Nonlinear Equation Resolution: Introduction to Bisection Method

This lecture focuses on the resolution of nonlinear equations, specifically introducing the bisection method. The instructor begins by discussing the importance of finding roots of functions within a specified interval. The lecture highlights the use of the Bolzano theorem, which states that if a continuous function changes signs over an interval, there exists at least one root within that interval. The instructor illustrates the bisection method, which involves dividing the interval into two halves and determining in which half the root lies, iteratively narrowing down the interval until a sufficiently accurate approximation of the root is found. The lecture also covers practical examples using Python and the NumPy library to demonstrate the implementation of the bisection method. Visual aids, including plots generated with Matplotlib, are used to enhance understanding. The session concludes with a discussion on the significance of numerical methods in solving equations that cannot be solved analytically, emphasizing the relevance of computational tools in modern mathematics.