Numerical Analysis: Introduction to Computational Methods

This lecture introduces the fundamentals of numerical analysis and computational mathematics, focusing on the use of Python for mathematical problem-solving. It covers essential topics such as number representation, non-linear equations, polynomial approximation through interpolation and least squares, numerical differentiation and integration, and direct and iterative methods for solving linear systems. The instructor emphasizes the importance of understanding algorithms for fixed-point problems and function roots, as well as the Fourier transform and ordinary differential equations. The course also highlights the significance of practical exercises using Jupyter notebooks, where students will apply theoretical concepts to real-world problems. By the end of the lecture, students will have a solid foundation in numerical methods and their applications in computational mathematics, preparing them for more advanced topics in the field.