Insight Definition and 88 Threads

Hi friends, Can anyone offer some insight into this challenging integral? I can't seem to think my way through this. Thank you Stevesie $$ \int_{0}^{\infty}\frac{1}{x}\exp\left(-\frac{1}{2}\left( \frac{\log\left( x \right)-\mu}{\sigma}\right)^{2} \right)\exp\left(-\frac{1}{2}\left( \frac{ x...

Lowly engineer here. I am struggling - I think like many - to develop intuition on DEs. From looking at the history and applications of DEs, general themes that come to mind are, conservation, energy (eg. isochrone problem), causality, feedback (control systems), etc. However, I can't seem to...

Hi,new college guy here,previewing next year's work. Been seeing these articles,written by reputed physicists. 1. https://www.mdpi.com/1099-4300/23/5/519 this one claims that quantum randomness is false.does this argument be strong enough to rule out QM's so-called randomness?I understand that...

https://scitechdaily.com/nasas-insight-mission-reveals-the-detailed-internal-structure-of-mars/ https://www.nationalgeographic.com/science/article/nasa-insight- spacecraft -reveals-first-peek-inside-mars-center https://www.nasa.gov/feature/jpl/nasa-s-insight-reveals-the-deep-interior-of-mars...

Though wordy, this New York Times magazine article wades through the murky morass of telemarketing scam centers located on the subcontinent. Worth a perusal by anyone affected by this ubiquitous menace. Journalist Bhattacharjee approaches the investigation without prejudice, even with some...

I am studying @Orodruin's Insight "Explore Coordinate Dependent Statements in an Expanding Universe". It looks pretty interesting. About three pages in it reads "expanding ##x^a## to second order in ##\xi^\mu## generally leads to$$ x^a=e_\mu^a\xi^\mu+c_{\mu\nu}^a\xi^\mu\xi^\nu+\mathcal{O}_3...

Summary:: Ideas for a novel I want to begin writing. Brainstorming ideas and need help with a certain concept. Any help is appreciated! Hello to you all, this is my first post, and I Google searched this astrophysics forum because I thought it might be a good place to begin asking for advice...

What are good books for learning about math? Not textbooks, but books that provide insight into mathematical phenomena.

The solution from my book: From $$\frac{3}{x+2}<\frac{13}{12}<\frac{3}{x} \tag1$$ It follows that ##13x<36<13(x+2)## x<3, i.e. x = 1 or 2. By checking, x=1 is not the solution and x = 2 satisfies the equation. However, how does the author deduce (1)?

I didn't really want to create another thread just to make a (hopefully) humorous observation but on the other hand to link to this paper under a "cranky science" header hardly seems fair. Especially when I really haven't read the thing in it's entirety. One very scientific statement piqued my...

I am learning to use polar coordinates to describe the motions of particles. Now I know how to use polar coordinates to solve problems and the derivations of many equations. However, the big picture of polar coordinates remains unclear to me. Would you mind sharing your insight with me so that I...

Hello. First of all, I'm really glad to have stumbled across this community. You guys seem amazing, and I can't wait to keep lurking (and hopefully, one day, participating). I'm in a strange situation and I could really use the guidance of some people with experience. If the explanation is...

I verified with others the equation below is an Euler method as well with ##a## can be any value such that it give the same ##\frac{dE}{dv}=-1.4\frac{p}{v}## but with ##a## other than one, it have no meaning in physics. For anyone that already understand Euler method can omit the part i have...

I recently started volunteer math tutoring in an after school program in a city near me. This is one of the poorest cities in the state, and the students' math preparation is about as bad as you'd expect. The after school program is not part of the school system, it's run by a non-profit. I work...

I’m writing a story about warfare several decades in the future. While I was doing research into possible directed-energy weapons, I came across something interesting. I don’t know if there is a name for the whole concept but it can be generally described as the use of brief laser pulses to...

While the now infamous Frauchiger and Renner publication generated a lot of buzz, it was largely concluded that they drew way too premature conclusions with a too wide brush. Especially the topic of its implication that "Single Universe" interpretations were mostly ruled out garnered quite a lot...

Hi everybody, This is my first time posting here and I hope I'm in the Right place. To give some back story, I'm Studying A-levels (international), I live in a 3rd world (developing) country where sciences are very neglected in terms of education, and job market for physical sciences (my 1st...

Greg Bernhardt submitted a new blog post A Numerical Insight for the Fundamental Theorem of Calculus Continue reading the Original Blog Post.

Hi, I teach a unit on bridge building for American high schools. We use software to show which members are in compression and tension and adjust design prior to physically building (ie doubling up members in compression). We use the equation: 2*Joints = Members + Reactions as a way to enable...

Hello, I was thinking that using AC to supply power to a lamp would cause it to flicker, considering that the potential difference keeps changing signs. This would mean that the current supplies voltage to the lamp, only to take it back after a really small amount of time. Voltage say's...

Hello, Consider the following: case 1: 2 parallel metal plates(sufficiently thick) separated by a di-electric and 1 plate is charged to a voltage exactly equal to break down of the di-electric. the other plate is tied to ground. case 2: same as case 1 but instead of the plate tied to...

TheAdmin submitted a new PF Insights post PF Insight Scavenger Hunt 2 Continue reading the Original PF Insights Post.

Hi, I have recently began studying quantum field theory and have just seen how the quantization of the complex scalar field, noting that there is invariance of the action under a phase rotation shows the existence of antiparticles. I just have a couple of questions, apologies in advance if...

Lately I have had the opportunity to experiment with a number of new and vintage guitar amp speakers. I was generally aware that different speakers sounded different. What I was not prepared for was the truly huge and amazing difference the various speakers made in not only sound but how they...

Hi, I'll try to keep this brief but this is a hard subject to keep brief. Thanks to all who take the time to read. I appreciate any advice even if it's just a repeat of what someone else has already said. I have a B.S. in physics from the University of Utah with a GPA of 3.4. I finished my...

If so, how.

I am doing a passion project that requires knowledge of physics I don't quite have, it mostly revolves around understanding human bodies and their interaction with velocity, impact, decibels, energy, etc. I'll be more specific later on.

Currently working through a chapter on op amp circuits, fundamentals. Came upon this practice problem in the section on inverting op amps imgur link: http://i.imgur.com/2DrQLXk.png imgur link: http://i.imgur.com/7KRKzKC.png A working of this problem is not given. I got the correct answer...

Ygggdrasil submitted a new PF Insights post What Causes Cancer: Bad Luck or Bad Lifestyles? Continue reading the Original PF Insights Post.

imgur: http://i.imgur.com/9VILpYL.jpg Now, I can easily solve this by applying the formula P_R = \frac{(\Delta V_R)^2}{R} and get all the correct answers. However, the answers feel strange to me intuitively. In the formula above, lowering the resistance increases the power that is dissipated...

In HS they just taught you the formula for it (the cofactor method) and a few other things, such as det(A) = 0 means A is singular. I finally reached Ch 5 of MIT OCW Intro to Linear Algebra, and I was really hoping that seeing how determinants are derived from first principles would give me...

Okay so this might be a little long, but I think it requires some length to explain and elicit answers. I am a junior at the University of North Texas. I originally came here to be a music major and spent a year and a half as such. I was and am very passionate about music, but for many reasons...

Homework Statement During an all-night cram session, a student heats up a 0.360 liter (0.360 x 10- 3 m3) glass (Pyrex) beaker of cold coffee. Initially, the temperature is 18.1 °C, and the beaker is filled to the brim. A short time later when the student returns, the temperature has risen to...

I want to have a simple and intuitive explanation of why the sin and cos waves have such a simple repetitive values for their derivatives at a specific point. Their derivative values are also periodic in respect to the derivative order. For example, e^-x is also periodic, but its derivatives are...

I just did this following exercise in my text If C is the line segment connecting the point (x_1,y_1) to (x_2,y_2), show that \int_C xdy - ydx = x_1y_2 - x_2y_1 I did, and I also noticed that if we put those points into a matrix with the first column (x_1,y_1) and the second column (x_2,y_2)...

I was wondering what the physical insight is of integrating a product of two functions. When we do that for a Fourier transform, we decompose a function into its constituent frequencies, and that's because the exponential with an imaginary x in the transform can be seen as a weighting function...

This paper looks interesting, but I haven't gotten a copy and read it yet. What do people here think? Is this the solution to the lithium problem?

Hello friends of Physics forum. I am a high school junior, I will be finishing up finals next week. This year, I took Honors Chemistry, arguably the hardest class i have taken so far. However, I also found it the most fascinating and intriguing class. I am a mathematically oriented person and I...

How to have better discrete math "insight" Greetings: I came a cross a textbook example in a discrete math book that I have been reading on my own, and I thought this example in the book was a good example of what I want to be good at: Given integers from 0-9 arranged in a circle, is...

High School Student looking for insight regarding engineering! Hi, I'm a junior in high school who is looking to focus on some type of engineering. I have researched a lot on the web and at interesting questions on this forum about the different types of engineers and what they do. What most...

Right now I am on track to be a math and physics double major, but I just finished my freshman year, so I haven't declared yet (all male liberal arts college). I won't know my GPA until May 15th and since it is freshman year, it doesn't matter a whole lot. I may have a 4.0 (on a 4 point scale)...

Hi all, I'm new to the forum. I chanced across some threads regarding medical physics but I didn't want to hijack someone else's post to ask some questions. So I'm just finishing up my first year of college and I've been trying to get more insight into various careers that I could pursue...

I'm trying to find a way to simplify a complicated proof. The worst step of the proof involves a product of five 4×4 matrices. I'm hoping, perhaps naively, that if I could understand why the result of this operation is so simple, I may be able to explain the proof to others without actually...

I have been doing some serious review of fluids in order to prep for some CFD. I have been re-deriving the NS Equations in all of their various forms. Something seems to have cropped up that I have worked myself in circles about. Let's take the momentum equation in Conservative Integral form...

Part of my basic understanding of the holographic principal is that the amount information in a given area of space is less than the surface area that surrounds that region (measured in Planck units squared). The exception being that in the case of a black hole the information stored within an...

I am a grade 12 high-school student in Ontario, Canada, and I am considering a career in Geological Engineering. I was hoping to get some insight from people who are specializing in it, and who can inform me on what the day to day life is like. So far, I have examined the "prospective...

Hello, I am new to the forum and I have made an account to ask this one simple question. Am I good at math or not? I have been deciphering whether I am or not for some time now. It's like a pendulum, I can pathetically fail a math test but answer immense logic problems easily. I taught myself...

My supervisor always talks about how a problem is convex or its nonconvex and we want to convexify it. I understand that convexity gives a lot of advantages for optimization, and I understand the geometric definition of convexity. How does my supervisor know something is convex? Like a...

Scientists reaching "The End of Insight" Has anyone else seen this article, or even heard of this before? Thoughts? Comments? Laughs? Screams? http://www.slate.com/articles/technology/robot_invasion/2011/09/robot_invasion_can_computers_replace_scientists_.html?wp_login_redirect=0

I watched a video explaining a card trick today, there were no tricks, it was all based on math. Here's the set up: 52 cards in the deck. person A takes some of them, then person B takes some as well. The dealer counts the remaining cards in his hand, say he has 18. Then he says...