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Non-linear Least Squares Comparison and Error Propagation

Learn how to do non-linear least squares and compare with linearized method. Combine error propagation with non-linear least squares, using partial derivatives and Excel. Understand the importance of controlling variables to minimize errors.

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Non-linear Least Squares Comparison and Error Propagation

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  1. Homework IDiscussion Terry A. Ring ChEN 4903 University of Utah

  2. What was I to learn from this HW? • Hw1-1 • Learn how to do a non-linear least squares.

  3. Comparison of Linearized and Non-linear Least Squares • Linearized Fit Arrhenius Expression • Non-linear Fit • Which is best?

  4. What was I to learn from this HW? • Hw1-2&3 • Learn how to combine Non-Linear least squares with error propagation. • Do Error propagation using two methods • Partial derivatives • G=f(y1,y2,y3,…) • Excel Method • fi = f(x1,x2,...,xi+si,...,xn)

  5. Non-linear Fit • Fit Results a

  6. Error Propagation • Partial Derivatives • Given D=0.010±0.001 m, V= 1.0±0.2 m/s, T= 358.0±2.5 K • Error (σ) in Nu • [(1.198* σV)2+(0.599* σD)2+(4.872* σT)2]1/2 Since dNu/dT is the largest piece of the error It is the variable that must be better controlled to lower the total error

  7. Error Results

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