Analysis Definition and 999 Threads

Hey, I would like to do an exchange year at Imperial. I would like to follow as a physicist the Functional Analysis course. However, I have not heard the best things about this peculiar course. What is the audience opinion on that?

Prove that each of the limits exists or does not exist. 1. ##\text{lim}_{x\rightarrow 2}(x^2-1)=3## ##\text{lim}_{x\rightarrow 2}(x^2-1)=3## if ##\forall \epsilon>0, \exists \delta ## such that ##|x-2|<\delta \Rightarrow |f(x)-3|<\epsilon##. \begin{align}&|x^2-1|=|x+1||x-1|\leq \epsilon\\...

Hello, I wanted to know some software used for plotting the positions of a point mass. I did an oscillation experiment and I used the tracker app, but I cannot get it to track my point mass Please mention if any alternative software exists for carrying out my experiment. Thanks in advance

Hello there. Could you please recommend me a book that focus on data/error analysis and that, at the same time, provides examples of how to use the R programming language to such things? It could be using the python or c++ languages instead. The only books i have came across use fortran, but...

Hi I've just done a question regarding a marble moving on a surface given by z = -1/(x2+y2) In this case what happens with dimensional analysis ? x and y have dimensions of length while z has dimensions of 1/(length)2. Is this question badly written or do i just accept that i won't be able to...

Hello Everyone, Hope you will be with good health in this situation. I am Ali and i need some help regarding DRAGON/DONJON Code for PWR Analysis if anyone help me i will be very glade Regards Ali

Hi, So say I have some data to process. I am trying, say, Linear/Multilinear Regression. I know how to do this within Python Pandas. I can learn how with Tensorflow (TF). Would TF produce the same output given the "right" choice of Activation Functions *? Or would it output a model that is...

Just to remind, ##C_\ell## is the variance of random variables ##a_{\ell m}## following a Gaussian PDF (in spherical harmonics of Legendre) : ##C_{\ell}=\left\langle a_{l m}^{2}\right\rangle=\frac{1}{2 \ell+1} \sum_{m=-\ell}^{\ell} a_{\ell m}^{2}=\operatorname{Var}\left(a_{l m}\right)## 1)...

Or is reading a proofs book enough

Hi all, Sorry of this is a silly question but it is one that recently came to mind and I cannot seem to find an answer to it: "should I change my mesh depending on the type of FEA analysis I am doing?" My feeling is that I should not change it, but that is a total guess on my part. Any...

Summary:: Hi anyone can explain me how to solve this circuit, finding the current I2 and I1? Really don't know where to start Thanks

Hi, Is there any tutorial or pdfs that can help me with the MCNP output data? I'm working on the criticality of the SCWR, and I designed the fuel assembly and run it on the MCNP, but I have no idea about data extraction.

Can anyone recommend a book in which complex eigenvalue problems are treated? I mean the FEM analysis and the theory behind it. These are eigenvalue problems which include damping. I think that it is used for composite materials and/or airplane engineering (maybe wing fluttering?).

For example given the circuit I make the graphs : and comment that or graph 1 as resistance grows larger the current grows smaller (is inversely proportional) I will use the simulation and experimental data to check the values and conclude that this act is true. Is this what I'm supposed to do?

Why does f attain its local maximum at r' in (p,q). Is it because we have f(x)<= f(r') for all x in (p,p+delta)?

I am in a mechanical design class that has been focusing on the slider crank mechanism. My professor tends to just provide derived equations without showing the analysis. I feel like I am missing out on some key understanding because of this. Specifically, I am trying to do what should be a...

Hi. I am making a 3D Ansys Maxwell project to design DC electromagnet. My model as in attached pictures. I have couple of questions. 1- How important the width value of sheet of coil terminal? Altough I did not change number of conductors and current of coil, changing the width of sheet of the...

I tried to use dimensional analysis, there is variable for part i) m= P,A and Y also parameter is used in analysis is n=3(M,L,T). So m-n=0 number of dimensionless analysis group. I am confused at this step however I did this calculation to reach solution: i) P=MLT-2 (Ice Force) m-n=4-3=1(number...

If I choose my axis of rotation for torque analysis to be the left-end of the plank, I can get the correct results. If I instead choose the com point -- I run into a dead end. Is there a way of a priori knowing this would happen? Thank you.

I am trying to understanding the inductor circuit. I have drawn the below circuit and try to simulate The Inductor current comes to 500mA and Vout is 5V as per simulation. The current in inductor should slowly increase from 0A to 500mA but i cannot see that in the waveform. Is my understanding...

The time domain analysis is easier to plot compared to analyzing the frequency with respect to the phase. But, LTSpice makes it look really easy. So, for a small signal AC analysis, LTSpice does use a AC voltage source for its frequency domain analysis function. This must be a really convenient...

Hi everyone, I recently started studying real analysis from baby Bruckner couple. It feels me like, "I am running too fast to reach my destination but in the process of running, I decreased my oxygen level." So, I stopped trying to complete uni coursework fast. But rather I started reading...

Summary:: SEM-EDX Analysis Hi! Just would like to ask for some insights. I needed to identify the material based on its SEM-EDX results. However, after several researches, I still have no idea what it is. Any idea would help. thanks. Edit: Another information given to me was that this is a...

I need help actually creating the proof. I've done the scratch needed for the problem, it's just forming the proof that I need help in. Bar(a+bi/c+di)= (a-bi) / (c-di) Bar ((a+bi/c+di)*(c-di/c-di)) = ((a-bi/c-di)*(c+di/c+di)) Bar((ac+bd/c^2 +d^2)+(i(bc-ad)/c^2+d^2)) =...

I wonder how to accurately perform data compression on the m x n matrix X using PCA. Each row is a data point, and each column is a feature. So m data points with n features. If I like to go k < n dimensions, how is the correct way of doing so? How to I accurately create the matrix W_k, which...

What are your opinions on Barry Simon's "A Comprehensive Course in Analysis" 5 volume set. I bought them with huge discount (paperback version). But I am not sure should I go through these books? I have 4 years and can spend 12 hours a week on them. Note- I am now studying real analysis from...

We know that ##P(A-) = (95\% \cdot 0.5\% + 5\% \cdot 98.5\% )## and ##P(guilty \ and \ A-) = (95\% \cdot 0.5\%)##, so letter a) is just ##P(guilty \ and \ A-)/P(A-)##. What I tried to do in letter b) was again using the conditional probability theorem. First calculating the probability that...

For letter a), i think that he is assuming that each hypothesis is independent, and that they are mutually exclusive.For letter b), I understand that it indeed admits the relative frequency interpretation, since the the experiment is being produced several times. For letter c) we do the...

Hello everyone, I am struggling with calculating the coefficients for second order transient analysis. For example, when analyzing a underdamped circuit, we know that the equation for voltage or current is xt=e-αt(K1cos(sqrt(ω2-α2)t ) + K2sin(sqrt(ω2-α2)t)). Then in order to determine for...

Mentor note: Edited to fix LaTeX problems ##f:C \rightarrow C## that solves ##\frac{df}{dx} = 6x + 6iy## ## f(x,y) = 3x^2 + 6xyi + C(y) = (3x^2 + C(y)) + i(6xy) ## ## \Delta u = 0 \rightarrow 6 + C''(y) = 0 \rightarrow C(y) =5 \frac{5}{5}##

For quite a long time I had just gone by the traditional explanation that when you place a straw vertically into water without fully submerging it and then you withdraw the straw from the water, the water column stays inside because the pressure from the atmosphere acting on the bottom of the...

I am simulating a hot forging process in LS-Dyna. A tool is contacting a hot workpiece for 2 sec every 10 sec (--0 sec--contact--2 sec--no contact---10 sec--) in a factory. Since this is a continuous process, the tool should, at some point, attain steady temperature. I have tried to recreate it...

Hi! the next semester i'll take a course on multivariable calculus but i'd like to study it now. I've "Principles of mathematical analysis" by W.Rudin but i heard that the sections about this are hard to read. If there is a textbook like "Understading analysis" by Stephen Abbott but in...

Summary:: Question: a car of mass 800kg, 3600N driving force experiences resistive forces of 120v Accelerates from rest. Form equation and show max speed is 30 ms^-1, assuming driving force does not change. my attempt at a solution -I can not see how to rectify it as I don’t think I did...

Is there any existing work focusing on analyzing finite element visualized results and how they differ from analytical solutions, rather than on the method?

I have been reading 2010: The Year We Make Contact, a sci-fi book belonging to a classic series by Arthur Clarke. The book involves a myraid of scientific concepts so I think it is worth it to verify if the scenes would be feasible in the real word. In this thread I'd like to focus on the scene...

https://en.wikipedia.org/wiki/Klein%27s_Encyclopedia_of_Mathematical_Sciences Originals are in German or French, the Japanese version cut all the historical content :( Do you think that some day we will see this published in English? Size is big, 20k pages, but it cannot be more interesting I...

THE ANSWER IS GIVEN: 6V, but according to me as the positive terminal is grounded the negative terminal will be virtually grounded (0V), from ohm's law (applying to the two series resistance) it is expected that Vo is 0V! I don't know where I am getting wrong!

I had deduced that B,E,H are the places where acceleration will be zero, but when I read the solutions it showed that K also has a = 0. It said it had maximum slope and then said a = 0. But I couldn't understand why? Please help.

Hello everyone, When working with variables in a data set to find the appropriate statistical model (linear, nonlinear regression, etc.), the variables can have different range, standard deviation, mean, etc. Should all the input variables be always standardized and scaled before the analysis...

Do you guys have techniques in solving for the Force in hydraulic IJ? I've been stucked for a while now and I can't seem to find the answer.The question says the answer should be = 11, 051.9516 N (T).

Hi friends, I have simulated two circuits, one is an RC filter and other is a Capacitance multiplier. My aim of experiment is to validate a decrease in Iout (load current) of CM circuit as compared to load current in RC filter circuit. Theoretically, Iout (CM circuit) < Iout (RC filter) Vp-p...

I am currently trying to self study Real analysis . I have completed Hubbard's Multivariable book & Strang's Linear algebra book. I have Apostol's Mathematical Analysis & Baby Rudin . I started with rudin yesterday and was making excellent headway until I encountered a theorem about 15 pages in...

My lecturer said that the cryptosystem one-time pad, has a weakness which is when it is subject to frequency analysis. But after him trying to explain why that is a weakness of this system I am still unable to see why. Because the frequency of letters is completely irrelevant to the structure of...

I attached a screenshot of the book (sorry no pdf available for this book). Right above the somewhat central line they give the theorem that if there are m currents and n nodes, then there will be n - 1 independent equations from the current law and m - n - 1 from the voltage law. I count 4...

The problems I am referring to are problems 4-10 and 4-11. There is no solution provided for 4-10, so I want to check my answer here. However, I don't understand the answer to problem 4-11. Shouldn't it also be 24 V since it is in parallel with the 200 k##\Omega## resistor? I am actually...