Exploring Partial Derivatives in GeoGebra 3D

Рет қаралды 12,772

Күн бұрын

Link to typed up directions: bit.ly/2S2nesk
In this video we use GeoGebra 3D (head to geogebra.org and pick the 3D graphing calculator) to get a sense of what partial derivatives really are and how we can visualize them. We're trying to answer the question, "But what are they?" We focus on partial x, dz/dx, but repeat the construction for partial y at the end.
Specifically we: plot a curve, plot a vertical plane, plot the trace of the curve in the plane, put a point on the trace, calculate the appropriate partial derivative, and write the equation of the line tangent to the trace at the point in the plane. There's a lot going on and we use some sliders to make things more dynamic.
Being able to see what you're talking and thinking about helps a ton. Even just playing around with this kind of construction once or twice can help you picture it in your head going forward.

Пікірлер: 24

@turksvids 5 жыл бұрын

Find typed up directions for this stuff here: bit.ly/2S2nesk I forgot to say it until pretty late in the video!

@flwi 3 жыл бұрын

Man, I wish I had this visualization during my studies. Awesome work!

@dpmike32819 3 жыл бұрын

Absolutely magnificent on understanding partial derivative… Thank you very much for your time

@danv8718 5 жыл бұрын

Fantastic video! thank you for sharing. This is really fantastic to get an intuitive feeling for partial derivatives.

@turksvids 5 жыл бұрын

Glad it helps a bit!

@xinzhang8793 3 жыл бұрын

Super helpful! Thanks a bunch!

@mathsriemann8778 5 жыл бұрын

great video. Keep it up

@alexgts1234 2 жыл бұрын

Amazing video...really.

@mathsonlineacademy9852 3 жыл бұрын

Thank you v much Sir. Rafi from Pakistan

@userutoob7 3 жыл бұрын

Great video! It is very informative. Did you post this project with the geogebra resources? If so, please share a link. Thanks. AB

@turksvids 3 жыл бұрын

I have a super bad habit of not even saving my GeoGebra sketches...I looked through and couldn't find it anywhere. Searching GeoGebra.org, though, I found some that look very similar, so give that shot! Glad you liked the video!

@userutoob7 3 жыл бұрын

@@turksvids I'll search. hope I can find one as good as yours. ab

@warrenyazzie9975 2 жыл бұрын

The weird shadow has to deal with the precision of the graphing software. If you go to Settings for the equation and then Style, you will see an option for "Level of Detail". Change that option from "Speed" to "Quality".

@turksvids 2 жыл бұрын

Thanks for the tip! I’ve never explored that option before.

@celsiusfahrenheit1176 2 жыл бұрын

In the end, it is almost like a ship sailing the ocean, heading and rocking on top of those waves.

@dpmike32819 2 жыл бұрын

How do I insert a directional vector (Gradient) to give max slope?

@turksvids 2 жыл бұрын

If you poke around in the algebra view of the linked sketch you might find your answer. If not, I can try to type something up a bit later. www.geogebra.org/classic/qjszthd8

@BenSmithMath 4 жыл бұрын

I love this video. The result was very helpful for teaching my multivariable calculus class today. But I wasn't able to get it to work completely, because geogebra is being very weird about the variable name yc, for some reason. Sometimes, when I typed the curve(...) function, with yc in it, it would replace the yc with zero, so that it wasn't dependent on the yc slider at all. Clicking on the curve to open the definition and properties showed that it was still in terms of yc, but the graph showed it stuck at y=0 no matter what the yc slider did. I tried it again with different variable names and it happened again. Sometimes, the first curve was fine but the second curve had the problem. Sometimes the first curve had the problem. It happened on both geogebra.org and on the geogebra 5 desktop app. There's something I'm missing about dependent objects based on sliders.

@BenSmithMath 4 жыл бұрын

Update: I asked the same question in the Geogebra help forums, and got a response. Apparently it is a bug which doesn't happen to everyone. But one way to fix it is to save the file, close it, and re-open it again.

@turksvids 4 жыл бұрын

Good deal! I'm glad you found a solution. I was not able to duplicate the problem so I guess I've gotten lucky so far!

@BenSmithMath 4 жыл бұрын

@@turksvids It looks like it is a problem on windows machines (using geogebra classic 5, classic 6, or the webapp) but not on macs which it looks like you've got.