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.
Offered By
Introduction to Ordinary Differential Equations
Korea Advanced Institute of Science and Technology(KAIST)About this Course
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Learner Career Outcomes
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Shareable Certificate
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Beginner Level
Approx. 15 hours to complete
English
Subtitles: French, Portuguese (Brazilian), Russian, English, Spanish
Learner Career Outcomes
25%
got a tangible career benefit from this course
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Beginner Level
Approx. 15 hours to complete
English
Subtitles: French, Portuguese (Brazilian), Russian, English, Spanish
Offered by
Korea Advanced Institute of Science and Technology(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.
Syllabus - What you will learn from this course
2 hours to complete
Introduction
2 hours to complete
9 videos (Total 76 min)
9 videos
1-2 Order and Normal Form6m
1-3 Linear and Nonlinear Equations5m
1-4 Solution5m
1-5 Implicit Solution11m
1-6 Types of Solutions12m
1-7 Initial Value Problem10m
1-8 Picard’s Theorem I10m
1-9 Picard’s Theorem II9m
1 practice exercise
Quiz130m
2 hours to complete
First Order Differential Equation 1
2 hours to complete
9 videos (Total 85 min)
9 videos
2-2 Separable Equations - Ex’s 1 & 28m
2-3 Separable Equations - Ex’s 3 & 49m
2-4 Integrating Factor12m
2-5 Does IVP Have a Unique Solution?6m
2-6 Exact Equations I8m
2-7 Exact Equations II18m
2-8 Exact Equations – Ex. 110m
2-9 Exact Equations – Ex. 25m
1 practice exercise
Quiz230m
2 hours to complete
FIRST ORDER DEFERENTIAL EQUATION 2
2 hours to complete
12 videos (Total 104 min)
12 videos
3-2 Integrating Factor II7m
3.3 Integrating Factor III10m
3-4 Substitutions, Ex 18m
3-5 Homogeneous Equations9m
3-6 Substitutions Ex's 2 & 39m
3-7 Bernoulli Equation9m
3-8 Equations with Linear Coefficients9m
3-9 Equations with Linear Coefficients - Ex. 57m
3-10 Ricatti's Equation - Ex. 69m
3-11 Clairaut's Equation8m
3-12 Clairaut's Equation - Ex. 76m
1 practice exercise
Quiz 330m
1 hour to complete
Mathematical Modeling and Applications
1 hour to complete
5 videos (Total 54 min)
5 videos
4-2 Population Dynamics I9m
4-3 Population Dynamics II7m
4-4 Population Dynamics III13m
4-5 Population Dynamics IV11m
1 practice exercise
Quiz430m
Reviews
TOP REVIEWS FROM INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS
by RVJan 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.
by CSJun 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
by SKJun 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 .
by RAMay 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.
Frequently Asked Questions
When will I have access to the lectures and assignments?
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
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- The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
What will I get if I purchase the Certificate?
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.
Is financial aid available?
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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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