商品簡介
本書對各種類型的積分進行了系統闡述，不僅證明了每種積分的基本性質，指出其異同點，還闡釋了它們的產生背景與應用場景，並融入了豐富的歷史資料。本書適合對各種類型的積分感興趣的高年級本科生、研究生、高校教師以及數學研究人員閱讀參考。The derivative and the integral are the fundamental notions of calculus. Though there is essentially only one derivative, there is a variety of integrals, developed over the years for a variety of purposes, and this book describes them. No other single source treats all of the integrals of Cauchy, Riemann, Riemann-Stieltjes, Lebesgue, Lebesgue-Stieltjes, Henstock-Kurzweil, Weiner, and Feynman. The basic properties of each are proved, their similarities and differences are pointed out, and the reason for their existence and their uses are given. There is plentiful historical information. The audience for the book is advanced undergraduate mathematics majors, graduate students, and faculty members. Even experienced faculty members are unlikely to be aware of all of the integrals in the Garden ofIntegrals and the book provides an opportunity to see them and appreciate their richness. Professor Burk's clear and well-motivatedexposition makes this book a joy to read. The book can serve as a reference, as a supplement to courses that include the theory of integration, and as a source of exercises in analysis. There is no other book like it.
