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.
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Introduction to Ordinary Differential Equations
韩国科学技术高等研究院 (KAIST)课程信息
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初级
完成时间大约为15 小时
英语（English）
字幕：法语（French）, 巴西葡萄牙语, 俄语（Russian）, 英语（English）, 西班牙语（Spanish）
学生职业成果
25%
通过此课程获得实实在在的工作福利
可分享的证书
完成后获得证书
100% 在线
立即开始，按照自己的计划学习。
可灵活调整截止日期
根据您的日程表重置截止日期。
初级
完成时间大约为15 小时
英语（English）
字幕：法语（French）, 巴西葡萄牙语, 俄语（Russian）, 英语（English）, 西班牙语（Spanish）
提供方
韩国科学技术高等研究院 (KAIST)
The Korea Advanced Institute of Science and Technology (KAIST) was established in 1971 by the Korean government as the nation’s first research-intensive graduate school for science, engineering and technology. It has now grown into one of the world’s best universities, delivering top notch education and research programs for undergraduate and graduate students. KAIST encourages interdisciplinary and convergent research across a wide spectrum of disciplines, as well as strong collaborations with industry and global institutions.
教学大纲 - 您将从这门课程中学到什么
完成时间为 2 小时
Introduction
完成时间为 2 小时
9 个视频 （总计 76 分钟）
9 个视频
1-2 Order and Normal Form6分钟
1-3 Linear and Nonlinear Equations5分钟
1-4 Solution5分钟
1-5 Implicit Solution11分钟
1-6 Types of Solutions12分钟
1-7 Initial Value Problem10分钟
1-8 Picard’s Theorem I10分钟
1-9 Picard’s Theorem II9分钟
1 个练习
Quiz130分钟
完成时间为 2 小时
First Order Differential Equation 1
完成时间为 2 小时
9 个视频 （总计 85 分钟）
9 个视频
2-2 Separable Equations - Ex’s 1 & 28分钟
2-3 Separable Equations - Ex’s 3 & 49分钟
2-4 Integrating Factor12分钟
2-5 Does IVP Have a Unique Solution?6分钟
2-6 Exact Equations I8分钟
2-7 Exact Equations II18分钟
2-8 Exact Equations – Ex. 110分钟
2-9 Exact Equations – Ex. 25分钟
1 个练习
Quiz230分钟
完成时间为 2 小时
FIRST ORDER DEFERENTIAL EQUATION 2
完成时间为 2 小时
12 个视频 （总计 104 分钟）
12 个视频
3-2 Integrating Factor II7分钟
3.3 Integrating Factor III10分钟
3-4 Substitutions, Ex 18分钟
3-5 Homogeneous Equations9分钟
3-6 Substitutions Ex's 2 & 39分钟
3-7 Bernoulli Equation9分钟
3-8 Equations with Linear Coefficients9分钟
3-9 Equations with Linear Coefficients - Ex. 57分钟
3-10 Ricatti's Equation - Ex. 69分钟
3-11 Clairaut's Equation8分钟
3-12 Clairaut's Equation - Ex. 76分钟
1 个练习
Quiz 330分钟
完成时间为 1 小时
Mathematical Modeling and Applications
完成时间为 1 小时
5 个视频 （总计 54 分钟）
5 个视频
4-2 Population Dynamics I9分钟
4-3 Population Dynamics II7分钟
4-4 Population Dynamics III13分钟
4-5 Population Dynamics IV11分钟
1 个练习
Quiz430分钟
审阅
来自INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS的热门评论
由 RV 提供Jan 12, 2020
The course is correctly paced. The lectures are extremely good and carries lots of details. Overall, the course is very well organized, extremely thankful to the instructor and others for the support.
由 CS 提供Jun 13, 2020
An excellent platform for the subject knowledge. Coursera teaches the different types of learning methods .in this couse I learned about differential equations applicable to physical concepts
由 SK 提供Jun 18, 2018
I heartily thankful to Coursera team who helped me lot to complete this course and last but not least I would like to say thanks to Prof. K.H.Kwon.I have learned lot thorough this course .
由 RA 提供May 19, 2018
I have enjoyed taking this course. The topics have been divided very well in that they are not too long and hard just the right amount. The lecturer was delightful and easy to understand.
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Is there any prerequisite for the course?
Yes. One must be familiar with the basic differential and integral calculus, which are the main contents of college level introductory Calculus course. Although the course does not require more than high school linear algebra, it will be very helpful if one has a little bit of knowledge on Linear Algebra such as the determinant of a square matrix, linear (in)dependence of vectors, and Cramer’s rule of solving a determined system of simultaneous linear algebraic equations.
"The beginner should not be discouraged if he finds that he does not have the prerequisites for reading the prerequisites.' from P. R. Halmos, I want to be a mathematician, Math. Assoc. America, 1985.
Q2. What are the main goals of the course?
The course is designed to introduce basic theory, techniques, and applications of differential equations to beginners in the field, who would like to continue their study in the subjects such as natural sciences, engineering, and economics etc. The course is emphasizing methods and techniques of solving certain differential equations.
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