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所在平台: Udemy |
课程主页: https://www.udemy.com/course/differential-equations-l/
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**课程名称：** 微分方程 **课程概述：** 本课程旨在为学生提供微分方程的深入理解，包括其建立、分类，以及解的存在性和唯一性概念。课程目标是培养学生解决初值问题和边值问题的能力，并发展解决一阶和二阶线性齐次与非齐次微分方程的理解和技能。 课程内容涵盖： * **一阶微分方程：** * 存在性与唯一性概念 * 变量可分离型 * 齐次方程 * 非齐次方程 * 恰当方程（Exact Equations） * 使非恰当方程恰当的方法 * 线性方程 * 初值问题 * **一阶微分方程的应用** * **高阶线性微分方程：** * 线性齐次方程 * 非齐次方程（待定系数法、常数变易法） **学习目标：** 完成本课程后，学生应能： * 阐述微分方程的基本概念。 * 利用课程开发的理论解决一阶、二阶微分方程以及偏微分方程。 * 应用常微分和偏微分的概念来建立物理系统的模型。 **学习建议：** 本课程需要大量的实践。学生应积极解决讲座中讨论的例题和习题，以及教材和参考资料中的大部分练习题。 **推荐教材：** * 《微分方程基础》（Fundamentals of Differential Equations）第9版，作者：R. Nagle, Edward Saff, Arthur Snider * 《微分方程》（Schaum's Outline of Differential Equations） **其他参考资料：** 推荐参考其他优秀的微分方程书籍。
The course is designed to equip students with the in-depth understanding of differential equations, their formulation, classification including the concept existence and uniqueness of solutions. The aim is to provide skill in solving initial value and boundary value problems and to develop understanding and skill in solving first and second order linear homogeneous and non- homogeneous differential equations.The course starts from First Order Differential Equations - including, existence and uniqueness concept, variables separable forms, homogenous equations, non-homogenous equations, exact equations, methods of making non-exact equations exact, linear equations, initial value problem. After that course moves to Applications of First Order DE's and then Higher Order Linear Differential Equations - linear homogeneous equations, non-homogeneous equations - method of undetermined coefficients, method of variation of parameters.By the end of this course, a student is expected be able to:Demonstrate the fundamental concepts of differential equations.Solve first and second order differential equations and partial differential equations using the concepts developed in the course.Apply the concepts of ordinary derivatives and partial derivatives for modeling of physical systems.his course needs extensive practice. Students are expected to solve each problem and example discussed in the lectures along with most of the exercise problems from the text book and ref material. Text Book recommended for this course is Fundamentals of Differential Equations 9th Editionby R. Nagle (Author), Edward Saff (Author), Arthur Snider (AuthorAlong with Schaum Series on Differential Equation will be helpful. There are plenty of other good books out there as well which may be referred to.
