Differential Equations: 2x2 Systems

开始时间: 04/22/2022 持续时间: 9 weeks

所在平台: EdxArchive 课程类别: 其他类别 大学或机构: MITx 授课老师： David Jerison

课程主页: https://www.edx.org/archive/differential-equations-2x2-systems-mitx-18-032x

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课程详情

Differential equations are the language of the models we use to describe the world around us. Most phenomena require not a single differential equation, but a system of coupled differential equations. In this course, we will develop the mathematical toolset needed to understand 2x2 systems of first order linear and nonlinear differential equations. We will use 2x2 systems and matrices to model:

• predator-prey populations in an ecosystem,
• competition for tourism between two states,
• the temperature profile of a soft boiling egg,
• automobile suspensions for a smooth ride,
• pendulums, and
• RLC circuits that tune to specific frequencies.

* Wolf photo by Arne von Brill on Flickr (CC BY 2.0)
* Rabbit photo by Marit & Toomas Hinnosaar on Flickr (CC BY 2.0)

课程大纲

• How to model real world problems by 2x2 systems of differential equations
• How to use matrix methods to solve homogeneous systems of 2 first order linear differential equations
• How to use graphical methods to understand the qualitative behavior of linear and nonlinear systems, and how to apply linear approximation to nonlinear (autonomous) 2x2 systems

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