SIMIODE

The matrix exponential is a powerful computational and conceptual tool for analyzing systems of linear, constant coefficient, ordinary differential equations (ODE's). This narrative offers a quick introduction to the technique, with examples and exercises. It also includes an introduction to Putzer's Algorithm for computing the matrix exponential, a topic not usually covered in introductory ODE courses. This simple algorithm allows one to compute the exponential of any matrix whose eigenvalues are known. A computer algebra system can be helpful for this material, since the computations can be a bit cumbersome. For the reader who wants to know a bit more, proofs for many results are included in an appendix. The analysis, however, relies only on elementary matrix algebra and techniques for series that most students see in a second semester calculus course.

Researchers should cite this work as follows:

• Kurt Bryan (2019), "5-010-S-MatrixExponential," https://www.simiode.org/resources/6424.

  BibTex | EndNote

1. constant coefficient
2. linear system
3. matrix exponential
4. ordinary differential equations
5. Putzer's Algorithm