Newton's Forward & Backward Difference Interpolation Formulas, Approximate e^(0.48) in a Spreadsheet

Numerical Methods course (Numerical Analysis course) Lecture #21 at Bethel University, St. Paul, MN, Spring 2020. This is a calculus-based advanced undergraduate numerical analysis course.

(0:00) Lecture plan
(2:33) Review divided differences
(5:55) Newton's forward difference formula for interpolation
(13:00) Example: approximate e^(0.48) (make a table of divided differences)
(16:58) Use the formula
(19:38) The forward difference operator delta and its "powers"
(22:28) Newton's forward difference formula in terms of the forward difference operator
(25:02) Check it on a spreadsheet
(33:28) Newton's backward difference formula
(39:02) The backward difference operator nabla and its "powers"
(41:14) Newton's backward difference formula in terms of the backward difference operator
(43:29) Check it on a spreadsheet

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[fcuantico]

Thank you so much for explaining how to handle and where the s-term comes in Both Newton Formulas

[ahmadbani]

is it valid if the difference a negative number?

[KenInYoutube]

5:53 hits different and not a good type of different