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
ofrecido por
Instituto Avanzado de Ciencia y Tecnología de Corea
Programa - Qué aprenderás en este curso
Semana
12 horas para completar
Introduction
9 videos (Total 76 minutos), 1 quiz
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 ejercicio de práctica
Quiz116m
Semana
22 horas para completar
First Order Differential Equation 1
9 videos (Total 85 minutos), 1 quiz
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 ejercicio de práctica
Quiz212m
Semana
32 horas para completar
FIRST ORDER DEFERENTIAL EQUATION 2
12 videos (Total 104 minutos), 1 quiz
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 ejercicio de práctica
Quiz 312m
Semana
41 hora para completar
Mathematical Modeling and Applications
5 videos (Total 54 minutos), 1 quiz
5 videos
4-2 Population Dynamics I9m
4-3 Population Dynamics II7m
4-4 Population Dynamics III13m
4-5 Population Dynamics IV11m
1 ejercicio de práctica
Quiz410m
50%
consiguió un beneficio tangible en su carrera profesional gracias a este curso
Principales revisiones
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.
Instructor
Kwon, Kil Hyun
ProfessorDepartment of Mathematical Sciences
Acerca de Instituto Avanzado de Ciencia y Tecnología de Corea
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.
Preguntas Frecuentes
¿Cuándo podré acceder a las lecciones y tareas?
Una vez que te inscribes para obtener un Certificado, tendrás acceso a todos los videos, cuestionarios y tareas de programación (si corresponde). Las tareas calificadas por compañeros solo pueden enviarse y revisarse una vez que haya comenzado tu sesión. Si eliges explorar el curso sin comprarlo, es posible que no puedas acceder a determinadas tareas.
¿Qué recibiré si compro el Certificado?
Cuando compras un Certificado, obtienes acceso a todos los materiales del curso, incluidas las tareas calificadas. Una vez que completes el curso, se añadirá tu Certificado electrónico a la página Logros. Desde allí, puedes imprimir tu Certificado o añadirlo a tu perfil de LinkedIn. Si solo quieres leer y visualizar el contenido del curso, puedes participar del curso como oyente sin costo.
¿Cuál es la política de reembolsos?
¿Hay ayuda económica disponible?
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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