Analysis Definition and 999 Threads

In this derivation above, I have to account for the fact that v is translational and opposite to the sign of w, and similarly for v_0 and w_0, so the real equation should look something like this: Now, what I don't understand is, in this second derivation using net change in linear and...

I am self-learning analysis. My steps are as follows, For any ##ε>0##, there is a ##\delta>0## such that, ##|(x^3+2x^2-4x-8) -0|<ε## when ##0 < |x-2|<\delta## Let ##\delta≤1## then ##1<x<3, x≠2##. ##|(x^3-2x^2-4x-8) -0|=|(x-2)(x+2)^2|=|x-2||(x+2)^2| <\delta |(x+2)^2|<19\delta## Taking...

I am trying to find a damping constant of this circuit and below is my analysis. I just want to confirm if my approach is correct. At t > infiniti, the switch will be closed. Therefore, Req for damping constant equation will just be Rx because R2 because R2 is neither in series or parallel...

TL;DR Summary: Hi everyone. I have this circuit problem. I know that vL=0 and iL is just a constant number at t-> infiniti. I have attempted this problem and got energy stored = 4.4J. Please confirm it with me if my approach to the problem is correct. Thank you all.

I need to do a brief report, introducing geochemical analysis on water and sediments, and its asked for Budgets (per sample) for analysis on Tributyltin Oxide (TBT), Per- and Polyfluorinated Alkyl Substances (PFAS) and Pesticides. Does anyone know how much those three would cost individually...

Has dogs Doesn't have dogs Total Has cats 3 5 8 Doesn't have cats 4 1 5 Total 7 6 13 The course I'm taking says the above is a 2-way frequency table because there are 2 categories: cats and dogs. So the table below is not a 2-way frequency table? Men Women Children Total Ate...

Help, im try to make one work in the RITM-200 reactor series, but cant find some informartion... any tip?

I'm reading in my probability book about characterizations of the law of a random variable, that is, the probability measure ##\mathbb P_X(A)=\mathbb P(X\in A)##. I read the following passage (I'm paraphrasing slightly): This extract is basically saying that if $$\mathbb E[\varphi(X)]:=\int...

Took calculus of a single variable almost a decade ago where every theorem had to be accepted without proof. Can I fill these gaps by studying a rigorous multivariable/vector analysis book? My justification for this is that R^1 is just a special case of R^n. Or am I looking at this the wrong way...

So I've been searching around for rigorous explanations for things like ##dx## in physics, I'm not looking to fully commit myself to reading the relevant literature at the moment but just want to know what I'll have to do in order to understand. Perhaps I'll make a separate thread about that...

Hi, I have completed an experiment at university as part of my internship and have now received several measurement results which I would like to analyze statistically and plot the results as a normal distribution in Mathematica. Is this even possible with Mathematica? Unfortunately, I haven't...

Hi, I have a plot of v(onoise) of my circle using noise simulation. I also have my V(output) from my ac frequency analysis. How do i divide between the graphs?

Hi all, I have to analyse a dataset containing real-world vehicle trajectories and in particular: 1. The trajectories were classified into states in the function of certain vehicle parameters and location (urban roads, country roads, etc.) and each state is characterised by an integer number...

suppose that we have an RLC circuit where initially, the capacitor is fully charged, the charge in the capacitor is given by ##q(t) = q_{max} e^{-Rt/2L} \cos(\omega t)##, if we want to find the current, we would differentiate the charge, so $$\Large i(t) = \frac{d q}{dt} = \frac{d}{dt} (q_{max}...

I figure one can dig around for plenty of quality problems online, but I'm hoping to skip right to the good stuff by you posting your favorite real analysis problems from college, internet, textbook, dream, imagination, etc. It would be so helpful to get some comments this time, and please don't...

Hi Everyone, I'm trying to do a "Random Vibration Fatigue Analysis" on a bracket assembly that is mounted on the headboard of a pickup truck. BACKGROUND: The bracket assembly is mounted on the headboard of the truck using 2xbolts (1 per each mount). The truck regularly travels on a rough...

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I came across this very interesting Thermodynamics problem in PhysicsStackExchange. It was deleted by the OP because the moderators, in their infinite wisdom, gave him a hard time about its being a homework problem which was, in their opinion, a "check my work" post, rather than a "I'm having...

I've read a proof from Complex Made Simple (David C. Ullrich) Proposition 4.3. Suppose that ##V## is an open subset of the plane. There exists a branch of the logarithm in ##V## if and only if there exists ##f \in H(V)## with ##f'(z) = \frac{1}{z}## for all ##z \in V##. Proof: One direction is...

O Brother, Where Art Thou is one of my favorite movies. I always knew it was loosely based on the Odessey because it says so at the beginning, but the guy in this reaction video makes way more connections between the two then I would have ever thought of. I was amazed. Some comments on...

##\require{physics}##The given circuit is this: The question is taken from this video. The Professor has solved it using Phasor analysis, the final solution being $$\begin{equation} i_x(t) = 7.59 \sin \qty( 4t + 108.4^\circ )~\mathrm{amps}. \end{equation}$$My aim, however, is to use Laplace...

Hi everyone in the following expression ##f(t)=\frac{1}{2 \pi} \int\left(\int f(u) e^{-i \omega u} d u\right) e^{i \omega t} d \omega ## the book says I can't swap integrals bacause the function ##f(u) e^{i \omega(t-u)}## is not ## L^1(\mathbb{R} \times \mathbb{R})## why ? complex...

Hi Everyone I have been doing further investigation into infinitesimals since I wrote my insight article. I had an issue with the original article; the link to the foundations of natural numbers, integers, and rational numbers was somewhat advanced. I did need to write an insights article at...

Let us say we have f analytic in ##Ball_1(0)##. which means, radius 1, starting at ##z_0 = 0## point. If I want to find the boundary of ##Ball_1(0)##. Will the boundary be ##{0}## or ##{\emptyset}##? Not homework, just an intuition to understand ##f(z)=\frac 1 z## function ( for example ) better.

Hi. Someone showed me a problem today regarding sequentially compact sets in ℝ. Ie., is the set of the image of sin(x) and x is an integer greater than one, sequentially compact? Yes or no. What is obvious is that we know that this set is a subset of [-1,1], which is bounded. So therefore...

I don't understand anything about how 1.18 came to be (Red Rectangle), any help would be greatly appreciated!

I have drawn the I-V characteristic graph of the diode. I am facing problems with drawing the load line. For what value of E (Source Voltage), should I draw the Load Line? To get the I-V graph, I had to continuously change E.

Mike Lindell offered a 5 million $ challenge to anyone who could prove that his election data was false. A computer expert won an arbitration decision that he had proven it. He thought that it would take a long time, or be impossible, but he says that it did not take long at all. Does anyone...

There's a some things I've been wanting to look into for a while now I just don't know where to access that kind of information. 1. I'm interested in any information/journals concerning Physicist Norma G. Sanchez (I might be wrong on her title, please correct me if I am) work on a unifying...

Given the definition of a smooth map as follows: A continuous map ##f : X → Y## is smooth if for any pair of charts ##\phi : U →R^m, \psi:V →R^n## with ##U ⊂ X, V ⊂Y##, the map ##\phi(U ∩f^{-1}(V)) → R^n## given by the composition $$\psi ◦ f ◦ \phi^{-1}$$ is smooth. Claim: A map ##f : X → Y##...

(NOTE: I should state that my circuit analysis knowledge is up to the level of a single comprehensive EE course, as per ME students.) I was thinking about the famous resistor cube problem, and I've come up with some observations: - Every branch (I think that's the term - i.e., a branch is any...

Hello, Regression analysis is about finding/estimating the coefficients for a particular function ##f## that would best fit the data. The function ##f## could be a straight line, an exponential, a power law, etc. The goal remains the same: finding the coefficients. If the data does not show a...

Hi im trying to understand truss bridges. Where would max stress be in single span truss bridge if it was evenly loaded across the bridge? I thought single span truss bridge, max stress would be in the ends of the bridge. it would act like a simple supported beam with max bending motion being...

Hey Im doing FEA and got stuck on question. The diagram go me stuck, because looking through the workbook it says high stresses are in red and low in blue, whereas they included both different kind of stresses on the same diagram and no data. Note: High Compressive strains are noted by blue...

If f(x) is the function of the "ground": My first assumption is that in a certain $$\bar{x}$$, $$f''(\bar{x})=0$$, and from that point I will analyse the situation. The object has initial energy $$E_0=\frac{mv^2}{2}+mgf(x),$$ then $$v=\sqrt{\frac{2}{m}}\sqrt{E_0-mgf(x)}.$$ In each point the...

Note: I am self-studying Material and Energy balance courses and I haven't done fluid mechanics yet. Case 1) Consider the manometer in the figure below. Levels on both sides of the manometer which are open to the atmosphere are equal. If we analyse the forces acting on the left side of the...

Hi there, I have managed to work out the kirchoff's law bit but for the other two bits I just cant get started as I can get my head around it, its due in on monday I dont know why I left it so late!

In this article((https://arxiv.org/pdf/2001.04581.pdf)), the authors use a Bayesian analysis based on the positions of astrophysical bodies and their errors in the medians. This statistical analysis uses the markov chain monte carlo chains. The uncertainties in the positions are large, so what...

Hi guys, Please see attached image - it's the part highlighted yellow that I'm stuck on. Here is what I got for linear velocity and angular velocity. (requested by mod) Thanks! c) Angular to velocity Dia=0.8m .. rad=0.4m v (linear velocity) = r (radius of circle) * omega (angular velocity)...

Consider a convex shape ##S## of positive area ##A## inside the unit square. Let ##a≤1## be the supremum of all subsets of the unit square that can be obtained as disjoint union of finitely many scaled and translated copies of ##S##. Partition the square into ##n×n## smaller squares (see...

I'm trying to calculate Forster's Resonance Energy Transfer rate, but I just can't seem to get the units right. I'm trying to teach my students how to calculate them. Here is the (relatively) original technical note of FRET equation, made by the original author...

i try to understand what physical entity mass or massdensity divided by speedquadrat could be? Any ideas? thanks

Hello. I read about smooth infinitesimal analysis and I have several questions: 1.What does "ε.1" and "ε.0" mean in this proof? (photo1) (https://publish.uwo.ca/~jbell/basic.pdf , page 5-6) 2. For what purpose do we use Kock-Lawvere axiom when we deal with law of excluded middle? (photo2)...

Hello. How to prove that in smooth infinitesimal analysis every function on R is continuous? (Every function whose domain is R, the real numbers, is continuous and infinitely differentiable.) Thanks.

Hello ! My question is how the energy levels and sublevels that atoms are considered to have were obtained, and if these energy levels and sublevels were obtained as a result of the different spectroscopic analyzes of energy emission and absorption of atoms, or as it was concluded that atoms...

I have wrote all feilds and potentials and I want to find the constants. My first question is " when we say in the a<x<2a the potential is V(x)" then the potential in the a is V(a) or V(0) ( cause it is 0 in our new area) ? Second one is " when I want to write the gausses law for the point x=a I...

Hello guys, I have conducted an experiment and got some results. I have 3 variables to vary, for example, five x1, five x2, and two x3 and 2 observation results, like y1, y2 I already make y1 y2 and x1 x2 x3 dimensionless since plot is 2D, what I am doing now is just plot when x3=1, x2=1, plot...

Proof: Suppose f is a function and x is in the domain of f s.t. there is a derivative at the point x and sppse. there are two tangent lines at the point (x,f(x)). Let t1 represent one of the tangent lines at (x,f(x)) and let t2 represent the other tangent line at (x,f(x)) s.t. the slopes of t1...

Has it ever happened that after a discovery, data from previous experiments were analyzed and it was noticed that there was already some evidence of the phenomenon in question?