Linear Recurrences and Applications

This lecture covers the motivation behind two superficial themes, linear recurrences, and the concept of applications between sets. The instructor discusses the importance of defining sets and applications in mathematics, emphasizing the relationship between functions and linear transformations. Various synonyms for applications, such as functions, transformations, and operators, are explored, highlighting their significance in different mathematical contexts. The lecture delves into the notion of linear independence in functions, using examples like sine and cosine functions. Additionally, the concept of operators on functional spaces is introduced, focusing on the derivative operator and its properties. The discussion extends to eigenvalues and eigenvectors in the context of operators, showcasing their relevance in mathematical and physical modeling.