Lecture 6 | Differential Equations | Geometrical Interpretation of Slope fields using Octave and Desmos.
Welcome to this lecture on the geometrical interpretation of slope fields and how to use octave and desmos to unlock the meaning. Slope fields are a great way to understand the derivative of a function, a vector field that helps us visualize how a given function changes with respect to its input. We'll take a look at interpreting slope fields, using octave and desmos to visualize them, and how to use them to gain a better understanding of the meaning of slope fields. We'll explore some examples and see how this can help us better understand the behavior of a given function. Join us and let's get started!
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Chapters
00:00 Geometric meaning of y'(x)=f(x,y)
01:25 Problem 1: dy/dy=x+y
02:03 Using GNU Octave 7.3 to plot the direction field (slope field) for the ODE given in Problem 1
02:42 Plot of the Slope Field
03:13 dy/dy=x+y has the implicit solution x+y+1=Ce^x
03:33 Using Desmos to plot the solution curves for x+y+1=Ce^x with different values of C
Get a free copy of GNU Octave 7.3 from the official website
[ Ссылка ]
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