# Introduction to First-order Systems of ODEs; Solution by Elimination, Geometric Interpretation of a System

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Taught by OCW
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Lesson Summary:

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.

Lesson Description:

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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Additional Resources:
Questions answered by this video:
• What are first-order systems of ODEs?
• How do you solve First-order systems of ODEs?
• How do you solve systems of ODEs by elimination?
• What is the geometric interpretation of a system?
• What is an application of systems of differential equations?
• What is an autonomous system?
• What is a velocity field?
• #### Staff Review

• Currently 4.0/5 Stars.
The beginning of first-order systems of differential equations. From this lecture on, this will be the topic of discussion of the course. These are interesting because they must be solved simultaneously. This is a very involved lesson that includes real-world applications of several circuits connected together.