Exercises in Analysis: Part 2: Nonlinear Analysis (Paperback)
暫譯: 分析學習題：第 2 部分：非線性分析 (平裝本)

Gasiński, Leszek, Papageorgiou, Nikolaos S.

Exercises in Analysis: Part 2: Nonlinear Analysis (Paperback)

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商品描述

This second of two Exercises in Analysis volumes covers problems in five core topics of mathematical analysis: Function Spaces, Nonlinear and Multivalued Maps, Smooth and Nonsmooth Calculus, Degree Theory and Fixed Point Theory, and Variational and Topological Methods. Each of five topics corresponds to a different chapter with inclusion of the basic theory and accompanying main definitions and results, followed by suitable comments and remarks for better understanding of the material. Exercises/problems are presented for each topic, with solutions available at the end of each chapter. The entire collection of exercises offers a balanced and useful picture for the application surrounding each topic.
This nearly encyclopedic coverage of exercises in mathematical analysis is the first of its kind and is accessible to a wide readership. Graduate students will find the collection of problems valuable in preparation for their preliminary or qualifying exams as well as for testing their deeper understanding of the material. Exercises are denoted by degree of difficulty. Instructors teaching courses that include one or all of the above-mentioned topics will find the exercises of great help in course preparation. Researchers in analysis may find this Work useful as a summary of analytic theories published in one accessible volume.

商品描述(中文翻譯)

這套《Analysis Exercises》共分為兩冊，本書為第二冊，涵蓋數學分析五個核心主題的問題：函數空間（Function Spaces）、非線性與多值映射（Nonlinear and Multivalued Maps）、光滑與非光滑微積分（Smooth and Nonsmooth Calculus）、度理論與不動點理論（Degree Theory and Fixed Point Theory），以及變分與拓撲方法（Variational and Topological Methods）。這五個主題各自對應一個章節，內容包括基礎理論，以及相關的重要定義與結果；接著則提供適當的評論與說明，以協助讀者更加理解教材內容。每個主題均附有習題與問題，並在各章末提供解答。整套習題完整而均衡地呈現了各主題的應用內容，具有高度實用價值。

本書幾乎以百科全書般的廣度涵蓋數學分析習題，在同類著作中尚屬首創，且適合廣泛讀者閱讀。研究生可藉由這套問題集準備預備考試或資格考試，也能用來檢驗自己對教材內容的深入理解。習題皆依難度分級。對於教授課程中涵蓋上述部分或全部主題的教師而言，這些習題將對課程準備提供很大幫助。從事分析學研究的研究人員，也能將本書視為一份實用的參考資料，在同一本易於閱讀的著作中掌握各種分析理論的概要。

作者簡介

Leszek Gasińksi is the Chair of Optimization and Control Theory in the Institute of Computer Science at Jagiellonian University in Krakow, Poland. He is the co-author, along with Nikolaos S. Papageorgiou, of "Nonlinear Analysis" (CRC 2005) and "Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems" (CRC 2006). Nikolaos S. Papageorgiou is a Professor of Mathematics in the School of Applied Mathematical and Physical Sciences at National Technical University in Athens, Greece. He is the co-author, along with Leszek Gasińksi, of "Nonlinear Analysis" (CRC 2005) and "Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems" (CRC 2006).

作者簡介(中文翻譯)

Leszek Gasińksi 是波蘭克拉科夫 Jagiellonian University 電腦科學研究所的最佳化與控制理論講座主任。他與 Nikolaos S. Papageorgiou 合著《Nonlinear Analysis》（CRC，2005）及《Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems》（CRC，2006）。

Nikolaos S. Papageorgiou 是希臘雅典 National Technical University 應用數學與物理科學學院的數學教授。他與 Leszek Gasińksi 合著《Nonlinear Analysis》（CRC，2005）及《Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems》（CRC，2006）。

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