ABSTRACT
This chapter presents the concept of differentiability of vector–valued functions, which is crucial for studying the theory of ordinary and partial differential equations, that will be presented in the following chapters of this book, and in particular in Chapters 4, 5 and 13. The notion of critical point, and the related definitions of gradient vector, Jacobian and Hessian matrices, and Lagrange multipliers, are recalled. The important Implicit function theorem is also stated and proved.
