(a) Use the Taylor series expansion to derive a three-point finite difference formula that evaluates the first derivative dy/dx at point x=x; with given points (x₁, yi), (Xi+1, Yi+1), (Xi+2, Yi+2), which are not equally spaced. Use three terms of the series plus the remainder. (b) Derive for the case when the spacing between the points is equal, a simpler finite difference formula. (c) Use the data in the table to derive in a MatLab scipt the derivative of the point x=x₁. No MatLab build-in function is allowed to be used. Submit for (a) and (b) your hand calculations and for (c) your MatLab files. Xi 5.49 Xi+1 5.58 Xi+2 5.63 Yi 8.08 Yi+1 8.12 Yi+2 8.15

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(a) Use the Taylor series expansion to derive a three-point finite difference formula that
evaluates the first derivative dy/dx at point x=x; with given points (xi,yi), (Xi+1,Yi+1), (Xi+2, Yi+2),
which are not equally spaced. Use three terms of the series plus the remainder. (b) Derive for
the case when the spacing between the points is equal, a simpler finite difference formula.
(c) Use the data in the table to derive in a MatLab scipt the derivative of the point x=x₁. No
MatLab build-in function is allowed to be used. Submit for (a) and (b) your hand calculations
and for (c) your MatLab files.
Xi
5.49
Xi+1
5.58
Xi+2
5.63
Yi
8.08
Yi+1
8.12
Yi+2
8.15
Transcribed Image Text:(a) Use the Taylor series expansion to derive a three-point finite difference formula that evaluates the first derivative dy/dx at point x=x; with given points (xi,yi), (Xi+1,Yi+1), (Xi+2, Yi+2), which are not equally spaced. Use three terms of the series plus the remainder. (b) Derive for the case when the spacing between the points is equal, a simpler finite difference formula. (c) Use the data in the table to derive in a MatLab scipt the derivative of the point x=x₁. No MatLab build-in function is allowed to be used. Submit for (a) and (b) your hand calculations and for (c) your MatLab files. Xi 5.49 Xi+1 5.58 Xi+2 5.63 Yi 8.08 Yi+1 8.12 Yi+2 8.15
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