Introduction to Analysis
暫譯: 分析導論

Dunn, Corey M.

Introduction to Analysis
  • 出版商: CRC
  • 出版日期: 2023-01-21
  • 售價: $2,070
  • 貴賓價: 9.5 折 $1,967
  • 語言: 英文
  • 頁數: 418
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 103247677X
  • ISBN-13: 9781032476773

    • 海外代購書籍(需單獨結帳)

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商品描述

Introduction to Analysis is an ideal text for a one semester course on analysis. The book covers standard material on the real numbers, sequences, continuity, differentiation, and series, and includes an introduction to proof. The author has endeavored to write this book entirely from the student's perspective: there is enough rigor to challenge even the best students in the class, but also enough explanation and detail to meet the needs of a struggling student.

From the Author to the student:

"I vividly recall sitting in an Analysis class and asking myself, 'What is all of this for?' or 'I don't have any idea what's going on.' This book is designed to help the student who finds themselves asking the same sorts of questions, but will also challenge the brightest students."

  • Chapter 1 is a basic introduction to logic and proofs.

  • Informal summaries of the idea of proof provided before each result, and before a solution to a practice problem.

  • Every chapter begins with a short summary, followed by a brief abstract of each section. Each section ends with a concise and referenced summary of the material which is designed to give the student a "big picture" idea of each section.

  • There is a brief and non-technical summary of the goals of a proof or solution for each of the results and practice problems in this book, which are clearly marked as "Idea of proof," or as "Methodology", followed by a clearly marked formal proof or solution.

  • Many references to previous definitions and results.

  • A "Troubleshooting Guide" appears at the end of each chapter that answers common questions.

    • 商品描述(中文翻譯)

    《分析導論》是適合一學期分析課程的理想教材。這本書涵蓋了實數、數列、連續性、微分和級數等標準內容，並包括對證明的介紹。作者努力從學生的角度撰寫這本書：內容具有足夠的嚴謹性以挑戰班上最優秀的學生，但也提供了足夠的解釋和細節以滿足有困難的學生的需求。

    從作者對學生的寄語：

    「我清楚地記得坐在分析課上，心中問自己，‘這一切是為了什麼？’或‘我完全不知道發生了什麼。’這本書旨在幫助那些也在問類似問題的學生，同時也會挑戰最聰明的學生。」

    - 第一章是邏輯和證明的基本介紹。
    - 在每個結果之前，以及在練習問題的解答之前，提供非正式的證明概念摘要。
    - 每一章以簡短的摘要開始，接著是每個部分的簡要概述。每個部分結尾都有簡潔且有參考的材料摘要，旨在讓學生對每個部分有一個「大局」的理解。
    - 本書中每個結果和練習問題都有簡短且非技術性的證明或解決方案目標摘要，這些摘要明確標記為「證明的概念」或「方法論」，隨後是明確標記的正式證明或解決方案。
    - 許多對先前定義和結果的參考。
    - 每章結尾都有一個「故障排除指南」，回答常見問題。

    作者簡介

    Dr. Corey M. Dunn is a Professor of mathematics at California State University, San Bernardino. His interests include Differential Geometry, Geometric Analysis, Linear Algebra, and involving undergraduates in his research. He received his PhD from the University of Oregon in 2006.

    作者簡介(中文翻譯)

    科里·M·鄧恩博士是加州州立大學聖貝納迪諾分校的數學教授。他的研究興趣包括微分幾何、幾何分析、線性代數，以及讓本科生參與他的研究。他於2006年在俄勒岡大學獲得博士學位。

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