Course description
Differential Equations: 2x2 Systems
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.
Upcoming start dates
Who should attend?
Prerequisites
18.031x Introduction to Differential Equations (Scalar equations)
Training content
Unit 1: Linear 2x2 systems
- Introduction to systems of differential equations
- Solving 2x2 homogeneous linear systems of differential equations
- Complex eigenvalues, phase portraits, and energy
- The trace-determinant plane and stability
Unit 2: Nonlinear 2x2 systems
- Linear approximation of autonomous systems
- Stability of autonomous systems
- Nonlinear pendulum
Course delivery details
This course is offered through Massachusetts Institute of Technology, a partner institute of EdX.
2-5 hours per week
Costs
- Verified Track -$75
- Audit Track - Free
Certification / Credits
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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