This title is printed to order. This book may have been self-published. If so, we cannot guarantee the quality of the content. In the main most books will have gone through the editing process however some may not. We therefore suggest that you be aware of this before ordering this book. If in doubt check either the author or publisher’s details as we are unable to accept any returns unless they are faulty. Please contact us if you have any questions.
The extraordinarily rapid advances made in mathematics since World War II have resulted in analysis becoming an enormous organism spread- ing in all directions. Gone for good surely are the days of the great French courses of analysis which embodied the whole of the ana- lytical knowledge of the times in three volumes-as the classical work of Camille Jordan. Perhaps that is why present-day textbooks of anal- ysis are disproportionately modest relative to the present state of the art. More: they have retreated to the state before Jordan and Goursat. In recent years the scene has been changing rapidly: Jean Dieudon- ne is offering us his monumentel Elements d'Analyse (10 volumes) written in the spirit of the great French Course d'Analyse. To the best of my knowledge, the present book is the only one of its size: starting from scratch-from rational numbers, to be precise-it goes on to the theory of distributions, direct integrals, analysis on com- plex manifolds, Kahler manifolds, the theory of sheaves and vector bun- dles, etc. My objective has been to show the young reader the beauty and wealth of the unsual world of modern mathematical analysis and to show that it has its roots in the great mathematics of the 19th century and mathematical physics. I do know that the young mind eagerly drinks in beautiful and difficult things, rejoicing in the fact that the world is great and teeming with adventure.
