|
所在平台: Udemy |
课程主页: https://www.udemy.com/course/differential/
课程评论：没有评论
Coursera 上的“微分方程深入”课程是一门全面的课程，旨在帮助学习者掌握微分方程。 **课程内容涵盖：** * **常微分方程 (ODEs)**：包括一阶和二阶方程。 * **拉普拉斯变换与傅里叶级数**：重要的数学工具，用于解决特定类型的微分方程。 * **偏微分方程 (PDEs)**：涵盖了常见的偏微分方程，如波动方程和热传导方程。 * **微分方程的数值解法**：介绍了欧拉方法、龙格-库塔法等数值求解技术。 * **使用 MATLAB 和 Maple 进行建模与求解**：演示如何运用计算机代数系统 (CAS) 来建模和求解微分方程。 **先修知识要求：** * 对微分和积分有基本理解。 * 熟悉常见的积分运算（分部积分、换元积分）。 * 对数值计算有基本了解（对数值方法部分是必需的）。 * 能够访问并基本使用常见的计算机代数系统 (CAS) 软件包，如 MATLAB、Maple、Mathematica 等。 **课程特点：** * 以手写讲座的形式呈现，深入讨论相关主题。 * 演示如何使用 CAS 软件包（如 MATLAB、Maple）来分析或符号化地求解微分方程。 * 鼓励学习者结合一本优质的微分方程教材进行学习。 * 课程将根据学员反馈持续改进和更新。 总而言之，这门课程为学习者提供了全面理解和应用微分方程的理论知识和实践技能，并强调了使用现代计算工具的重要性。
This course has everything you need to learn and understand Differential Equations. Differential equations are a class of equation that involves the use of differentials (derivatives) in their construction. Differential equations are used in many areas of science, particularly in physics, where they are used to model real-world phenomena such as the propagation of waves.This course covers: Ordinary differential equations (ODEs) - first and second orderLaplace Transform and Fourier SeriesPartial differential equations (PDEs) - including common equations such as the Wave Equation and the Heat Conduction EquationNumeric solutions of differential equations - e.g., Euler's Method, Runge-KuttaModeling and solving differential equations using MATLAB and Maple.Course pre-requisites:Fundamental understanging of differentiation and integrationKnowledge of common integration operations (integration by parts, integration by substitution)Basic understanding of numerical computing (required for numerical methods)Access and basic knowledge of common CAS packages such as MATLAB, Maple, Mathematica, etc.This course is presented as a series of hand-written lectures where we discuss the relevant topics. I also present approaches to using CAS (Computer-aided Algebra Systems) to solving differential equations either analytically or symbolically.It is recommended that you augment your study of differential equations on this course with a good textbook on differential equations.This course will continue to evolve and improve based on feedback from the course participants. Please leave feedback!
