Numerical Methods: Stopping Criteria, SciPy, and Matplotlib

This lecture covers numerical methods focusing on stopping criteria, the use of SciPy for optimization, and data visualization with Matplotlib. The instructor begins by discussing the convergence of Newton's method, emphasizing the importance of the second derivative for quadratic convergence. The lecture then transitions to the criteria for stopping iterative processes, highlighting two main types: residual control and increment control. The instructor explains how to implement these criteria effectively in numerical algorithms. Following this, the lecture introduces SciPy, detailing its functionalities for scientific computing, including optimization and root-finding methods. The instructor demonstrates how to use SciPy to find zeros of functions and perform curve fitting. Finally, the lecture explores Matplotlib for data visualization, showcasing how to create various plots, including 2D and 3D representations of functions. The instructor emphasizes the importance of visualizing data to better understand numerical methods and their applications in real-world scenarios.