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Level curvesInstructor: David JordanView the complete course: http://ocw.mit.edu/18-02SCF10License: Creative Commons BY-NC-SAMore information at http://ocw.m...
- 10 min
- 353.4K
- MIT OpenCourseWare
Feb 28, 2021 · Calculus 3 video that explains level curves of functions of two variables and how to construct a contour map with level curves. We begin by introducing a typical temperature map as an...
- 21 min
- 22K
- Houston Math Prep
Given a function [latex]f\,(x,\ y)[/latex] and a number [latex]c[/latex] in the range of [latex]f[/latex], a level curve of a function of two variables for the value [latex]c[/latex] is defined to be the set of points satisfying the equation [latex]f\,(x,\ y)=c[/latex].
One way to collapse the graph of a scalar-valued function of two variables into a two-dimensional plot is through level curves. A level curve of a function $f(x,y)$ is the curve of points $(x,y)$ where $f(x,y)$ is some constant value. A level curve is simply a cross section of the graph of $z=f(x,y)$ taken at a constant value, say $z=c$. A ...
Level curves and contour plots are another way of visualizing functions of two variables. If you have seen a topographic map then you have seen a contour plot. Example: To illustrate this we first draw the graph of z = x2 + y2. On this graph we draw contours, which are curves at a fixed height z = constant.
Overview. In this session you will: Watch a lecture video clip and read board notes. Read course notes and examples. Watch two recitation videos. Work with a Mathlet to reinforce lecture concepts. Do problems and use solutions to check your work. Lecture Video. Video Excerpts. Clip: Level Curves and Contour Plots.
People also ask
What are level curves & contour plots?
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What is a level curve plot?
What is a level curve?
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Level Curves: The level curves of a function f of two variables are the curves with equations. f ( x, y ) = k. where k is a constant in the RANGE. of the function. A level € curve f ( x, y ) = k is a curve in the domain of f along which the graph of f has height k. € Contour Maps: A contour map is a collection of level curves.
