雷恩·第斯卡兹发现一种用代数方法研究几何问题的方法，称为解析几何学。
Rene Descartes found a way to study geometric problems by methods of algebra called analytic geometry.
数量和空间在解析几何，微分几何和代数几何中都发挥作用。
Quantity and space both play a role in analytic geometry, differential geometry, and algebraic geometry.
解析几何是高中数学的重要部分，它将代数与几何有机地结合在一起。
Analytic geometry is the very important part in senior high school, it combine algebra with geometry.
课程内容包括常微分方程、空间解析几何与向量代数、多元函数微分学、多元函数积分学和无穷级数等几大板块。
This course consists of several major parts such as ordinary differential equation vectors and analytic geometry derivatives integration and series.
这些结果不仅扩大了解析能控性所适用的区域，更重要的是可以用于更一般的具有无穷维控制李代数的量子力学控制系统。
These results enlarge the domain of analytic controllability, and more essentially, they are applicable to more general quantum mechanical systems with infinite dimensional control Lie algebras.
课程内容包括空间解析几何与向量代数、多元函数微分学、多元函数积分学和无穷级数等几大板块。
This course consists of several major parts such as vectors and analytic geometry derivatives integration and series.
其结构对称优美，在中学代数、三角、平面几何、平面解析几何中都有广泛应用。
Cauchy's inequality is characterized by its structurally symmetrical grace, which finds wide application in middle school algebra, geometory, plane geometory and analytic plane geometry.
解析的使用，属于，或可能属于包括代数和积分在内的方法学。
Using, subjected to, or capable of being subjected to a methodology involving algebra and calculus.
本课程主要内容包括：向量代数与空间解析几何、多元函数微积分、无穷级数等。
This course mainly includes: vector algebra and analytic geometry in space, multivariable calculus and infinite series.
对多孔介质快速干燥过程的传热与传质耦合方程组导出了两套代数显式解析特解。
Two algebraically explicit analytical solutions of the governing equation set for the coupled heat and mass transfer process of rapid drying in porous media are derived.
用倍角公式可将该三角函数方程转化成一个四次代数方程，然后用求根公式直接求出解析解。
Double Angle formula can transform the circular function equation to a biquadratic algebraic equation, and the analysis solution can be solved by extract equation directly.
结果在拉格朗日的视野中，微积分是关于函数的一种代数形式演算，而函数是由一个解析表达式给出并且均可展成幂级数。
Results in perspective of Lagrange, the calculus was a kind of algebraic calculation of the function given by an analytical expression, which could be developed into power series.
该文讨论了单位圆盘上解析函数的加权代数ap中的闭理想问题，并且利用加权系给出了一个闭理想成为AP中的补子空间的判断准则。
In this paper, we deal with the closed ideals in the weighted algebras of analytic functions on the unit disc, and give a criterion to decide whether a closed ideal is complemented subspace in ap.
将代数学中的幂零元概念作适当的解析学上的推广，可以绘出一个很满意回答。
A very satisfactory answer can be given in terms of the appropriate analytic generalization of the algebraic concept of nilpotence.
你需要代数，和一些理解解析几何的知识。
You need that. And a basic understanding of Cartesian geometry, too.
这一理论是几何学、代数学、复分析、微分方程解析理论交叉的产物，体现了数学的统一性。
The theory of automorphic function is the result of the intersection of geometry, algebra, complex analysis and differential equation, which manifest the unity of mathematics.
对气液两相非定常一元流动方程组导出了两套代数显式解析解。
Two sets of algebraically explicit analytical solution are derived for the partial differential equation set describing the one dimensional unsteady gas-liquid two phase flow.
文化代数和解析运算中的清晰性远远胜过任何缺点。
Its clarity in algebraic and analytical operations far outweighs any drawbacks.
对多钉连接件钉传载荷的计算问题提出了一个解析分析方法，推导了求解钉载的线性代数方程组并给出了若干算例。
A new analytical method of pin load computation for joints with multi-rivets or multi-bolts is presented by means of mathematical theory of elasticity and classical principle of structural mechanics.
本文所要进行的研究是对于当代数字动画前沿技术的解析。
This study to be undertaken is the cutting edge of contemporary digital animation technology analysis.
热声学是一门较新的学科，其理论与实验研究尚在蓬勃发展中，已知的代数显式解析解目前还很少。
Besides theoretical value, it can also be the benchmark solution to promote the development of computational thermoacoustics.
热声学是一门较新的学科，其理论与实验研究尚在蓬勃发展中，已知的代数显式解析解目前还很少。
Besides theoretical value, it can also be the benchmark solution to promote the development of computational thermoacoustics.
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