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数学中计算曲线积分 数学工具中常用到这样的方法(Calculated curve integral mathematics math tools commonly used in such a way)

适合于稀薄流动计算的气体动力学格式源码，该源码为xukun老是JCP论文中的算例一致(UGKS1D- shock structure calculation using Unified Gas-Kinetic Scheme)

欧拉法解微分方程方程组，对于变成基础薄弱的人，易于理解，相信会有用处(Euler method for solving differential equations, to become a person, the weak foundation is easy to understand, I believe there will be.)

说明：  基于M估计的迭代最小二乘算法，其中估计量有Huber,Andrews,Hampel,Ramsay等。(M is estimated based on the iterative least-squares algorithm, which estimates there are Huber, Andrews, Hampel, Ramsay and so on.)

BP神经网络的整个训练过程,matlab编写的元胞自动机，独立成分分析算法降低原始数据噪声。( The entire training process BP neural network, matlab prepared cellular automata, Independent component analysis algorithm reduces the raw data noise.)

阵列处理作业，MVDR或者其他高分辨方法，由于信号源无法确定，造成估计误差，采用对角加载的 增加单位阵法 ,以及 六源准则法 获取优化结果。(Array processing, MVDR, or other high-resolution method, the source can not be determined, resulting in the estimated error, the use of diagonal loading ' to increase the unit matrix method' , and ' six-source criteria method' to obtain optimal results.)

一个短时傅里叶变换的C语言实现，对3万个数据进行加窗、FFT处理(A short time Fourier transform of C language, for 30,000 data windowing, FFT processing)

最小二乘曲面拟合程序（m文件），对一组三维数据z=f(x,y)拟合，成为关于x和y的多项式(least squares fitting procedure Surface (m), a group of three-dimensional data z = f (x, y) fitting, be on the x and y polynomial)

基于全相位谱分析的相位差频谱校正法，结合了全相位FFT与传统FFT谱分析法。(Phase Difference Correcting Spectrum Method)

说明：  本書介紹現代的數值近似方法，解釋這些方法如何、為何，以及何時有用，以作為進一步研讀數值分析與科學計算的基礎。修習本書，學生將學會辨別須使用數值方法求解之問題的種類，及使用這些方法時，誤差傳遞的實例；對無法求得確解的問題，應能求得精確的近似解，並學會估計此近似解誤差界限的方法。書中介紹的數值方法，由數學分析、計算法則到實例，皆有系統的說明。本書對於任何要使用數值方法的學系，均可作為良好的基礎教材，同時也是一本內容完備的參考書籍。(This book introduces modern numerical approximations, explaining how, why, and when they are useful as a basis for further study of readings and scientific calculations. In this book, students will learn to identify the types of problems that must be solved using numerical methods, and examples of error propagation when using these methods; for problems that cannot be solved, an accurate approximate solution should be obtained and learn to estimate this. The numerical methods introduced in the method of approximating the error bounds are systematically explained by mathematical analysis, calculation rules and examples. This book can be used as a good basic textbook for any department that wants to use numerical methods. It is also a complete reference book.)