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.
Introduction to Ordinary Differential Equations
proposé par
Introduction to Ordinary Differential Equations
Korea Advanced Institute of Science and Technology
Programme du cours : ce que vous apprendrez dans ce cours
Semaine
1Introduction
9 vidéos (Total 76 min), 1 quiz
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
Semaine
2First Order Differential Equation 1
9 vidéos (Total 85 min), 1 quiz
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
Semaine
3FIRST ORDER DEFERENTIAL EQUATION 2
12 vidéos (Total 104 min), 1 quiz
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
Semaine
4Mathematical Modeling and Applications
5 vidéos (Total 54 min), 1 quiz
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
4.6
34 avisMeilleurs avis
par SK•Jun 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 .
par RA•May 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.
Enseignant
Kwon, Kil Hyun
ProfessorDepartment of Mathematical Sciences
À propos de 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.
Foire Aux Questions
Quand aurai-je accès aux vidéos de cours et aux devoirs ?
Une fois que vous êtes inscrit(e) pour un Certificat, vous pouvez accéder à toutes les vidéos de cours, et à tous les quiz et exercices de programmation (le cas échéant). Vous pouvez soumettre des devoirs à examiner par vos pairs et en examiner vous-même uniquement après le début de votre session. Si vous préférez explorer le cours sans l'acheter, vous ne serez peut-être pas en mesure d'accéder à certains devoirs.
À quoi ai-je droit si j'achète le Certificat ?
Lorsque vous achetez un Certificat, vous bénéficiez d'un accès à tout le contenu du cours, y compris les devoirs notés. Lorsque vous avez terminé et réussi le cours, votre Certificat électronique est ajouté à votre page Accomplissements. À partir de cette page, vous pouvez imprimer votre Certificat ou l'ajouter à votre profil LinkedIn. Si vous souhaitez seulement lire et visualiser le contenu du cours, vous pouvez accéder gratuitement au cours en tant qu'auditeur libre.
Quelle est la politique de remboursement ?
Une aide financière est-elle possible ?
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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