The Method of Least square with example — Lesson 4

This lesson covers the concept of curve fitting and uncertainty analysis in fluid mechanics. It begins with an explanation of why curve fitting is necessary, particularly in experimental methods where data is captured and analyzed. The lesson then delves into the least square method used in curve fitting analysis, explaining how it minimizes the difference between the curve and the data. The lesson also discusses the importance of selecting an appropriate function for curve fitting and how to calculate the best parameters for the data set. The lesson concludes with an explanation of uncertainty analysis, highlighting how it is an inherent part of experimental methods and how it can be calculated.

Video Highlights

00:49 - Why curve fitting is necessary, and how it can be used to predict values based on recorded data
07:54 - Method of least square
19:18 - How to select an appropriate function for curve fitting
31:44 - Steps to follow for curve fitting using a given data set, including selecting an appropriate function and finding the best parameters
41:11 - Example of curve fitting analysis using a given data set, and how to calculate the best parameters for the curve

Key Takeaways

- Curve fitting is a crucial aspect of fluid mechanics, particularly in experimental methods where data is captured and analyzed.
- The least square method is a popular technique used in curve fitting analysis. It aims to minimize the difference between the curve and the data.
- Selecting an appropriate function for curve fitting is vital. If a physical law guides the data set, that functional form can be used.
- The best parameters for the data set can be calculated using the Kramer's rule, ensuring the smallest mean square difference between the curve and the data.
- Uncertainty analysis is an inherent part of experimental methods. It can be calculated using specific formulas, considering the uncertainties in the independent variables.