什么是微积分？从简单代数到深入分析英文原版 What Is Calculus? 数学科学下载 mobi epub pdf 电子书 2024

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R. Michael Range 著

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发表于2024-11-27

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出版社： World Scientific

ISBN：9789814644488

商品编码：16005744082

出版时间：2015-10-06

页数：372

正文语种：英语

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什么是微积分？从简单代数到深入分析英文原版 What Is Calculus? From Simple Algebra To Deep Analysis

作者：R. Michael Range
Publisher: World Scientific Publishing Co Pte Ltd (2015/10/6)
平装: 372 pages
Language: 英语
ISBN: 981464448X
EAN: 9789814644488
Product Dimensions: 15.2 x 2.1 x 22.9 cm
ASIN: 981464448X

内容简介

This unique book provides a new and well-motivated introduction to calculus and analysis, historically significant fundamental areas of mathematics that are widely used in many disciplines. It begins with familiar elementary high school geometry and algebra, and develops important concepts such as tangents and derivatives without using any advanced tools based on limits and infinite processes that dominate the traditional introductions to the subject. This simple algebraic method is a modern version of an idea that goes back to René Descartes and that has been largely forgotten. Moving beyond algebra, the need for new analytic concepts based on completeness, continuity, and limits becomes clearly visible to the reader while investigating exponential functions.

The author carefully develops the necessary foundations while minimizing the use of technical language. He expertly guides the reader to deep fundamental analysis results, including completeness, key differential equations, definite integrals, Taylor series for standard functions, and the Euler identity. This pioneering book takes the sophisticated reader from simple familiar algebra to the heart of analysis.

Furthermore, it should be of interest as a source of new ideas and as supplementary reading for high school teachers, and for students and instructors of calculus and analysis.

媒体推荐

"It is a well-written and worthwhile addition to the long list of books on calculus. The treatment of derivatives and the basics of real analysis are excellent."
——Professor John P D'Angelo，University of Illinois at Urbana Champaign

"The book can be recommended for interested students as well as for teachers in mathematical analysis."
——Zentralblatt Math

"It certainly would provide excellent corrective revision of calculus for those who have been taught it simplistically. Another attractive feature of the book is its historical element, which includes reference to the algebraic/geometric method of Apollonius for finding tangents etc. This, together with the above-mentioned features, make this book a uniquely imaginative introduction to real analysis alongside a cogent account of the principles, and applications, of differentiation and the Riemann integral."
——MAA

"This alternate presentation of basic calculus can serve as a course text or as a very useful supplement to the more standard introductory calculus courses. The author’s discussions of the motivations for various concepts and the need for more sophisticated tools will be particularly useful to the beginning student. The book would be a valuable addition to high-school and undergraduate mathematics libraries."
——Mathematical Reviews Clippings

作者简介

R.Michael Range is an expert in multidimensional complex analysis. He has written numerous articles for professional journals, and he is the author of a widely known book in the field that was first published in 1986. He has also won a Lester R Ford award of the American Mathematical Association for one of his expository articles.
Besides advanced graduate level courses, he has taught calculus and analysis at all levels over many years. These experiences have led him to search for alternate approaches and simplifications that are reflected in this path-breaking book.

目录

    Prelude to Calculus:
        Introduction
        Tangents to Circles
        Tangents to Parabolas
        Motion with Variable Speed
        Tangents to Graphs of Polynomials
        Rules for Differentiation
        More General Algebraic Functions
        Beyond Algebraic Functions
    The Cast: Functions of a Real Variable:
        Real Numbers
        Functions
        Simple Periodic Functions
        Exponential Functions
        Natural Operations on Functions
        Algebraic Operations and Functions
    Derivatives: How to Measure Change:
        Algebraic Derivatives by Approximation
        Derivatives of Exponential Functions
        Differentiability and Local Linear Approximation
        Properties of Continuous Functions
        Derivatives of Trigonometric Functions
        Simple Differentiation Rules
        Product and Quotient Rules
    Some Applications of Derivatives:
        Exponential Models
        The Inverse Problem and Antiderivatives
        "Explosive Growth" Models
        Acceleration and Motion with Constant Acceleration
        Periodic Motions
        Geometric Properties of Graphs
        An Algorithm for Solving Equations
        Applications to Optimization
        Higher Order Approximations and Taylor Polynomials
    The Definite Integral:
        The Inverse Problem: Construction of Antiderivatives
        The Area Problem
        More Applications of Definite Integrals
        Properties of Definite Integrals
        The Fundamental Theorem of Calculus
        Existence of Definite Integrals
        Reversing the Chain Rule: Substitution
        Reversing the Product Rule: Integration by Parts
        Higher Order Approximations, Part 2: Taylor's Theorem
        Excursion into Complex Numbers and the Euler Identity

什么是微积分？从简单代数到深入分析英文原版 What Is Calculus? 数学科学下载 mobi epub pdf txt 电子书格式