Continuum Mechanics: Fundamentals and Applications

This lecture introduces the concept of Continuum Mechanics, emphasizing the continuum hypothesis and its application in solving engineering and physical science problems. It explains how the hypothesis allows for the effective modeling of bodies as continuous entities, disregarding their molecular nature. The instructor discusses the use of asymptotics and scaling to handle approximations semi-quantitatively, highlighting the importance of understanding the continuum hypothesis as a mathematical modeling tool. The lecture concludes by mentioning the significant research in mechanics conducted at EPFL.