About this course
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,
- Three or more species competing for resources in an ecosystem,
- The trajectory of a rider on a zipline.
*Zipline photo by teanitiki on Flickr (CC BY-SA 2.0)
What you'll learn
- 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.
- Solving linear systems: elimination and RREF
- Nullspace, vector space
- Column space, determinants, and inverses
- eigenvalues, eigenvectors, and diagonalization
- Solving homogeneous NxN systems of differential equations
- Matrix exponential and diagonalization
- Decoupling and solving inhomogeneous systems of equations
- Solving nonlinear systems with MATLAB
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Frequently asked questions
We assume familiarity with both 18.031x Introduction to Differential Equations and 18.032x Differential Equations: 2x2 systems. Knowledge from 18.03Lx is not required to succeed in this course.
Who can take this course?
Unfortunately, learners from one or more of the following countries or regions will not be able to register for this course: Iran, Cuba and the Crimea region of Ukraine. While edX has sought licenses from the U.S. Office of Foreign Assets Control (OFAC) to offer our courses to learners in these countries and regions, the licenses we have received are not broad enough to allow us to offer this course in all locations. EdX truly regrets that U.S. sanctions prevent us from offering all of our courses to everyone, no matter where they live.