Newton's Interpolating Polynomials in Mechanical Engineering
Explore Newton's Interpolating Polynomials in Mechanical Engineering, specifically focusing on first-order, second-order, and third-order polynomials. Learn how to calculate coefficients, understand divided differences, and apply these concepts in practical examples such as determining windmill power output based on wind speed measurements.
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Faculty of Engineering Mechanical Engineering Department MATH 2140 Numerical Methods Instructor: Dr. Mohamed El-Shazly Associate Prof. of Mechanical Design and Tribology melshazly@ksu.edu.sa Office: F072 1
Newton's Interpolating Polynomials First-order Newton's polynomial 2
Second-order Newton's polynomial 3
A general form of Newton's polynomial and its coefficients For two points, (x1, y1), and (x2, Y2) , the first divided difference, written as f [x2, x1], is defined as the slope of the line connecting the two points: 6
EXAMPLE 2 The power generated by a windmill varies with the wind speed. In an experiment, the following five measurements were obtained in table below. Determine the fourth-order Newton s interpolating polynomial that passes through the data points. Use the polynomial to calculate the power at a wind speed of 26 mph. 15
Solution 2 16
