Explore the unique programming language Modelica in this 42-minute conference talk from Strange Loop. Learn how Modelica incorporates mathematical constructs and physical interactions to create graphical, component-oriented models of complex physical systems. Discover the wide-ranging industrial applications of Modelica, from automotive to aerospace. Delve into the fascinating algorithms used to transform hybrid differential-algebraic equations from Modelica models into imperative simulation code. Gain insights into the compilation process, which differs significantly from typical programming languages, and observe similarities to functional reactive programming extended to continuous behavior. Cover topics including the history of computational modeling, mathematical foundations, Modelica's key features like connectors and inheritance, industrial applications, equation transformation, matrix operations, and equation sorting techniques.