Mathematical Analysis: Functions of Several Real Variables and Applications
暫譯: 數學分析：多變數實函數及其應用
Fusco, Nicola, Marcellini, Paolo, Sbordone, Carlo
- 出版商: Springer
- 出版日期: 2023-01-02
- 售價: $2,900
- 貴賓價: 9.5 折 $2,755
- 語言: 英文
- 裝訂: Quality Paper - also called trade paper
- ISBN: 303104150X
- ISBN-13: 9783031041501
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商品描述
This work is a textbook on Mathematical Analysis written by expert lecturers in the field. This textbook, other than the classical differentiation and integration tools for functions of several real variables, metric spaces, ordinary differential equations, implicit function and so on, also provides opportunities to go deeper into certain topics: among them, the Ascoli-Arzelà theorem, the regularity of convex functions in R n, L p spaces and absolutely continuous functions, all topics that are paramount in modern Mathematical Analysis. Other instances include the Weierstrass theorem on polynomial approximation of continuous functions or Peano's existence theorem (typically only existence, without uniqueness) for nonlinear ODEs and systems under general assumptions.
The content is discussed in an elementary way and, at a successive stage, some topics are examined from several, more penetrating, angles. The agile organization of the subject matter helps instructors to effortlessly determine which parts to present during lectures and where to stop. The authors believe that any textbook can contribute to the success of a lecture course only to a point, and the choices made by lecturers are decisive in this respect.
The book is addressed to graduate or undergraduate honors students in Mathematics, Physics, Astronomy, Computer Science, Statistics and Probability, attending Mathematical Analysis courses at the Faculties of Science, Engineering, Economics and Architecture.
商品描述(中文翻譯)
這本書是由該領域的專家講師撰寫的《數學分析》教科書。這本教科書除了涵蓋多個實數變數的經典微分和積分工具、度量空間、常微分方程、隱函數等內容外，還提供了深入探討某些主題的機會：其中包括阿斯科利-阿爾澤拉定理、R^n 中凸函數的正則性、L^p 空間和絕對連續函數，這些主題在現代數學分析中至關重要。其他例子包括維爾斯特拉斯定理（Weierstrass theorem）關於連續函數的多項式逼近或佩阿諾存在定理（Peano's existence theorem）（通常僅存在性，無唯一性）針對一般假設下的非線性常微分方程及系統。
內容以基礎的方式進行討論，並在後續階段從多個更深入的角度檢視某些主題。靈活的主題組織幫助講師輕鬆決定在講座中應該呈現哪些部分以及何時停止。作者認為，任何教科書對於講座課程的成功貢獻都是有限的，講師所做的選擇在這方面是決定性的。
本書針對數學、物理、天文學、計算機科學、統計學和概率論的研究生或本科榮譽學生，適合參加科學、工程、經濟和建築學院的數學分析課程。
作者簡介
Nicola Fusco is Full Professor of Mathematical Analysis at University of Naples "Federico II" and member of Accademia dei Lincei. He was awarded the 1994 Caccioppoli Prize of the Italian Mathematical Union (UMI). His research revolves around calculus of variations, regularity theory for partial differential equations, symmetrization problems and isoperimetric inequalities. He was visiting professor at Australian National University, Canberra; Carnegie Mellon University, Pittsburgh; Heriot-Watt University, Edinburgh; University of Oxford; Technische Universität, München and University of Jyväskylä.
Paolo Marcellini is Emeritus Professor of Mathematical Analysis at University of Florence. His research interests are in calculus of variations and regularity theory for partial differential equations. He was Dean of the Faculty of Sciences at University of Florence and President of GNAMPA (National Group for Mathematical Analysis, Probability and their Applications). He was visiting professor at University of California, Berkeley; Collège de France, Paris; Institute for Advanced Study, Princeton; Center for Nonlinear Analysis, Carnegie Mellon University, Pittsburgh; Mathematical Institute, University of Oxford; University of Texas, Austin and Institut Mittag-Leffler, Stockholm.
Carlo Sbordone is Emeritus Professor of Mathematical Analysis at University of Naples "Federico II", member of Accademia dei Lincei and was President of the Italian Mathematical Union (UMI). His research interests regard calculus of variations, Sobolev maps and function spaces. He was visiting professor at Scuola Normale Superiore in Pisa; Collège de France, Paris; Institut für Mathematik, Universität Zürich; Center for Nonlinear Analysis, Carnegie Mellon University, Pittsburgh; University of California, Berkeley; Mathematical Institute, University of Oxford and University of Helsinki.
作者簡介(中文翻譯)
尼科拉·福斯科是那不勒斯「費德里科二世」大學的數學分析全職教授，也是林切伊學院的成員。他於1994年獲得意大利數學聯盟（UMI）的卡喬波利獎。其研究領域包括變分法、偏微分方程的正則性理論、對稱化問題及等周不等式。他曾擔任訪問教授於澳大利亞國立大學（堪培拉）、卡內基梅隆大學（匹茲堡）、赫瑞瓦特大學（愛丁堡）、牛津大學、慕尼黑工業大學及於尤維斯基拉大學。
保羅·馬切里尼是佛羅倫斯大學的名譽數學分析教授。他的研究興趣集中於變分法及偏微分方程的正則性理論。他曾擔任佛羅倫斯大學科學院院長及全國數學分析、概率及其應用小組（GNAMPA）主席。他曾擔任訪問教授於加州大學伯克利分校、法國高等學院（巴黎）、普林斯頓高等研究院、卡內基梅隆大學非線性分析中心、牛津大學數學研究所、德克薩斯大學奧斯汀分校及斯德哥爾摩米塔格-萊夫勒研究所。
卡洛·斯博爾多尼是那不勒斯「費德里科二世」大學的名譽數學分析教授，林切伊學院成員，並曾擔任意大利數學聯盟（UMI）主席。他的研究興趣包括變分法、索博列夫映射及函數空間。他曾擔任訪問教授於比薩高等師範學校、法國高等學院（巴黎）、蘇黎世大學數學研究所、卡內基梅隆大學非線性分析中心、加州大學伯克利分校、牛津大學數學研究所及赫爾辛基大學。
