Fundamental confusions of calculus

[Pete]

Thanks again temur, you have been most helpful.
AlphaNumeric,
I'm good again now, so don't let this exchange stop you from closing the thread if you see fit - make your judgment based on the przyk/Tach/Trippy conversation. I'll open another thread if/when I have more to ask

 

[Tach]

No, I wouldn't have any difficulty answering any of these questions, and nor would anyone else participating in this thread, and you know it. What does that have to do with anything?

It has to do with answering a simple question. So, please answer it.

 

[Tach]

...would that be interpreted as equivalent to

$$\frac{\partial}{\partial \theta}z(\theta,u,v) = \frac{\partial}{\partial \theta}(3\theta + u + v)$$​

So after 200 posts it is still not obvious? Is the presence of v making things so difficult? It isn't a trick question. Maybe you'll find this easier to answer:


$$z=3 \theta +u$$
$$u=sin^2(\theta)$$


What is $$\frac{\partial z}{\partial \theta}$$?
What is $$\frac{d z}{d \theta}$$?

 

[prometheus]

The fact that six of you (AN, you, rpenner, przyk, Guest254, prometheus) argue(d) against only one of me doesn't make you right and me wrong. At least, prometheus stopped arguing, once he realized that he might be on the wrong side of the argument.

For the record you were wrong and you are still wrong. The reason my posting has been sporadic recently is we're quite busy at work at the moment, I'm trying to buy a house and the other 5 people you mention raise the issues I think of before I have a chance to do it.

 

[prometheus]

So after 200 posts it is still not obvious? Is the presence of v making things so difficult? It isn't a trick question. Maybe you'll find this easier to answer:


$$z=3 \theta +u$$
$$u=sin^2(\theta)$$


What is $$\frac{\partial z}{\partial \theta}$$?
What is $$\frac{d z}{d \theta}$$?

Since I'm here, for a function of one variable $$\frac{\partial z}{\partial \theta} = \frac{d z}{d \theta}$$. If this wasn't the case then the method of separation of variables for solving PDE's wouldn't work.

 

[Tach]

Because of your insistence that you defined u in the first place, which you didn't, followed by your insistence that you defined u as being a particular thing, when you've defined it as being two different things.

Any person in good faith could link in the first part of post 18 with the example and easily identify $$u$$ . Now, it takes extreme bad faith , especially given multiple clarifications to still not understand the example. I admit that post 18 was terse (since I had been trying to explain the issue of derivatives of composite functions to Pete for about 50 posts already spread over two threads) but the repeated clarifications do not leave any room to misinterpret things. Having said that , $$u$$ can be defined as either one of the cases $$sin^2(\theta)$$ or $$sin(\theta)$$ and the result is exactly the same. So, once again, why do you bring this up?

 

[Guest254]

Could we change the thread title to:

**Tach's** Fundamental confusions of calculus

Please? And just in case Tach's ridiculous errors are being buried in a sea of deflection and chest beating, here they are again.

$$f(\theta, x) =3 \theta+ sin^2(\theta)+ln(x) \\
\frac{\partial }{\partial \theta} f(\theta, x)= 3 + 2 \sin(\theta) \cos (\theta)$$​

Your claim that $$\frac{\partial }{\partial \theta} f(\theta, x)= 3 + 2 \sin(\theta) \cos (\theta)$$ is outright wrong because it shows that you do not understand the meaning of partial differentiation.

Either way , your claim that $$\frac{\partial}{\partial \theta} \Bigl( 3 \theta \,+\, \sin(\theta)^{2} \,+\, \ln(x) \Bigr) \,=\, 3 \,+\, \sin(2\theta)$$ is false since the partial derivative is always taken wrt the direct variable (in this case, $$\theta$$) and not through a function (in this case $$\sin(\theta)$$).

 

[Trippy]

Any person in good faith could link in the first part of post 18 with the example and easily identify $$u$$ . Now, it takes extreme bad faith , especially given multiple clarifications to still not understand the example.

I'm done with this stupidity, feel free to rename and close the thread AN.

 

[AlphaNumeric]

Sorry, I was a little tardy getting back to the thread. Blame a broken washing machine and a pile of drenched clothes for taking my attention this morning. Tach's complete lack of mathematical aptitude and general dearth of honesty has been shown again and again and everyone who wanted their pound of flesh has had a chance to use their butter knives. There's nothing to be further gained from this. If Tach feels he is surrounded by idiots with PhD after their names then he's welcome not to bother with the forum again. I'm sure we'll struggle on with our research without his 'gems of wisdom'.

[Mod action] : And so we're done.

 

[Tach]

Since I'm here, for a function of one variable $$\frac{\partial z}{\partial \theta} = \frac{d z}{d \theta}$$. If this wasn't the case then the method of separation of variables for solving PDE's wouldn't work.

That would be extremely difficult , if not downright impossible since :

$$\frac{\partial z}{\partial \theta}=3$$

and

$$\frac{d z}{d \theta}=3+sin(2 \theta)$$

Incidentally, this is also Guest254's error , posted in very large fonts, lest someone misses it.

 

[AlphaNumeric]

It seems Tach got in between my post and clicking the lock button. Fortunately it basically sums up his misunderstanding, which gives a nice round to the thread.