## Mathematics & Science
Learning Center |
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## Solving Systems## General IntroductionIf you think back to your course in - The concept of the
*variable*was introduced. *Equations of a single variable*were introduced, along with the idea that they had*solutions*(which consisted of either real or complex numbers) that satisfied the equation when substituted for the variable.- Methods of finding
*exact solutions*were discussed, starting with very basic methods for solving linear equations, and then leading into more sophisticated methods for solving non-linear equations of various types. - If you had a really good course, then it was admitted that sometimes it
would be necessary to
*find the solutions approximately using numerical algorithms*.
Doesn't this sequence look familiar when compared to the concepts you have
been learning in So, if you're wondering what might come next in your differential equations
course, you might look back to what came next in your algebra course for a
hint. You'll recall that The parallel between your algebra course and this differential equations course keeps
right on track here! In thousands of physical situations we encounter several
functions which are related to one another, and are all dependent on an
independent variable, say time. In such instances we develop ## An Introductory ExampleAs is often the case when introducing a new idea in mathematics, we'll learn the most efficiently if we start with an example. Let's say that we have two time dependent functions,
You can check on paper that a solution set of Let's use |
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ODE Laboratories: A Sabbatical Project by Christopher A. Barker©2017 San Joaquin Delta College, 5151 Pacific Ave., Stockton, CA 95207, USA e-mail: cbarker@deltacollege.edu |