Скачать или смотреть Plotting a Slope Field with TikZ (Unlocking LaTeX Graphics, Ep. 60)

In this episode of Unlocking LaTeX Graphics, applied mathematician Tammy Kolda shows how to draw slope fields in LaTeX using pure TikZ. A slope field visualizes a differential equation dy/dx = f(x,y) by drawing short normalized line segments at each grid point. She explains slope fields for differential equations of the form dy/dx = f(x,y) and demonstrates how to build a plot by manually drawing axes and tick marks, then using nested foreach loops to place normalized line segments on a grid. Starting with f(x,y) = x − y, she derives how to compute segment endpoints so every line has fixed length, then adds a title and swaps in other functions such as f(x,y)=sin(x)+y and f(x,y)=sin(xy). She also shows a case where TikZ fails, previewing a future PGFPLOTS-based approach. She concludes with a workaround for vertical slopes in f(x,y)=2cos(x)/y using if-then-else. This is part one of a multi-part series; a future video will cover the PGFPLOTS approach using quiver plots.

00:00 Welcome and Intro
01:20 What is a Slope Field
02:15 Document Setup
02:34 Drawing Axes
03:26 Adding Axis Tick Marks
04:32 Drawing the Slope Field for dy/dx = x-y
07:16 Adding a Title
07:26 Changing the Function to dy/dx = sin(x)+y
07:53 Changing the function to dy/dx = sin(xy)
08:04 Problems Plotting an Exponential
08:28 Handling Vertical Slopes for dy/dx = cos(x)/y
09:32 Thanks for Watching

Key terms: texlatex, TikZ, slope field, differential equations, foreach loop, pgfmathsetmacro

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