课程信息
4.6
69 ratings
24 reviews
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....
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Beginner Level

初级

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建议:2-3 hours/week

完成时间大约为18 小时
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English

字幕:English
Globe

100% 在线课程

立即开始,按照自己的计划学习。
Calendar

可灵活调整截止日期

根据您的日程表重置截止日期。
Beginner Level

初级

Clock

建议:2-3 hours/week

完成时间大约为18 小时
Comment Dots

English

字幕:English

教学大纲 - 您将从这门课程中学到什么

1

章节
Clock
完成时间为 2 小时

Introduction

...
Reading
9 个视频(共 76 分钟), 1 个测验
Video9 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
Quiz1 个练习
Quiz116分钟

2

章节
Clock
完成时间为 2 小时

First Order Differential Equation 1

...
Reading
9 个视频(共 85 分钟), 1 个测验
Video9 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
Quiz1 个练习
Quiz212分钟

3

章节
Clock
完成时间为 2 小时

FIRST ORDER DEFERENTIAL EQUATION 2

...
Reading
12 个视频(共 104 分钟), 1 个测验
Video12 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
Quiz1 个练习
Quiz 312分钟

4

章节
Clock
完成时间为 1 小时

Mathematical Modeling and Applications

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Reading
5 个视频(共 54 分钟), 1 个测验
Video5 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
Quiz1 个练习
Quiz410分钟
4.6

热门审阅

创建者 SKJun 19th 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 .

创建者 RAMay 20th 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.

讲师

Kwon, Kil Hyun

Professor
Department of Mathematical Sciences

关于 Korea Advanced Institute of Science and Technology

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....

常见问题

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

  • 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.

  • 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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