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.
教学大纲 - 您将从这门课程中学到什么
周
1完成时间为 2 小时
Introduction
9 个视频 （总计 76 分钟）, 1 个测验
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
Quiz116分钟
周
2完成时间为 2 小时
First Order Differential Equation 1
9 个视频 （总计 85 分钟）, 1 个测验
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
Quiz212分钟
周
3完成时间为 2 小时
FIRST ORDER DEFERENTIAL EQUATION 2
12 个视频 （总计 104 分钟）, 1 个测验
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 312分钟
周
4完成时间为 1 小时
Mathematical Modeling and Applications
5 个视频 （总计 54 分钟）, 1 个测验
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
Quiz410分钟
4.6
44 个审阅50%
通过此课程获得实实在在的工作福利
热门审阅
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 .
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
ProfessorDepartment of Mathematical Sciences
关于 韩国科学技术高级研究院
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
我什么时候能够访问课程视频和作业？
注册以便获得证书后，您将有权访问所有视频、测验和编程作业（如果适用）。只有在您的班次开课之后，才可以提交和审阅同学互评作业。如果您选择在不购买的情况下浏览课程，可能无法访问某些作业。
我购买证书后会得到什么？
您购买证书后，将有权访问所有课程材料，包括评分作业。完成课程后，您的电子课程证书将添加到您的成就页中，您可以通过该页打印您的课程证书或将其添加到您的领英档案中。如果您只想阅读和查看课程内容，可以免费旁听课程。
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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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