Differential Equations
2x2 Systems
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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.
The five modules in this seriesare being offered as an XSeries on edX. Please visit the Differential EquationsXSeries Program Page to learn more and to enroll in the modules.
Wolf photo by Arne von Brill on Flickr (CC BY 2.0)
Rabbit photo by Marit & Toomas Hinnosaar on Flickr (CC BY 2.0)
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What you'll learn
- 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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| Rating | 5.0★ based on 4 ratings |
|---|---|
| Length | 10 weeks |
| Effort | 10 weeks, 2–5 hours per week |
| Starts | On Demand (Start anytime) |
| Cost | $75 |
| From | Massachusetts Institute of Technology, MITx via edX |
| Instructors | David Jerison, Kristin Kurianski, Jennifer French, Duncan Levear |
| Download Videos | On all desktop and mobile devices |
| Language | English |
| Subjects | Mathematics Science |
| Tags | Math Engineering Physics |
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What people are saying
differential equations
One of the best MOOC on topic of differential equations.
While there's plenty of challenge in this course, the third installment in MIT's five-part tour of differential equations, there is nothing to be afraid of.
math nerds need no
Math nerds need no encouragement to take this course, but those like me who appreciate math more for what it lets you do than for its own sake will find this course edifying, tractable and rewarding.
opens whole new possibilities
Building on the earlier courses, this one treats pairs of differential equations, which, it turns out, opens whole new possibilities for their application.
from romeo & juliet
The applications used for showing different scenarios are rich: From Romeo & Juliet to typical Predator & Pray and more.
done an outstanding job
The staff have done an outstanding job to bring this course on the edx platform.
doing fancy bits
Doing fancy bits of analysis such as creating "phase portraits" allows you to see how the system evolves from an arbitrary starting point, e.g., if you start with more wolves than deer, will the populations reach a stable equilibrium or will one or both populations go extinct?
arbitrary starting point
each including well-considered
There are six lecture sequences, each including well-considered problems that solidify your understanding, and "recitation" problems that, while graded, can be discussed freely.
interconnected mixing tanks
In pairs, differential equations can be used to simplify a higher-order equation, or more interestingly to model systems of interacting entities -- predator-prey populations, interconnected mixing tanks, and mechanical and electrical systems.
most intimidatingly nerdy
"2x2 Systems of Differential Equations" wins the prize for most intimidatingly nerdy course title ever (though the trophy will pass to the NxN systems course when that one launches).
2x2 systems
jen french
Thank you Jen French.
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| Rating | 5.0★ based on 4 ratings |
|---|---|
| Length | 10 weeks |
| Effort | 10 weeks, 2–5 hours per week |
| Starts | On Demand (Start anytime) |
| Cost | $75 |
| From | Massachusetts Institute of Technology, MITx via edX |
| Instructors | David Jerison, Kristin Kurianski, Jennifer French, Duncan Levear |
| Download Videos | On all desktop and mobile devices |
| Language | English |
| Subjects | Mathematics Science |
| Tags | Math Engineering Physics |
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