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
от партнера
Корейский ведущий научно-технический институт
Программа курса: что вы изучите
Неделя
12 ч. на завершение
Introduction
9 видео ((всего 76 мин.)), 1 тест
9 видео
1-2 Order and Normal Form6мин
1-3 Linear and Nonlinear Equations5мин
1-4 Solution5мин
1-5 Implicit Solution11мин
1-6 Types of Solutions12мин
1-7 Initial Value Problem10мин
1-8 Picard’s Theorem I10мин
1-9 Picard’s Theorem II9мин
1 практическое упражнение
Quiz116мин
Неделя
22 ч. на завершение
First Order Differential Equation 1
9 видео ((всего 85 мин.)), 1 тест
9 видео
2-2 Separable Equations - Ex’s 1 & 28мин
2-3 Separable Equations - Ex’s 3 & 49мин
2-4 Integrating Factor12мин
2-5 Does IVP Have a Unique Solution?6мин
2-6 Exact Equations I8мин
2-7 Exact Equations II18мин
2-8 Exact Equations – Ex. 110мин
2-9 Exact Equations – Ex. 25мин
1 практическое упражнение
Quiz212мин
Неделя
32 ч. на завершение
FIRST ORDER DEFERENTIAL EQUATION 2
12 видео ((всего 104 мин.)), 1 тест
12 видео
3-2 Integrating Factor II7мин
3.3 Integrating Factor III10мин
3-4 Substitutions, Ex 18мин
3-5 Homogeneous Equations9мин
3-6 Substitutions Ex's 2 & 39мин
3-7 Bernoulli Equation9мин
3-8 Equations with Linear Coefficients9мин
3-9 Equations with Linear Coefficients - Ex. 57мин
3-10 Ricatti's Equation - Ex. 69мин
3-11 Clairaut's Equation8мин
3-12 Clairaut's Equation - Ex. 76мин
1 практическое упражнение
Quiz 312мин
Неделя
41 ч. на завершение
Mathematical Modeling and Applications
5 видео ((всего 54 мин.)), 1 тест
5 видео
4-2 Population Dynamics I9мин
4-3 Population Dynamics II7мин
4-4 Population Dynamics III13мин
4-5 Population Dynamics IV11мин
1 практическое упражнение
Quiz410мин
4.6
Рецензии: 5133%
получил значимые преимущества в карьере благодаря этому курсу
Лучшие рецензии
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.
Преподаватели
Kwon, Kil Hyun
ProfessorDepartment of Mathematical Sciences
О Корейский ведущий научно-технический институт
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.
Часто задаваемые вопросы
Когда я получу доступ к лекциям и заданиям?
Зарегистрировавшись на сертификацию, вы получите доступ ко всем видео, тестам и заданиям по программированию (если они предусмотрены). Задания по взаимной оценке сокурсниками можно сдавать и проверять только после начала сессии. Если вы проходите курс без оплаты, некоторые задания могут быть недоступны.
Что я получу, оплатив сертификацию?
Оплатив сертификацию, вы получите доступ ко всем материалам курса, включая оцениваемые задания. После успешного прохождения курса на странице ваших достижений появится электронный сертификат. Оттуда его можно распечатать или прикрепить к профилю LinkedIn. Просто ознакомиться с содержанием курса можно бесплатно.
Какие правила возврата средств?
Можно ли получить финансовую помощь?
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.
Остались вопросы? Посетите Центр поддержки учащихся.
Coursera делает лучшее в мире образование доступным каждому, предлагая онлайн-курсы от ведущих университетов и организаций.
© Coursera Inc., 2019 Все права защищены.
