什麼是微積分?從簡單代數到深入分析 英文原版 What Is Calculus? 數學科學 epub 下載 mobi 下載 pdf 下載 txt 電子書 下載 2025
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什麼是微積分?從簡單代數到深入分析 英文原版 What Is Calculus? 數學科學 epub 下載 mobi 下載 pdf 下載 txt 電子書 下載 2025
什麼是微積分?從簡單代數到深入分析 英文原版 What Is Calculus? 數學科學 pdf epub mobi txt 電子書 下載
具體描述
什麼是微積分?從簡單代數到深入分析 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) 平裝: 372 pages Language: 英語 ISBN: 981464448X EAN: 9789814644488 Product Dimensions: 15.2 x 2.1 x 22.9 cm ASIN: 981464448X
內容簡介
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.
媒體推薦
"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
作者簡介
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.
目錄
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