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所在平台: Udemy |
课程主页: https://www.udemy.com/course/numerical-solution-of-odes-and-pdes/
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Coursera 课程《数值解：常微分方程与偏微分方程》将为 STEM 专业本科生提供常微分方程和偏微分方程数值解法的入门介绍。课程将根据需要逐步引入所需的前置知识，因此具备一定的数值方法知识会更有帮助，但并非必需。若想自行编写代码，则需要掌握一门科学编程语言（课程中提供的 Fortran 和 Python 代码可供下载）。 课程内容涵盖： * **常微分方程 (ODE) 的数值解法** * 初值问题（或称传播问题） * 边值问题（或称平衡问题） * 特征值问题（或称本征值问题） * **偏微分方程 (PDE) 的数值解法** * 主要关注二阶偏微分方程的有限差分方法。 * 介绍椭圆型、抛物型和双曲型方程的分类，以及如何根据分类选择最优的数值解法。 * 重点讲解椭圆型和抛物型偏微分方程的求解。 课程以章节形式展开，主要包括： * **第二部分：ODE 初值问题** * **第三部分：ODE 边值问题** * **第四部分：ODE 特征值问题** * **第五部分：椭圆型偏微分方程** * **第六部分：抛物型偏微分方程** 课程提供所有用于演示方法和解决示例问题的代码（Fortran 和 Python）以及课堂笔记供下载。
The course provides an introduction to the numerical solution of ordinary and partial differential equations and is at a level appropriate for undergraduate-level STEM students. Prior knowledge of numerical methods is helpful but not necessary as (most) prerequisite material is introduced on an as-needed basis. Knowledge of a scientific programming language is necessary for those wishing to write their own codes. All codes used to demonstrate methods and solve example problems (primarily in both Fortran and Python) are available for downloading, as are the class notes. For the ordinary differential equations, we will study numerical techniques to solve:1) Initial value (or propagation) problems2) Boundary value (or equilibrium) problems3) Eigenvalue (or characteristic value) problemsIn terms of partial differential equations, we will concentrate on finite-difference approaches to solve second-order partial differential equations.These equations may be classified as elliptic, parabolic, or hyperbolic. The classification helps determine the best approach to obtain a numerical solution. We will focus on elliptic and parabolic partial differential equations.The primary course sections are:SECTION 2: ODE's: INITIAL VALUE PROBLEMSSECTION 3: ODE's: BOUNDARY VALUE PROBLEMSSECTION 4: ODE's: EIGENVALUE PROBLEMSSECTION 5: ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONSSECTION 6: PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS
