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 | 英語（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
Cada curso es como un libro de texto interactivo, con videos pregrabados, cuestionarios y proyectos.
Conéctate con miles de estudiantes y debate ideas y materiales del curso, y obtén ayuda para dominar los conceptos.
Obtén reconocimiento oficial por tu trabajo y comparte tu éxito con amigos, compañeros y empleadores.
amazing knowledge
I learnt all the basics I wanted to very properly, the course was very helpful.
Great course - very clear and practical. I appreciate the professor's teaching as well as the exams.
good