of analytic functions"

"Optimal polynomial approximants of reciprocals of analytic functions"

Frame created in Chaoscope, polynomial function

Algebra Quadratic Equations As this is the second degree polynomial the solution of this expression have two roots and may or may not be distinct. This is also not necessary that the roots will be real the roots can have complex value. The solutions of the maths quadratic equations are given where the equation becomes zero. These two solutions are named as “roots” and “zeros”.

polynomials orthogonal over the unit disk

Using long division to divide polynomials.

"Roots of polynomials and parameter spaces"

polynomials orthogonal over the unit disk

"Roots of polynomials and parameter spaces"

polynomials orthogonal over the unit disk

polynomials orthogonal over the unit disk

polynomials orthogonal over the unit disk

polynomials orthogonal over the unit disk

"Gauss–Lucas Theorem and its Consequences in Polynomial Dynamics"

"Optimal polynomial approximants of reciprocals of analytic functions"

polynomials orthogonal over the unit disk

"A Natural Invariant Measure for Polynomial Semigroups, and its Properties"

"Optimal polynomial approximants of reciprocals of analytic functions"

polynomials orthogonal over the unit disk

polynomials orthogonal over the unit disk

"Roots of polynomials and parameter spaces"

polynomials orthogonal over the unit disk

You really can calculate work (and thus potential energy) from any force that you have a force function for. I made this one up entirely.

 

Note that at far right we then took our answer and took its derivative and got back to the original function. Practice doing this with a couple of polynomials. You'll be happy.

"Roots of polynomials and parameter spaces"

polynomials orthogonal over the unit disk

polynomials orthogonal over the unit disk

polynomial function, quadratic

polynomials orthogonal over the unit disk

AKA the Babbage Difference Engine (of intense adding and subtracting.)

 

After our chess break, we decided to check out the Babbage demo going on close by...

polynomials orthogonal over the unit disk

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