Lecture 2 - Curve Fitting

The primary objective of this lecture is to introduce students to the concept of curve fitting and its importance in civil engineering applications. By the end of this lecture, students will:

1. Understand the Basics of Curve Fitting:
   Learn what curve fitting is, why it is used, and how it helps in finding mathematical relationships between variables in experimental data. Students will explore how curve fitting is essential in approximating real-world data with an appropriate mathematical model.
2. Learn the Least Squares Method:
   Gain a solid understanding of the least squares method, which is one of the most common techniques used for fitting a curve to data. Students will learn how this method minimizes the error between the actual data points and the predicted values from the model.
3. Apply Curve Fitting in Real-World Engineering Problems:
   Explore how curve fitting is applied in civil engineering contexts, such as in material testing, load-deflection analysis, and geotechnical investigations. Students will see practical examples of how curve fitting is used to interpret and predict behavior based on data.
4. Calculate the Correlation Between Variables:
   Be introduced to the concept of the linear correlation coefficient, which quantifies the strength and direction of the linear relationship between two variables. This will help students assess the quality of the fit and determine whether a linear model is appropriate for the data.