Fluid Dynamics Fundamentals

This lecture focuses on deriving the fundamental equations of fluid dynamics in a differential form, specifically discussing differential conservation laws and stress-strain relationships. The instructor explains the process of converting Lagrangian physical laws into Eulerian laws for extended control volumes, leading to the development of the Navier-Stokes equations. Additionally, key concepts such as mass conservation, Newton's second law, Einstein notation, the Gauss theorem, and the outer product of vectors are discussed to provide a comprehensive understanding of fluid mechanics principles.