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Math Help - Understanding contours and level curves, drawing functions of several variables

  1. #1
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    Understanding contours and level curves, drawing functions of several variables

    This topic has me increasingly confused.

    At some point I realised that essentially contours are really just a way of visualising 3d shapes in a 2d plane. Please correct me if I'm not entirely right.
    for example, as seen here:
    http://i.imgur.com/XgtalfW.jpg

    But then during a lecture, the lecturer drew this:
    http://i.imgur.com/MxyMzsC.jpg

    Why are there dashed lines parallel to all sides of the triangle in the first example?
    And the contour representation shown, wouldn't that form a rectangle and not a triangle? This has me incredibly confused.
    We use the Stewarts Multivariable calculus (7th ed) textbook, would any of you recommend a different textbook or any online resources to understand this topic? I have a test on drawing functions of several variables in 4 days and just cannot seem to get a grasp on it, in addition to drawing their contours and level curves.

    For the life of me I have no idea what the dashed lines in this diagram mean. Are they the contour lines for the graph of sin(x+y) ?
    http://i.imgur.com/IhI2cJP.jpg
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  2. #2
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    Re: Understanding contours and level curves, drawing functions of several variables

    Hey 99.95.

    The contours represent the region that lies on a particular plane.

    The first image literally only has a cross section but the second one encompasses the whole plane since the triangle is itself a flat object on that plane that is defined by the relevant contour and a plane extends to an infinite area.
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  3. #3
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    Re: Understanding contours and level curves, drawing functions of several variables

    I'm starting to better understand this.

    the MIT Lectures on this topic REALLY helped
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