Level curves Instructor: David Jordan View the complete course: ocw.mit.edu/18-... License: Creative Commons BY-NC-SA More information at ocw.mit.edu/terms More courses at ocw.mit.edu
For example C, instead of breaking x^2-y^2=0 into (x+y)(x-y), you could set y^2=x^2. Taking the square root of both sides gives you y=x and y=-x, which are the 2 lines which form the X shape through the origin.
take different constants of z. z=0 will give you two straight lines, z=1 and onwards will give you the curved lines that are symmetric to the y-axis and z=-1 and lower will give you the curved lines that are symmetric to the x-axis
im glad im not the only one struggling with 3d graphing and visualization. this guy had a hard time explaining the shape for C, understandably so. 3d->2d is a bit harsh for professors to make us do when we have computer software for it.
thats the engineering system day by day theyre changing the curiculum maybe when our generation have kids we will see that changing in the science department courses
At 6:29 David says it's a Hyperboloid of Two Sheets, but I think it is actually a Hyperbolic Paraboloid. The general formula for the graph of that Quadric Surface is z = x^2 - y^2, which matches the saddle description he gives.
Jeremiah Brookes I think it is too. A hyperbolic paraboloid has the saddle shape and the form z=(x/a)^2-(y/b)^2. For it to be a 2 sheet hyperboloid it'd have to be equal to 1 and all variables squared.
really good video, very informative and easy to learn from. One thing though is that I believe that at 7:30 when you start to draw the hyperbola only the first two you draw are correct, if you rearrange z=x^2 -y^2 you get -/+x=(y^2+z)^1/2 so the absolute value of x will always be greater than y, the saddle you draw later on actually adheres to this idea.
wouldn't part C be considered a hyperbolic paraboloid? not a hyperboloid of 2 sheets? standard form for a hyperboloid of 2 sheets is (x/a)^2+(y/b)^2=(z/c)^2-1
I'll admit. The last time I seen or used a chalk board was 2001. And with computers, touch screen and stylus, and smartboards, I'm seeing less usage of whiteboard too. Very informative video! :)
BeyondSkys09 Your comment is dumb. If you attended any accredited university, except perhaps an online school like the University of Phoenix, you would find that all math departments still use chalk boards especially for large introductory classes like Calculus III, which this video is for. Blackboards are big enough to see in large lecture halls and provide professors the mobility they need to lecture easily and get rid of mistakes they may possibly make quickly.
BeyondSkys09 Dawg are you for real. Its MIT. They can write on toilet paper for all I care. If it wasn't for opencourseware I and many other engineers/ scientists would be screwed. And yah I dont mind white boards. My only problem is that I have been unfortunate enough to have most of my professors right in green marker in a room that has an overall green tint. It just straines the eyes after a while.
+Michael Donovan same here at University of Wisconsin - Madison. All math and chemistry lecture halls/classrooms all use chalkboards. They don't smell bad like whiteboards lol.
They use projectors at my uni. They lecturer can switch between slide shows or a camera which can show them working things out on pen and paper. Its good for us who only watch lectures online.
Yeah. Basically we're in big troubles. It is a simple manner to let you decide how you're going to manage your life at this point. Once again. It is a guide-life you're free to just trash or whatever. Take it like a general idea of what success could be if you decide to follow what sounds thrilling to your self. It's free so help yourself. *It is entirely up to you* #bestpart
Only person I've understood so far thank you! Very well explained. Good boy. Good little boy you. Come and have a cookie. Have a little cookie. Come her you good little boy. Have a cookie. Yes. Yes. Take the cookie. Good boy. Eat that cookie up. Such a good boy. You like that cookie don't you. Good boy. Good little boy.
I think there is a tiny mistake in how he drew the axes of the coordinate system: The arrow which is captioned with some variable should be pointing in the direction where the variable increases, therefore it is not crrect to draw an axis pointing in BOTH directions ;)
