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.
提供方
Introduction to Ordinary Differential Equations
韩国科学技术高等研究院 (KAIST)
課程信息
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初級
完成時間大約為12 小時
建議：2-3 hours/week
英語（English）
字幕：英語（English）
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.
教學大綱 - 您將從這門課程中學到什麼
完成時間為 2 小時
Introduction
完成時間為 2 小時
9 個視頻 （總計 76 分鐘）
9 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
1 個練習
Quiz116分鐘
完成時間為 2 小時
First Order Differential Equation 1
完成時間為 2 小時
9 個視頻 （總計 85 分鐘）
9 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
1 個練習
Quiz212分鐘
完成時間為 2 小時
FIRST ORDER DEFERENTIAL EQUATION 2
完成時間為 2 小時
12 個視頻 （總計 104 分鐘）
12 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
1 個練習
Quiz 312分鐘
完成時間為 1 小時
Mathematical Modeling and Applications
完成時間為 1 小時
5 個視頻 （總計 54 分鐘）
5 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
1 個練習
Quiz410分鐘
審閱
4.7
來自INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS的熱門評論
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 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.
由 NS 提供Feb 10, 2018
Really Helpful. Very structured and enough examples to illustrate the concepts. The quizzes are good and sometimes need an extrapolation of the knowledge in the lecture.
由 BS 提供Oct 9, 2019
coursera is best online platform to learning. i recommend every college school student to learn from coursera it's far better than your school and college teacher
由 YY 提供Oct 4, 2018
This is a very good course ,It helps me to be an expert in the field of Ordinary differential equation\n\nThanks a lot to Coursera for to provide this course
由 MA 提供Feb 12, 2020
It's a great course I recommend to everyone. And we are looking forward to a partial differential equation (PDE) course sooner.\n\nThank you!
由 EH 提供Jan 5, 2018
It's a really amazing course. Really glad that I take. Some of the video has little sound, but overall it's really good and clear.
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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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