Clip 3: Linear Approximation and the Definition of the Derivative | Single Variable Calculus | Mathematics | MIT OpenCourseWare
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Clip 3: Linear Approximation and the Definition of the Derivative | Single Variable Calculus | Mathematics | MIT OpenCourseWare
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2022年4月1日
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SOLVED: Accuracy of a difference approximation can be improved by a linear combination of two difference approximations so that the lowest-order (or leading) truncation errors of the two approximations are cancelled. The improved difference approximation is given by: fea = I - 2htSrL (1 - a)rn 2f1 fi - 2h? 4h?(a) Determine the value of a for the following approximation so that the accuracy is optimized or maximized. Also, determine the truncation error. (15 pt)(b) Follow (a) to determine the
SOLVED: Accuracy of a difference approximation can be improved by a linear combination of two difference approximations so that the lowest-order (or leading) truncation errors of the two approximations are cancelled. The improved difference approximation is given by: fea = I - 2htSrL (1 - a)rn 2f1 fi - 2h? 4h?(a) Determine the value of a for the following approximation so that the accuracy is optimized or maximized. Also, determine the truncation error. (15 pt)(b) Follow (a) to determine the
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SOLVED: Accuracy of a difference approximation can be improved by a linear combination of two difference approximations so that the lowest-order (or leading) truncation errors of the two approximations are cancelled. The improved difference approximation is given by: fea = I - 2htSrL (1 - a)rn 2f1 fi - 2h? 4h?(a) Determine the value of a for the following approximation so that the accuracy is optimized or maximized. Also, determine the truncation error. (15 pt)(b) Follow (a) to determine the
SOLVED: Accuracy of a difference approximation can be improved b…
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