数学专业英语介绍

Taylor formula is very important in the mathematical analysis, it is the basic content in function and widely applied in approximate calculation. Also, the function extreme value theory of power series, etc. Of the basic theory of mathematics is the basic thought of Taylor formula with polynomial function approximation to a known, but the coefficients of polynomial function by a derivative of this approach, and are effectively. Therefore a comprehensive understanding of Taylor formula is particularly important. This paper introduces a pluralistic Taylor formula and the definition, then respectively from the proof of formula, to testify inequality, the median estimate, derivative boundary estimate about the limits of infinity, and the limit value point limit function, approximate calculation, the function equation, the application of Taylor formula aspects of application.Keywords: Taylor formula, More than skin jarno type, Lagrange more, Ms McLaughlin formula

Abstract Taylor's formula is the mathematical analysis of the basic content is very important, it is similar in function estimation and calculation of such widely used. Is also a function of extreme value theory, and many other mathematical theory of power series basis. Taylor formula for the basic idea is to use polynomials to approximate a known function, and the coefficients of the polynomial by the given function to determine the derivative , and this approach gives an effective estimate. Therefore, comprehensive understanding of Taylor's formula is particularly important. This paper introduces the Taylor formula of one dollar and multi-definition, then the proof of the value from the formula, respectively, that inequality, the median estimate derivatives, on industry estimates, demand infinity limit, the median point of the limit function limits, approximation, function equations and so on Taylor formula to do the induction. 【Key words】: Taylor's formula; Peano-type remainder; Lagrange remainder; Maclaurin formula （PS：以上由综合外语团倾情奉献，望楼主满意，O(∩_∩)O~！！）

【纯手工翻译】Mathematics is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. 数学是一个以数量，结构，空间以及变化等概念 为中心的知识体系，同时也是研究它们的学术学科。Benjamin Peirce called it "the science that draws necessary conclusions".本杰明.皮尔斯(Benjamin Peirce )称之为“得出必要结论的科学”Other practitioners of mathematics maintain that mathematics is the science of pattern, and that mathematicians seek out patterns whether found in numbers, space, science, computers, imaginary abstractions, or elsewhere.其他数学专业工作者认为数学是有关于规律的科学，数学家们寻找各种规律，比如数字中的，空间中的，科学中的，计算机中的，抽象概念的等等。 Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.数学家探索很多概念，目的是为了阐述新的猜想 并通过严密的推理演绎来证实它的正确性，这个过程中需要选择合适的公理和定义。希望我的回答对您有帮助~O(∩_∩)O~

这是介绍级别的英文，最好不翻译，如果这种级别的都需要翻译成了中文才能懂，真正进入专业了就没戏了。