变分法

Chapter 7 considers application of variation methods to systems with infinite degrees of freedom, and Chapter 8 deals with direct methods in the calculus of variations.

第7章认为，变异的系统方法的应用与自由无限度，和第8章在变分法直接的方法处理。

Calculus of variations is a field of mathematics that deals with functionals , as opposed to ordinary calculus which deals with functions .

变分法是处理函数的函数的数学领域，和处理数的函数的普通微积分相对。

The shape optimization is studied by adopting the domainintegrated method which is based on the calculus of variations during the shape design sensitivity analysis.

探讨了基于变分法的敏度分析在形状优化设计中的应用，提出敏度分析过程中提高速度场求解效率和有限元网格质量的新方法。

As functions of the function of mathematics, the Key theorem of calculus of variations is Euler LaGrange, it can be used to the pan-seeking function of the maximum and minimum of mathematical.

变分法是处理函数的函数的数学领域，关键定理是欧拉－拉格朗日方程，用来求的泛函数的极大值和极小值的数学方法。

This is an introduction to advanced analysis at the beginning graduate level that blends a modern presentation with concrete examples and applications, in particular in the areas of calculus of variations and partial differential equations.

这开始一调和与具体例子和应用一起的一现代演出的毕业生水平的介绍先进分析，尤其在变分法和偏微分方程的区域内。

It provides a streamlined and quick introduction to read.freeduan.com the fundamental concepts of Banach space and Lebesgue integration theory and the basic notions of the calculus of variations, including Sobolev space theory.

天气提供一精简和迅速的的介绍read.freeduan.com Banach 空间和Lebesgue综合理论和变分法的基本观念的基本概念，包括Sobolev 空间理论。

Then, corresponding to the particular form of the functional, a generalized BPTT algorithm is provided and its realization using calculus of variations is given.

文中针对泛函J=ψ+∫〓Fdt的形式，推导了相应的BPTT算法，并给出BPTT算法的变分法推导。

Based on intensive investigation of original sources and research literatures on the subject in consideration,and under the paradigm why mathematics was done in the history of mathematics,the dissertation studies systematically the origin and invention of the calculus of variations by means of source analysis and comparative argumentation.

变分法是研究泛函极值的数学分支，它不仅与数学中众多分支联系紧密，而且也为物理学提供了重要的原理，同时又有着十分广泛的应用，凶此，对其历史进行研究，具有极为重要的理论价值和现实意义。

Using some hypothesis,in this paper,a function of the number of check-verifying times in unit time for safety mornitor systems is presented the extreme functional value by the calculus of variations is evaluated and a mathematical model of check-verifying period with the minimum of check-verifying and losing cost is obtained.

在一系列假设的基础上，给出了安全监测系统单位时间内校验次数的泛函，用变分法求泛函极值，得出了校验费和损失费最小的校验周期数学模型。

By the analysis of Euler\'s three earlier papers on the calculus of variations and that of his mistake on the fundamental principle,and the comparison with Euler\'s and his pioneers\' solutions,the refinement of Euler\'s two core achievements,i.e., fundamental equation and isoperimetric rule,is explained.

通过对欧拉与伯努利兄弟和泰勒等人的解法进行比较和分析，揭示了欧拉对变分法一般性研究的背景、切入点、思想来源和演变；通过对欧拉所犯错误的原因及其影响进行深入分析，指出《技巧》一书并不仅仅是欧拉对早期研究的系统总结和改进，还包含着某种突破和变革。4。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。