Treatise on Analysis
Treatise on Analysis is a translation by Ian G. Macdonald of the nine-volume work Éléments d'analyse on mathematical analysis by Jean Dieudonné, and is an expansion of his textbook Foundations of Modern Analysis. It is a successor to the various Cours d'Analyse by Augustin-Louis Cauchy, Camille Jordan, and Édouard Goursat.
Contents and publication history
Volume I
The first volume was originally a stand-alone graduate textbook with a different title. It was first written in English and later translated into French, unlike the other volumes which were first written in French. It has been republished several times and is much more common than the later volumes of the series.The contents include
- Chapter I: Sets
- Chapter II Real numbers
- Chapter III Metric spaces
- Chapter IV The real line
- Chapter V Normed spaces
- Chapter VI Hilbert spaces
- Chapter VII Spaces of continuous functions
- Chapter VIII Differential calculus
- Chapter IX Analytic functions
- Chapter X Existence theorems
- Chapter XI Elementary spectral theory
Volume II
The second volume includes- Chapter XII Topology and topological algebra
- Chapter XIII Integration
- Chapter XIV Integration in locally compact groups
- Chapter XV Normed algebras and spectral theory
Volume III
The third volume includes chapter XVI on differential manifolds and chapter XVII on distributions and differential operators.Volume IV
The fourth volume includes- Chapter XVIII Differential systems
- Chapter XIX Lie groups
- Chapter XX Riemannian geometry