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所在平台: Udemy |
课程主页: https://www.udemy.com/course/numerical-methods-in-java/
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课程名称：Python中的数值方法与优化 课程概述：本课程主要介绍在Python编程语言中应用的数值方法和优化算法。我们不讨论与数值方法相关的所有理论（例如如何解决微分方程），而是专注于具体的实现和数值原则。课程分为几个部分： 第一部分：数值方法基础 我们将探讨数值方法的基本概念，包括浮点表示、舍入误差，以及C、Java和Python的性能比较。 第二部分：线性代数与高斯消元法 本部分将介绍线性代数的基本知识，包括矩阵乘法、高斯消元法及其在投资组合优化中的应用。 第三部分：特征值与特征向量 我们将讨论特征值和特征向量，并探讨其在机器学习中的应用，如主成分分析（PCA）以及谷歌的PageRank算法。 第四部分：插值 本部分将介绍拉格朗日插值理论及其实现和应用。 第五部分：根查找算法 我们将学习如何解决非线性方程，包括牛顿法和二分法。 第六部分：数值积分 我们将探讨不同的数值积分方法，包括矩形法、梯形法、辛普森法和蒙特卡洛积分。 第七部分：微分方程 本部分将介绍如何求解微分方程，包括欧拉法和龙格-库塔法，并以摆动问题和弹道学为例。 第八部分：机器学习中的数值优化 我们将分析数值优化的技术，包括梯度下降、随机梯度下降、ADAGrad、RMSProp和ADAM优化器，以及这些算法的理论与实现。 如果您对Python编程不熟悉，可以在课程的最后章节中学习Python的基础知识。感谢您加入本课程，让我们开始吧！
This course is about numerical methods and optimization algorithms in Python programming language. *** We are NOT going to discuss ALL the theory related to numerical methods (for example how to solve differential equations etc.) - we are just going to consider the concrete implementations and numerical principles ***The first section is about matrix algebra and linear systems such as matrix multiplication, gaussian elimination and applications of these approaches. We will consider the famous Google's PageRank algorithm.Then we will talk about numerical integration. How to use techniques like trapezoidal rule, Simpson formula and Monte-Carlo method to calculate the definite integral of a given function.The next chapter is about solving differential equations with Euler's-method and Runge-Kutta approach. We will consider examples such as the pendulum problem and ballistics.Finally, we are going to consider the machine learning related optimization techniques. Gradient descent, stochastic gradient descent algorithm, ADAGrad, RMSProp and ADAM optimizer will be discussed - theory and implementations as well.*** IF YOU ARE NEW TO PYTHON PROGRAMMING THEN YOU CAN LEARN ABOUT THE FUNDAMENTALS AND BASICS OF PYTHON IN THA LAST CHAPTERS ***Section 1 - Numerical Methods Basicsnumerical methods basicsfloating point representationrounding errorsperformance C, Java and PythonSection 2 - Linear Algebra and Gaussian Eliminationlinear algebramatrix multiplicationGauss-eliminationportfolio optimization with matrix algebraSection 3 - Eigenvectors and Eigenvalueseigenvectors and eigenvaluesapplications of eigenvectors in machine learning (PCA)Google's PageRank algorithm explainedSection 4 - InterpolationLagrange interpolation theoryimplementation and applications of interpolationSection 5 - Root Finding Algorithmssolving non-linear equationsroot findingNewton's method and bisection methodSection 6 - Numerical Integrationnumerical integrationrectangle method and trapezoidal methodSimpson's methodMonte-Carlo integrationSection 7 - Differential Equationssolving differential-equationsEuler's methodRunge-Kutta methodpendulum problem and ballisticsSection 8 - Numerical Optimization (in Machine Learning)gradient descent algorithmstochastic gradient descentADAGrad and RMSProp algorithmsADAM optimizer explained*** IF YOU ARE NEW TO PYTHON PROGRAMMING THEN YOU CAN LEARN ABOUT THE FUNDAMENTALS AND BASICS OF PYTHON IN THA LAST CHAPTERS ***Thanks for joining my course, let's get started!
