In this lecture, we learn about first-order systems of ODEs and how to solve them using elimination. A system of differential equations has to be solved simultaneously, meaning there are multiple dependent variables. We discuss the terminology of linear systems, constant coefficient systems, and homogenous systems. The lecture then takes an example of a problem of heat conduction with an egg that has white and yolk, and shows how to write the system in standard form. Finally, we learn that the number of arbitrary constants that appear is the total order of the system, and the same number of initial conditions must be specified.
Introduction to First-order Systems of ODEs; Solution by Elimination, Geometric Interpretation of a System -- Lecture 24. A very complete lecture on systems of differential equations.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 27, 2008). License: Creative Commons BY-NC-SA.
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