总之，就是用几何方法或是在曲面上建立二重积分。
Use geometry or you need to set up for double integral of a surface.
就像做功一样，当计算这线积分时，通常不这样用几何方法来做。
Just as we do work, when we compute this line integral, usually we don't do it geometrically like this.
就是做F·dS或是F·ndS的二重积分，为了能建立积分，需要用到曲面的几何性质，这与该曲面的类型有关。
Double integral of F.dS or F.ndS if you want, and to set this up, of course, I need to use the geometry of the surface depending on what the surface is.
几何和量子场论课程是用泛函积分的语言对微扰量子场论的严谨的介绍，主要针对数学家设计。
Geometry and quantum field theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals.
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.
几何，三角，微分，积分，圆锥曲线，微分方程，和他们的多维和多元——这些都有重要的应用。
Geometry, trigonometry, differentiation, integration, conic sections, differential equations, and their multidimensional and multivariate versions - these all have important applications.
将镜像变换、平移、旋转、缩放等几何变换手段与积分投影等方法相结合来增加虚拟样本。
It increases the virtual samples by the method of combining mirror transform, integral map and geometric transform such as shifting, rotating and zooming.
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.
微分几何包含这样的概念：纤维束和流形上的微积分，特别是矢量与张量微积分。
Within differential geometry are the concepts of fiber bundles and calculus on manifolds, in particular, vector and tensor calculus.
本文给出了圆面探测器对圆面源的几何因子的一元积分形式。
The solid angle for a disc source parallel to a disc detector has been determined using a one dimension integral.
本文把有限个数的调和、几何、算术加权平均值不等式推广到无穷多个数的形式和广义积分的形式。
In this paper, we prove the infinite weighted mean inequalities. Furthermore, some results are established in infinite integral case.
经过他们的工作，微积分不再是古希腊几何的附庸和延展。
After their work, the calculus was no longer an appendage and extension of Greek geometry.
高余维子流形是仿射微分几何中难于处理的问题，鉴此，主要研究在余维数为2的情况下，中心仿射微分几何的积分公式。
Multi-condimensional submanifold is a difficultly problem in the study, and this paper investigates the integration formula of centroaffine differential geometry of codimension 2.
他还爱上了几何学以及几何学中的定理证明，到16岁时就已经精通微积分了。
He fell in love with geometry and its clear proofs, and mastered calculus at age 16.
证明了规范场不仅沿入射电子在复连通区域运动路径的积分，而且还可沿入射标量或其他旋量粒子之一在复连通区域的运动路径积分，各自都将贡献一几何相因子。
It is justified that the integral of the gauge potential along path of not only electron but also scalar particle or spinor particle will contribute a geometric phase factor.
对求解过程中的关键问题进行了全面阐述，如目标的几何建模，基函数、权函数的选择，格林函数积分奇异性的加减同阶奇异项处理方法等。为后面的研究工作打下良好的基础。
The key points in the calculation are introduced such as the selection of the basis function and testing function, the way to solve the integral singularity of Green function and so on.
传统的几何积分法、概率积分法解决不了的一些难题，用力学方法可能得到解决。
Some difficult problems which can not be solved by the conventional methods, such as geometric method and probability integration.
本文提出了一种新的用于描述蛋白质表面几何性质的方法—平滑原子体积分数方法。
We developed a new method named Smoothed Atomic Volume Percentage (SAVP) to describe geometric properties of protein surface.
无论你使用几何学，三角形学或者微积分法，你都。
No matter whether you use geometry, trigonometry or calculus, you use the simple rules of arithmetic.
利用几何光学原理和轴外像差理论，设计一种应用于大功率CO_2激光陶瓷烧结实验的反射型正交双带式积分镜均束装置。
Using geometrical optics theory and off-axis aberration analysis, a set of crossed double strip integrators for high power CO_2 laser beam homogenizing has been designed.
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.
在一般教材中二重积分变量代换公式的证明通常采用几何的方法，也有部分数学分析教材给与了严格的分析证明，但证明不便直观的几何说明。
With proper method of variable substitution, the soluble method to two kinds of inegrable equation of Riccati form is found, and the general integral expressions are given.
牛顿研究微积分着重于从运动学来考虑，莱布尼茨却是侧重于几何学来考虑的。
Newton's study focused on the calculus from the kinematic considerations, Leibniz is focused on the geometry to be considered.
牛顿研究微积分着重于从运动学来考虑，莱布尼茨却是侧重于几何学来考虑的。
Newton's study focused on the calculus from the kinematic considerations, Leibniz is focused on the geometry to be considered.
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