關於此課程：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.
此課程適用人群：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.
教學方： Kwon, Kil Hyun, Professor
Department of Mathematical Sciences
| 級別 | 初級 |
| 承諾學習時間 | 2-3 hours/week |
| 語言 | English |
| 如何通過 | 通過所有計分作業以完成課程。 |
| 用戶評分 |
- 視頻: 1-2 Order and Normal Form
- 視頻: 1-3 Linear and Nonlinear Equations
- 視頻: 1-4 Solution
- 視頻: 1-5 Implicit Solution
- 視頻: 1-6 Types of Solutions
- 視頻: 1-7 Initial Value Problem
- 視頻: 1-8 Picard’s Theorem I
- 視頻: 1-9 Picard’s Theorem II
- 視頻: 2-2 Separable Equations - Ex’s 1 & 2
- 視頻: 2-3 Separable Equations - Ex’s 3 & 4
- 視頻: 2-4 Integrating Factor
- 視頻: 2-5 Does IVP Have a Unique Solution?
- 視頻: 2-6 Exact Equations I
- 視頻: 2-7 Exact Equations II
- 視頻: 2-8 Exact Equations – Ex. 1
- 視頻: 2-9 Exact Equations – Ex. 2
- 視頻: 3-2 Integrating Factor II
- 視頻: 3.3 Integrating Factor III
- 視頻: 3-4 Substitutions, Ex 1
- 視頻: 3-5 Homogeneous Equations
- 視頻: 3-6 Substitutions Ex's 2 & 3
- 視頻: 3-7 Bernoulli Equation
- 視頻: 3-8 Equations with Linear Coefficients
- 視頻: 3-9 Equations with Linear Coefficients - Ex. 5
- 視頻: 3-10 Ricatti's Equation - Ex. 6
- 視頻: 3-11 Clairaut's Equation
- 視頻: 3-12 Clairaut's Equation - Ex. 7
- 視頻: 4-2 Population Dynamics I
- 視頻: 4-3 Population Dynamics II
- 視頻: 4-4 Population Dynamics III
- 視頻: 4-5 Population Dynamics IV
- 視頻: 5-2 Superposition Principle
- 視頻: 5-3 Unique Existence of Solution
- 視頻: 5-4 Linear independence
- 視頻: 5-5 Wronskian test
- 視頻: 6-2 General solutions
- 視頻: 6-3 Nonhomogeneous equations I
- 視頻: 6-4 Nonhomogeneous equations II
- 視頻: 6-5 Reduction of order I
- 視頻: 6-6 Reduction of order II
- 視頻: 6-7 Homogeneous linear equations with constant coefficients
- 視頻: 6-8 Homogeneous linear equations – Example
- 視頻: 6-9 Higher order equations
- 視頻: 7-2 Annihilator – Ex. 2
- 視頻: 7-3 Method of undetermined coefficients I
- 視頻: 7-4 Method of undetermined coefficients II – Ex. 3
- 視頻: 7-5 Method of undetermined coefficients - Ex. 4
- 視頻: 8-2 Variation of parameters II
- 視頻: 8-3 Variation of parameters III – Ex. 1
- 視頻: 8-4 Variation of parameters IV – Ex. 2
- 視頻: 9-2 Free undamped motion – Ex. 1
- 視頻: 9-3 Free & Forced damped motion
- 視頻: 9-4 Spring-mass system – Ex’s 2 & 3
- 視頻: 9-5 Pendulum
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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 .