Ebook: Differential Calculus

Professor Avez' approach to Differential Calculus is original, rigorous and lively, and is characterized by his clear and concise discussion of both classical and contemporary topics. The subject is presented in a Banach Space setting, and among the topics covered are vector fields, one-parameter groups of diffeomorphisms, the Morse-Palais Lemma, and differentiable submanifolds. There is also an investigation of applications to differential equations and the calculus of variables. This material is based on courses given by the author at the Universite Pierre et Marie Curie, and it is presented in such a way as to encourage the reader to pursue the subject in greater depth. To support this, an extensive bibliography has been included, and reference is made to this throughout the text. Like the original French edition, this book will be extremely useful for senior first-degree and graduate students studying analysis.