Recent content by TheFerruccio

So that was the first thing I did when posed with this problem but there is probably a mental block that I am missing that is completely obvious here. Even with the explanations I still don't understand what is being done. I understand the case of finding sqrt(x) using just the C and D scales...

I would have replied to the older thread but it seems that is not possible, so I will have to post my question here. https://www.physicsforums.com/threads/slide-rule.245855/ @BobG mentioned being able to solve a particular problem: exp(x)=x^4 really quickly using a slide rule. He emphasized...

Both of these are very good ideas. I will see if I can do these. I went to the professor and he said that it's probably in a table somewhere, so I do not think he did the algebra either. After seeing a square root of squares, I did default to thinking it must be some kind of triangle equality...

Homework Statement Evaluate the integral. Homework Equations $$\int{\arccos{\frac{a}{a+\alpha}}\sqrt{\frac{(a+\alpha)^2}{(a+\alpha)^2-x^2}}d(a+\alpha)}$$ For reference, this is the solution, but I do not know how to get here: $$\frac{a}{2}\ln{\frac{\xi+1}{\xi-1}}...

Unfortunately not. I have come to the conclusion that there is no one here who knows this particular material. It is a blend of math and engineering and computation. I will update the threads with solutions once I find them. I eventually do, but I have never gotten a single question of this...

Homework Statement I am looking for some quick methods to integrate while leaving each step in its vector form without drilling down into component-wise integration, and I am wondering whether it is possible here. Suppose I have a square domain over which I am integrating two functions w and...

I suppose I will dig this neglected, ancient thread out from the grave to provide a solution, since this must be the first time this has been discussed on PF! For the purpose of making this available on Google search, here is what I did: The purpose of the weak form of a differential equation...

I'll help you out with the formatting, at least. This might help you if you want to post future questions. Let ##A \in\mathbb R^{m\times n}## and ##B \in\mathbb R^m##. Compute the gradient of$$f:\mathbb R^n\rightarrow\mathbb R,f(x)=\frac{1}{2}x^Tx+log\left(e^TE(Ax+b)\right),$$ where ##...

Well, maybe not? No replies in the engineering section either. I hope I am not being too ambiguous with my wording. Does anyone have experience with weighted residuals for deriving the weak form of a differential equation? Let me be more specific with the question: What is the "weak form"...

It is clear I must be in the wrong section. I will post this question in the engineering section.

You're welcome! That was usually my biggest hang-up with vector calculus was realizing the interplay between the functions and their domain, and how the domain of the function could be realized through simple direct substitution (say, x=f(t) and y=g(t) then integrate over t)

You're basically asked to do a weighted line integral. It is similar to finding the length of C (the "line" in question), except, instead of f=1, you have f=xy. So, you want to convert x and y to r and θ. Then, r and θ will be expressed in terms of t. Do you know how to convert x and y to...

Here is a "solution" I ended up with. I am not sure if I am right or not. It is hard for me to figure out what form something should be into constitute the weak form. I do know that I have effectively reduced the order of the system, though. So, there are fewer boundary conditions that need...

Homework Statement Given a strong form boundary value problem, derive the weak form using weighted residuals. Homework Equations ##(2-x)u''(x)-u'(x)+u(x)=f(x)## for ##x\in(0,1)## with $$u(0)=u(1)=0$$ The Attempt at a Solution I must multiply both sides of this equation by an arbitrary test...

Thanks for the info.