On the Fundamental Theorem of Algebra

In the paper, it is shown how, by using the minimal means and without introducing complex numbers, one can prove the fundamental theorem of algebra for real polynomials. The fundamental theorem for polynomials with complex coefficients is an immediate corollary of the theorem mentioned.     

微积分学中中值定理的统一证明

由一个定理的结论,给出Lagrange中值定理,Cauchy中值定理,积分中值定理和Taylor中值定理的统一证明及一个计算待定型极限的方法.     

Mathematical features of the Calculus

The fundamental theorems of the calculus describe the relationships between derivatives and integrals of functions. The value of any function at a particular location is the definite derivative of its integral and the definite integral of its derivative. Thus, any value is the magnitude of the slope of the tangent of its integral at that position, and any two subtracted values are the area under its derivative. The slope formula of secant lines actually is the mean value theorem for the derivative function in addition to representing the well-known Fermat definition of the derivative. The sine and other functions are discussed.     

Complex eigenvalues before the Fundamental Theorem of Algebra

We present an elementary proof of the existence of an eigenvalue for an endomorphism of a complex vector space and we derive the Fundamental Theorem of Algebra as a corollary of this existence. We also present new proofs for the corresponding results for endomorphisms of real vector spaces.     

Fundamental Theorem of Calculus

A simple but rigorous proof of the Fundamental Theorem of Calculus is given in geometric calculus, after the basis for this theory in geometric algebra has been laid out. Various classical examples of this theorem, such as the Green’s and Stokes’ theorem are discussed, as well as the theory of monogenic functions which generalizes analytic functions of a complex variable to higher dimensions.     

关于线性规划基本定理的一点注记

本就线性规划基本定理的证明方法及过程提出一点修改意见。     

代数体函数第二基本定理的一个推广

利用亚纯函数的Nevanlinna值分布理论,研究代数体函数第二基本定理的扩展形式,将该定理推广到两列互异且次数不超过d的多项式的情况,拓展了熊庆来、MillouX H等人的结果.     

代数体函数第二基本定理的推广

把代数体函数第二基本定理推广到了p个次数不超过d的多项式的情形,得到了类似于亚纯函数理论中Dufresnoy J推出的结果.     

非时齐马氏过程的耦合基本定理

本文将耦合方法应用于非时齐马氏过程,推广了时齐情形的耦合基本定理,为后续研究非时齐马氏过程的耦合提供了理论基础.     

弱HOPF代数的中心构建与基本定理

范畴D(H)^M与范畴H^M的中心是同构的，并将Hopf模的结构定理推广到弱Hopf代数上。     

代数基本定理的复分析证法

从复分析的角度总结了代数基本定理的证法.     

The First Fundamental Theorem of Calculus

<正>The Fundamental Theorem of Calculus establishes a connection between the two branches of calculus:differential calculus and integral calculus.Integral calculus arose from the area problem.Differential calculus arose from the tangent problem.Two parts seem unrelated.But the great Mathematician Newton realized that differentiation and integration are inverse processes.So the Fundamental Theorem of Calculus gives the pre-     

概率逻辑学基本定理在多值命题逻辑系统中的推广

通过引入概率测度空间,在n值Lukasiewicz命题逻辑系统中提出了满足Kolmogorov公理的命题公式的概率;证明了概率逻辑学基本定理,并将概率逻辑学基本定理推广到了更一般的形式,改进了对推理结论的不可靠度上界的估计;将概率逻辑学的基本方法引入计量逻辑学,建立了更一般的逻辑度量空间;通过概率逻辑学基本定理,证明了逻辑度量空间中概率MP,HS规则,它是真度MP,HS规则的推广.     

微积分基本定理的一个证明和理解

Newton- Leibniz公式 (微积分基本定理 )在微积分学中占有极为重要的地位 ,它第一次在定积分(和式的极限 )计算和微分的逆运算 (求导数的原函数过程 )这两个似乎毫不相干的概念之间发现了内在联系 ,并且建立了精确的数学关系 ,从根本上超越了自公元前三世纪至公元十七世纪中叶以来几乎一直沿用的阿基米德 (Archimedes,2 87- 2 1 2 B.C.)时代的“分割求和”的方法 (method ofexhaustion) [6,2 - 3] ,从而把定积分的计算极为简便地转化为求原函数的运算 ,因此 ,微积分基本定理在微积分学的理论发展和实际应用中都有极为重大的贡献和意义 .值…     

关于变上限函数求导的教学实例

从变上限函数的基本概念以及求导公式出发,通过几组教学实例,阐述对简单变上限函数、复合变：上（下）限函数、以及需要作变量替换才能求导的变上限函数求导的方法．     

Lagrange、Cauchy、积分中值定理与Taylor公式的统一证明

通过一个定理的结论,给出L agrange、C auchy、积分中值定理和T ay lor公式的统一证明,同时得出计算不定型极限的L′Hosp ita l法则的推广定理.     

剖析"最少的微积分"

对《微积分快餐》中主要概念(相对误差)、定理(基本定理)和应用(面积)做了剖析.     

积分中值定理的改进

本改进了(第一)积分中值定理的结论，证明了定理中的中间值ζ属于开区间(α，b)．在将定理条件适当加强后，(第一)积分中值定理可由微分中值定理证得，揭示了它们之间的内在联系。     

On the Fundamental Theorem of Geometric Algebra Over SF-Rings

For free modules over FS-rings, perspective maps are studied and thus the first ring version of the fundamental theorem of geometric algebra about the representation of perspective maps by the linear functions is proved. The results were announced in Kvirikashvili and Lashkhi (2005 Kvirikashvili , T. G. , Lashkhi , A. A. ( 2005 ). Perspective maps for modules . Math. Notes 7 ( 6 ): 876 – 877 . [Google Scholar]).     

Units of measurement

It is shown that the symbols for the fundamental units of mechanics, namely length, time and mass, are capable of a meaningful interpretation as positive real parameters. Then a suitable parameter domain allows one to take the derived units into account. The formal manipulations usually carried out with symbols of physical quantities, involving real coefficients and units of different kinds affected by rational exponents, are consistent with that interpretation. The note is expected to serve as a well-motivated introduction to a deeper study of dimensional analysis.