In this lesson, the geometrical view of differential equations is explored, specifically direction fields and integral curves. The lecture begins by assuming the viewer already knows how to separate variables and solve basic physical problems with differential equations. The focus is on first-order ODEs, which are written with the derivative of y isolated on the left and everything else on the right. The lecture explains how to draw a direction field and integral curves, and how they relate to finding solutions to differential equations. The importance of understanding the geometrical view of differential equations is emphasized, especially for blue equations that cannot be solved analytically.
The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves -- Lecture 1. Understanding the geometrical view of differential equations.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 23, 2008). License: Creative Commons BY-NC-SA.
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