Differential Equations: Linear Algebra and NxN Systems of Differential Equations
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Brief Introduction
Learn how to use linear algebra and MATLAB to solve large systems of differential equations.
Description
Differential equations are the mathematical language we use to describe the world around us. Most phenomena can be modeled not by single differential equations, but by systems of interacting differential equations. These systems may consist of many equations. In this course, we will learn how to use linear algebra to solve systems of more than 2 differential equations. We will also learn to use MATLAB to assist us.
We will use systems of equations and matrices to explore:
- The original page ranking systems used by Google,
- Balancing chemical reaction equations,
- Tuned mass dampers and other coupled oscillators,
- Threeor more species competing for resources in an ecosystem,
- The trajectory of a rider on a zipline.
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.
*Zipline photo by teanitiki on Flickr (CC BY-SA 2.0)
Knowledge
- After this course, you will be able to
- Model and solve different real world phenomena with systems of differential equations.
- Find the dimension and a basis for a (finite dimensional) vector space.
- Formulate and solve eigenvalue and eigenvector problems.
- Use MATLAB to explore solutions to large systems of equations.
Differential Equations: Linear Algebra and NxN Systems of Differential Equations
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Learn how to use linear algebra and MATLAB to solve large systems of differential equations. Differential equations are the mathematical language we use to describe the world around us....
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