Introduction to Analysis

Dunn, Corey M.

Introduction to Analysis
  • 出版商: CRC
  • 出版日期: 2023-01-21
  • 售價: $2,180
  • 貴賓價: 9.5 折 $2,071
  • 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》是一本適合一學期分析課程的理想教材。本書涵蓋了關於實數、數列、連續性、微分和級數的標準內容，並包含了對證明的介紹。作者致力於從學生的角度撰寫本書：內容足夠嚴謹，可以挑戰課堂上最優秀的學生，同時也提供了足夠的解釋和細節，以滿足有困難的學生的需求。

    作者對學生的話：
    「我清楚地記得坐在分析課堂上，問自己『這一切是為了什麼？』或者『我完全不知道發生了什麼』。這本書旨在幫助那些問出同樣問題的學生，同時也會挑戰最聰明的學生。」

    本書的特點包括：
    1. 第一章是關於邏輯和證明的基本介紹。
    2. 在每個結果和練習問題的解答之前，提供了對證明概念的非正式摘要。
    3. 每章開始時都有一個簡短的摘要，接著是每個小節的簡要摘要。每個小節結束時都有一個簡潔且有參考文獻的摘要，旨在給學生提供每個小節的整體概念。
    4. 對於本書中的每個結果和練習問題，都有一個簡短且非技術性的目標摘要，清楚標記為「證明概念」或「方法」，接著是清楚標記的正式證明或解答。
    5. 多次引用先前的定義和結果。
    6. 每章末尾都有一個「疑難排解指南」，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)

    Dr. Corey M. Dunn 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年從俄勒岡大學獲得博士學位。

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