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.
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Introduction to Ordinary Differential Equations
Institut supérieur coréen des sciences et technologies (KAIST)À propos de ce cours
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Résultats de carrière des étudiants
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Niveau débutant
Approx. 12 heures pour terminer
Anglais
Sous-titres : Anglais
Résultats de carrière des étudiants
25%
ont bénéficié d'un avantage concret dans leur carrières grâce à ce cours
Certificat partageable
Obtenez un Certificat lorsque vous terminez
100 % en ligne
Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Dates limites flexibles
Réinitialisez les dates limites selon votre disponibilité.
Niveau débutant
Approx. 12 heures pour terminer
Anglais
Sous-titres : Anglais
Offert par
Institut supérieur coréen des sciences et technologies (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.
Programme du cours : ce que vous apprendrez dans ce cours
2 heures pour terminer
Introduction
2 heures pour terminer
9 vidéos (Total 76 min)
9 vidéos
1-2 Order and Normal Form6 min
1-3 Linear and Nonlinear Equations5 min
1-4 Solution5 min
1-5 Implicit Solution11 min
1-6 Types of Solutions12 min
1-7 Initial Value Problem10 min
1-8 Picard’s Theorem I10 min
1-9 Picard’s Theorem II9 min
1 exercice pour s'entraîner
Quiz116 min
2 heures pour terminer
First Order Differential Equation 1
2 heures pour terminer
9 vidéos (Total 85 min)
9 vidéos
2-2 Separable Equations - Ex’s 1 & 28 min
2-3 Separable Equations - Ex’s 3 & 49 min
2-4 Integrating Factor12 min
2-5 Does IVP Have a Unique Solution?6 min
2-6 Exact Equations I8 min
2-7 Exact Equations II18 min
2-8 Exact Equations – Ex. 110 min
2-9 Exact Equations – Ex. 25 min
1 exercice pour s'entraîner
Quiz212 min
2 heures pour terminer
FIRST ORDER DEFERENTIAL EQUATION 2
2 heures pour terminer
12 vidéos (Total 104 min)
12 vidéos
3-2 Integrating Factor II7 min
3.3 Integrating Factor III10 min
3-4 Substitutions, Ex 18 min
3-5 Homogeneous Equations9 min
3-6 Substitutions Ex's 2 & 39 min
3-7 Bernoulli Equation9 min
3-8 Equations with Linear Coefficients9 min
3-9 Equations with Linear Coefficients - Ex. 57 min
3-10 Ricatti's Equation - Ex. 69 min
3-11 Clairaut's Equation8 min
3-12 Clairaut's Equation - Ex. 76 min
1 exercice pour s'entraîner
Quiz 312 min
1 heure pour terminer
Mathematical Modeling and Applications
1 heure pour terminer
5 vidéos (Total 54 min)
5 vidéos
4-1 Radioactive Decay12 min
4-2 Population Dynamics I9 min
4-3 Population Dynamics II7 min
4-4 Population Dynamics III13 min
4-5 Population Dynamics IV11 min
1 exercice pour s'entraîner
Quiz410 min
Avis
Meilleurs avis pour INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS
par RV12 janv. 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.
par CS13 juin 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
par SK18 juin 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 .
par RA19 mai 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.
Foire Aux Questions
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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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