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
Korea Advanced Institute of Science and Technology(KAIST)Über diesen Kurs
235,271 kürzliche Aufrufe
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25%
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Zertifikat zur Vorlage
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100 % online
Beginnen Sie sofort und lernen Sie in Ihrem eigenen Tempo.
Flexible Fristen
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Stufe „Anfänger“
Ca. 12 Stunden zum Abschließen
Englisch
Untertitel: Englisch
Karriereergebnisse der Lernenden
25%
ziehen Sie für Ihren Beruf greifbaren Nutzen aus diesem Kurs
Zertifikat zur Vorlage
Erhalten Sie nach Abschluss ein Zertifikat
100 % online
Beginnen Sie sofort und lernen Sie in Ihrem eigenen Tempo.
Flexible Fristen
Setzen Sie Fristen gemäß Ihrem Zeitplan zurück.
Stufe „Anfänger“
Ca. 12 Stunden zum Abschließen
Englisch
Untertitel: Englisch
von
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.
Lehrplan - Was Sie in diesem Kurs lernen werden
2 Stunden zum Abschließen
Introduction
2 Stunden zum Abschließen
9 Videos (Gesamt 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 praktische Übung
Quiz116m
2 Stunden zum Abschließen
First Order Differential Equation 1
2 Stunden zum Abschließen
9 Videos (Gesamt 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 praktische Übung
Quiz212m
2 Stunden zum Abschließen
FIRST ORDER DEFERENTIAL EQUATION 2
2 Stunden zum Abschließen
12 Videos (Gesamt 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 praktische Übung
Quiz 312m
1 Stunde zum Abschließen
Mathematical Modeling and Applications
1 Stunde zum Abschließen
5 Videos (Gesamt 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 praktische Übung
Quiz410m
Bewertungen
Top-Bewertungen von INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS
von RV12. Jan. 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.
von CS13. Juni 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
von SK18. Juni 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 .
von 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.
Häufig gestellte Fragen
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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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