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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/ordinary-differential-equations
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课程名称：常微分方程导论 概述：在这门常微分方程的入门课程中，我们首先介绍微分方程的基本术语，然后讲解各种类型常微分方程的求解方法。课程涵盖一阶微分方程和二阶线性微分方程，并讨论一些相关的具体数学建模问题，这些问题可以通过课程中介绍的方法来处理。 课程内容结构严谨，具有自给自足的特性；但如有必要，您可以参考任何入门级的常微分方程教材。例如，W. E. Boyce 和 R. C. DiPrima 的《基础微分方程及边值问题》是进一步学习该主题的良好参考书。 课程主要通过视频讲座进行传授。在每个模块结束时，将进行一次测验，内容涉及当周讲座的相关问题。 课程大纲： 1. 引言 2. 一阶微分方程 1 3. 一阶微分方程 2 4. 数学建模与应用 5. 二阶线性微分方程 1 6. 二阶线性微分方程 2 7. 二阶线性微分方程 3 8. 二阶线性微分方程 4 9. 二阶方程的应用 通过该课程，学生将掌握常微分方程的基本理论和应用技巧，为进一步的学习和研究打下基础。
Name:Introduction
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Name:First Order Differential Equation 1
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Name:FIRST ORDER DEFERENTIAL EQUATION 2
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Name:Mathematical Modeling and Applications
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Name:LINEAR SECOND ORDER EQUATIONS 1
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Name:Linear Second order equations 2
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Name:Linear Second order equations 3
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Name:Linear Second order equations 4
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Name:APPLICATIONS OF SECOND ORDER EQUATIONS
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In this introductory course on Ordinary Differential Equations, we first provide basic terminologies on the theory of differential equations and then proceed to methods of solving various types of ordinary differential equations. We handle first order differential equations and then second order linear differential equations. We also discuss some related concrete mathematical modeling problems, which can be handled by the methods introduced in this course. The lecture is self contained. However, if necessary, you may consult any introductory level text on ordinary differential equations. For example, "Elementary Differential Equations and Boundary Value Problems by W. E. Boyce and R. C. DiPrima from John Wiley & Sons" is a good source for further study on the subject. The course is mainly delivered through video lectures. At the end of each module, there will be a quiz consisting of several problems related to the lecture of the week.
