Newton's Interpolating Polynomials in Mechanical Engineering

Explore Newton's interpolating polynomials in the context of Mechanical Engineering, specifically focusing on numerical methods and interpolation techniques. Dr. Mohamed El-Shazly, an Associate Professor of Mechanical Design and Tribology, guides students through the concepts and applications of Newton's polynomials. The content includes discussions on first-order, second-order, and third-order Newton's polynomials, along with a general form and its coefficients. A practical example illustrates the use of a fourth-order Newton's interpolating polynomial to determine the power generated by a windmill at a specific wind speed. Various images and explanations enhance the understanding of these mathematical concepts.

• Newtons Polynomials
• Mechanical Engineering
• Numerical Methods
• Interpolation Techniques
• Dr. Mohamed El-Shazly

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1. 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

2. Newton's Interpolating Polynomials First-order Newton's polynomial 2

3. Second-order Newton's polynomial 3

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5. Third-order Newton's polynomial 5

6. 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

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15. 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

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