henrch1,HenryC,github

adaptive-integration-methods

This program is coded using Python and uses two adaptive variable step-size integration methods (adaptive trapezoidal rule and adaptive Simpson's rule) to calculate the numerical integral value of a function. /本程序使用Python进行编程，使用两种自适应变步长积分方法（自适应梯形法与自适应辛普森法）计算函数的数值积分值。

birthday-greetings

一个简单的html文件，实现生日祝福/A simple HTML file to achieve birthday wishes

bisection-method

This program is written in Python and uses the bisection method to find the roots of nonlinear equations./本程序使用Python编写，采用二分法求解非线性方程的根。

buffon-s-needle

The program is written in Python and uses the Monte Carlo method to simulate Buffon's Needle experiment. /该程序使用Python编写，运用蒙特卡洛方法来模拟蒲丰投针实验。

euler-approximation

This program is programmed using Python and uses two methods, namely the first-order Euler approximation method and the second-order Euler approximation method, to approximate solutions to ordinary differential equations./该程序使用 Python 进行编程，使用了一级欧拉近似法和二级欧拉近似法两种方法来求解常微分方程的近似解。

finite-difference-for-diffusion-equation

The program is written in Python and aims to solve the one-dimensional diffusion equation using the finite difference method./该程序使用Python编写，旨在使用有限差分法解决一维扩散方程。

finite-difference-for-laplace-equation

The program is written in Python and aims to solve the Laplace equation using the finite difference method. /该程序使用Python编写，旨在使用有限差分法解决拉普拉斯方程。

finite-difference-for-poisson-equation

The program is written in Python and aims to solve the Poisson equation using the finite difference method./该程序使用Python编写，旨在使用有限差分法解决泊松方程。

function-iteration-and-aitken-acceleration

This program is written in Python and uses the function iteration method and Aitken acceleration method to find the roots of nonlinear equations. /本程序使用Python编写，采用函数迭代法和埃特金加速法求解非线性方程的根。

gaussian-elimination

This program is programmed using Python and can be used to solve linear equations with two methods: Gaussian Elimination and Improved Column Principal Gaussian Elimination. /本程序使用Python编程，可以使用两种方法（高斯消去法和改进后的列主元高斯消去法）来解决线性方程组。这两种方法的主要操作相似，区别在于改进后的方法每次在第k行消元时会将具有第k列最大元素的行与第k行交换，然后再进行消元。

hermite-interpolation

This program is written in Python and is used to calculate the interpolation polynomial of a function using the Hermite interpolation method./该程序使用Python编写，使用Hermite插值法计算函数的插值多项式。

inconsistent-equations

This program is written in Python and is used to solve inconsistent systems of equations using the method of least squares./该程序使用Python编写，用于使用最小二乘法求解矛盾方程组。

iterative-methods

This program is written in Python and uses two iterative methods, Jacobi iteration and Gauss-Seidel iteration, to solve linear equations. /这个程序使用Python编写，采用雅可比迭代法和高斯-赛德尔迭代法两种方法解决线性方程组问题。

iterative-methods-for-nonlinear-equation-sets

This program is written in Python and uses iterative methods to solve the solutions of nonlinear equation sets./这个程序使用Python编写，用迭代法求解非线性方程组的解。

lagrange-interpolation

The program is written in Python and uses the three-point Lagrange interpolation method to calculate the interpolation of the function. /该程序使用Python编写，使用三点拉格朗日插值法计算函数的插值。

least-squares

The program is written in Python and aims to fit data points using the method of least squares, and returns the fitted function expression. /该程序使用Python编写，旨在利用最小二乘法对数据点进行拟合，并返回拟合的函数表达式。

monte-carlo-calculate-pi

The program is written in Python and uses the Monte Carlo method to calculate the value of pi./该程序使用Python编写，采用蒙特卡洛方法计算圆周率。

monte-carlo-for-complex-roots

The program is written in Python and aims to approximate the complex roots of an equation using the Monte Carlo method./该程序使用Python编写，旨在使用蒙特卡洛法来近似求解方程的复数根。

monte-carlo-for-image-processing

The program is written in Python and uses the Monte Carlo method for image processing to calculate the area of a specific shape in an image. /该程序使用Python编写，采用蒙特卡洛方法进行图像处理，计算图片中某个图形的面积。

monte-carlo-for-integrals

The program is written in Python and uses the Monte Carlo method to calculate definite integrals, with two main approaches./该程序使用Python编写，采用蒙特卡洛方法计算定积分，主要有两种思路。

monte-carlo-for-volume-estimation

The program is written in Python and aims to estimate the mass of the remaining portion of a sphere using the Monte Carlo method. /该程序使用Python编写，旨在使用蒙特卡洛方法来估计球体剩余部分的质量。

multiple-players-gambling

This program is written in Python and uses Monte Carlo simulation to estimate the expected value for multiple players in multiple rounds of gambling./本程序使用Python编写，利用蒙特卡罗模拟来估计多人多次赌博游戏的期望值。

newton-interpolation

The program is written in Python and is used to calculate the interpolation of a function using Newton's interpolation method./该程序使用Python编写，用于使用牛顿插值法计算函数的插值。

newton-raphson-method

The program is written in Python and uses the Newton-Raphson method and the secant method to solve roots for nonlinear equations./这个程序使用Python编写，采用牛顿迭代法和弦截法求解非线性方程的根。

rayleigh-ritz-method

The program is written in Python and aims to use the Rayleigh-Ritz method to solve extremal problems for functionals./该程序使用Python编写，旨在使用瑞利-里兹法求解泛函的极值问题。

romberg-integration

本程序使用Python进行编程，采用龙贝格积分方法计算函数的数值积分值。/This program is coded using Python and uses the Romberg integration method to calculate the numerical integral value of a function.

runge-kutta

This program is written in Python and uses the Runge-Kutta method to approximate the numerical solutions of first-order and second-order initial value problems for ordinary differential equations./本程序使用Python编写，使用龙格-库塔方法分别求解一阶和二阶常微分方程的初值问题以获得数值逼近解。

single-player-multiple-rounds-gambling

This program is written in Python and uses Monte Carlo simulation to estimate the expected value for a single player in multiple rounds of gambling./这个程序是用Python编写的，使用蒙特卡罗模拟计算单个玩家在多次赌博游戏中的期望值。

successive-over-relaxation-sor-method

This program is written in Python and uses the Successive Over-Relaxation (SOR) method to solve linear equations./本程序使用Python编写，采用超松弛迭代法（SOR）求解线性方程组。

three-methods-of-solving-definite-integral-with-python

A Python library for numeric integration, providing three different methods: rectangle rule, trapezoidal rule, and Simpson's rule. you can conveniently compute definite integrals in your own code and choose the desired algorithm and precision level.

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