Differential Equations: 2x2 Systems (edX)

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, Differential EquationsXSeries Program .

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:
Introduction to Differential Equations (Scalar equations)

Syllabus

Unit 1: Linear 2x2 systems

1. Introduction to systems of differential equations

2. Solving 2x2 homogeneous linear systems of differential equations

3. Complex eigenvalues, phase portraits, and energy

4. The trace-determinant plane and stability

Unit 2: Nonlinear 2x2 systems

5. Linear approximation of autonomous systems

6. Stability of autonomous systems

7. Nonlinear pendulum