課程信息
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

初級

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建議:2-3 hours/week

完成時間大約為18 小時
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English

字幕:English
Globe

100% 在線課程

立即開始,按照自己的計劃學習。
Calendar

可靈活調整截止日期

根據您的日程表重置截止日期。
Beginner Level

初級

Clock

建議:2-3 hours/week

完成時間大約為18 小時
Comment Dots

English

字幕:English

教學大綱 - 您將從這門課程中學到什麼

1

章節
Clock
完成時間為 2 小時

Introduction

...
Reading
9 個視頻(共 76 分鐘), 1 個測驗
Video9 個視頻
1-2 Order and Normal Form6分鐘
1-3 Linear and Nonlinear Equations5分鐘
1-4 Solution5分鐘
1-5 Implicit Solution11分鐘
1-6 Types of Solutions12分鐘
1-7 Initial Value Problem10分鐘
1-8 Picard’s Theorem I10分鐘
1-9 Picard’s Theorem II9分鐘
Quiz1 個練習
Quiz116分鐘

2

章節
Clock
完成時間為 2 小時

First Order Differential Equation 1

...
Reading
9 個視頻(共 85 分鐘), 1 個測驗
Video9 個視頻
2-2 Separable Equations - Ex’s 1 & 28分鐘
2-3 Separable Equations - Ex’s 3 & 49分鐘
2-4 Integrating Factor12分鐘
2-5 Does IVP Have a Unique Solution?6分鐘
2-6 Exact Equations I8分鐘
2-7 Exact Equations II18分鐘
2-8 Exact Equations – Ex. 110分鐘
2-9 Exact Equations – Ex. 25分鐘
Quiz1 個練習
Quiz212分鐘

3

章節
Clock
完成時間為 2 小時

FIRST ORDER DEFERENTIAL EQUATION 2

...
Reading
12 個視頻(共 104 分鐘), 1 個測驗
Video12 個視頻
3-2 Integrating Factor II7分鐘
3.3 Integrating Factor III10分鐘
3-4 Substitutions, Ex 18分鐘
3-5 Homogeneous Equations9分鐘
3-6 Substitutions Ex's 2 & 39分鐘
3-7 Bernoulli Equation9分鐘
3-8 Equations with Linear Coefficients9分鐘
3-9 Equations with Linear Coefficients - Ex. 57分鐘
3-10 Ricatti's Equation - Ex. 69分鐘
3-11 Clairaut's Equation8分鐘
3-12 Clairaut's Equation - Ex. 76分鐘
Quiz1 個練習
Quiz 312分鐘

4

章節
Clock
完成時間為 1 小時

Mathematical Modeling and Applications

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Reading
5 個視頻(共 54 分鐘), 1 個測驗
Video5 個視頻
4-2 Population Dynamics I9分鐘
4-3 Population Dynamics II7分鐘
4-4 Population Dynamics III13分鐘
4-5 Population Dynamics IV11分鐘
Quiz1 個練習
Quiz410分鐘
4.6

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創建者 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 .

創建者 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.

講師

Kwon, Kil Hyun

Professor
Department of Mathematical Sciences

關於 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....

常見問題

  • 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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