Differential Equations: 2x2 Systems
In order to understand most phenomena in the world, we need to understand not just single equations, but systems of differential equations. In this course, we start with 2x2 systems.
Course Information
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About this Course
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
- RLC circuits that tune to specific frequencies
This is part of a 5-part series in Differential Equations:
- 18.03.1x: Introduction to Differential Equations
- 18.03.2x: Differential Equations: 2x2 Systems
- 18.03.3x: Linear Algebra and NxN Systems
- 18.03.Fx: Differential Equations: Fourier Series and Heat Equation
- 18.03.Lx: Systems Functions and the Laplace Transform
- Wolf photo by Arne von Brill on Flickr (CC BY 2.0)
- Rabbit photo by Marit & Toomas Hinnosaar on Flickr (CC BY 2.0)[1]
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
Prerequisites
Meet your instructors
David Jerison
Professor of Mathematics
David Jerison received his Ph.D. from Princeton University in 1980, and joined the mathematics faculty at MIT in 1981. In 1985, he received an A.P. Sloan Foundation Fellowship and a Presidential Young Investigator Award. In 1999 he was elected to the American Academy of Arts and Sciences. In 2004, he was selected for a Margaret MacVicar Faculty Fellowship in recognition of his teaching. In 2012, the American Mathematical Society awarded him and his collaborator Jack Lee the Bergman Prize in Complex Analysis.
Professor Jerison's research focuses on PDEs and Fourier Analysis. He has taught single variable calculus, multivariable calculus, and differential equations at MIT several times each.
