The lesson begins with an in-depth exploration of the Taylor Series, a powerful mathematical tool for approximating functions through a series expansion. Participants will learn how to express a function as an infinite sum of its derivatives and evaluate the convergence properties of the series. The participant will work on real-world governing equations such as heat-transfer, wave-equation and descretize them numerically in different orders with help of taylor series.

In this lesson, participants will embark on a comprehensive exploration of the classification of Partial Differential Equations (PDEs) based on their types: Parabolic, Elliptic, and Hyperbolic. By the end of this lesson, participants will have a clear conceptual grasp of the classifications of PDEs, setting the stage for further exploration into numerical methods and advanced topics in Computational Fluid Dynamics.

This lesson introduces the concept of Finite Difference Formulation, a fundamental technique in numerical analysis. Participants will explore how finite differences are applied to approximate derivatives and solve differential equations

This lesson focuses on Stability Analysis, a critical aspect in numerical methods, and specifically explores the Von Neumann method. Participants will delve into the principles of stability analysis and learn how the Von Neumann method is applied to assess the stability of numerical schemes in solving partial differential equations.

This lesson provides a comprehensive introduction to the Finite Volume Method (FVM), a widely used numerical technique for solving partial differential equations (PDEs). Participants will gain insights into the principles of the FVM, its applications, and its role in simulating fluid flow and heat transfer problems.