Numerical Integration: Introduction to SciPy and Matplotlib

This lecture introduces numerical integration techniques using Python's SciPy library. The instructor discusses the importance of numerical methods for calculating integrals of continuous functions over specified intervals. The lecture covers advanced representations in 2D and 3D using Matplotlib, including parametric curves and contour plots. The instructor explains how to visualize functions and create figures with multiple subplots. The lecture also delves into specific numerical methods such as the midpoint rule and Riemann sums for approximating integrals. The instructor emphasizes the significance of partitioning intervals and the concept of the partition's fineness in achieving accurate numerical results. Additionally, the lecture highlights the use of SciPy's optimization functions, including Newton's method and the secant method, for finding roots of equations. The session concludes with practical examples and coding demonstrations to illustrate the application of these numerical techniques in Python, providing students with a solid foundation for further exploration in numerical analysis and computational mathematics.