Differential Equations: 2x2 Systems

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Course Description

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)

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Reviews 9/10 stars
1 Review for Differential Equations: 2x2 Systems

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Steven Frank profile image
Steven Frank profile image
10/10 starsCompleted
  • 59 reviews
  • 57 completed
1 year, 6 months ago
"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). 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. Building on the earlier courses, this one treats pairs of differential equations, which, it turns out, opens whole new possibilities for their application. 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. 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 populatio... "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). 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. Building on the earlier courses, this one treats pairs of differential equations, which, it turns out, opens whole new possibilities for their application. 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. 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? The instruction in this course is unsurpassed, as befits MIT, never soaring above your head. There are six lecture sequences, each including well-considered problems that solidify your understanding, and "recitation" problems that, while graded, can be discussed freely. Together these count as 20% of the grade. There are also three A and B problem sets; the B-set problems are substantially more challenging than the A-set problems and count more heavily toward the final grade. The also-challenging but doable final exam counts for 45% of the final grade, so you don't want to blow that one. 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.
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