Об этом курсе: 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.
Для кого этот курс: This course is recommended for undergraduate students in mathematics, physics, engineering and the social sciences who want to learn basic concepts and ideas of ordinary differential equations. Learners are required to know usual college level calculus including differential and integral calculus.
Преподаватели: Kwon, Kil Hyun, Professor
Department of Mathematical Sciences
| Уровень | Начинающий |
| Выполнение | 2-3 hours/week |
| Язык | English |
| Как пройти курс | Чтобы пройти курс, выполните все оцениваемые задания. |
| Оценки пользователей |
- Видео: 1-2 Order and Normal Form
- Видео: 1-3 Linear and Nonlinear Equations
- Видео: 1-4 Solution
- Видео: 1-5 Implicit Solution
- Видео: 1-6 Types of Solutions
- Видео: 1-7 Initial Value Problem
- Видео: 1-8 Picard’s Theorem I
- Видео: 1-9 Picard’s Theorem II
- Видео: 2-2 Separable Equations - Ex’s 1 & 2
- Видео: 2-3 Separable Equations - Ex’s 3 & 4
- Видео: 2-4 Integrating Factor
- Видео: 2-5 Does IVP Have a Unique Solution?
- Видео: 2-6 Exact Equations I
- Видео: 2-7 Exact Equations II
- Видео: 2-8 Exact Equations – Ex. 1
- Видео: 2-9 Exact Equations – Ex. 2
- Видео: 3-2 Integrating Factor II
- Видео: 3.3 Integrating Factor III
- Видео: 3-4 Substitutions, Ex 1
- Видео: 3-5 Homogeneous Equations
- Видео: 3-6 Substitutions Ex's 2 & 3
- Видео: 3-7 Bernoulli Equation
- Видео: 3-8 Equations with Linear Coefficients
- Видео: 3-9 Equations with Linear Coefficients - Ex. 5
- Видео: 3-10 Ricatti's Equation - Ex. 6
- Видео: 3-11 Clairaut's Equation
- Видео: 3-12 Clairaut's Equation - Ex. 7
- Видео: 4-2 Population Dynamics I
- Видео: 4-3 Population Dynamics II
- Видео: 4-4 Population Dynamics III
- Видео: 4-5 Population Dynamics IV
- Видео: 5-2 Superposition Principle
- Видео: 5-3 Unique Existence of Solution
- Видео: 5-4 Linear independence
- Видео: 5-5 Wronskian test
- Видео: 6-2 General solutions
- Видео: 6-3 Nonhomogeneous equations I
- Видео: 6-4 Nonhomogeneous equations II
- Видео: 6-5 Reduction of order I
- Видео: 6-6 Reduction of order II
- Видео: 6-7 Homogeneous linear equations with constant coefficients
- Видео: 6-8 Homogeneous linear equations – Example
- Видео: 6-9 Higher order equations
- Видео: 7-2 Annihilator – Ex. 2
- Видео: 7-3 Method of undetermined coefficients I
- Видео: 7-4 Method of undetermined coefficients II – Ex. 3
- Видео: 7-5 Method of undetermined coefficients - Ex. 4
- Видео: 8-2 Variation of parameters II
- Видео: 8-3 Variation of parameters III – Ex. 1
- Видео: 8-4 Variation of parameters IV – Ex. 2
- Видео: 9-2 Free undamped motion – Ex. 1
- Видео: 9-3 Free & Forced damped motion
- Видео: 9-4 Spring-mass system – Ex’s 2 & 3
- Видео: 9-5 Pendulum
Each course is like an interactive textbook, featuring pre-recorded videos, quizzes and projects.
Connect with thousands of other learners and debate ideas, discuss course material, and get help mastering concepts.
Earn official recognition for your work, and share your success with friends, colleagues, and employers.
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.
A very useful lesson for those students wanting to take a step further than AP/ALevel and freshmen that are struggling with math classes.
Great work! now i have knowledge about differential equation after completions of this course. i learned some basic concept related to differential equations and also physical meaning of differential equations.
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 .