Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development.The word comes from the Ancient Greek ἀνάλυσις (analysis, "a breaking-up" or "an untying;" from ana- "up, throughout" and lysis "a loosening"). From it also comes the word's plural, analyses.
As a formal concept, the method has variously been ascribed to Alhazen, René Descartes (Discourse on the Method), and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery (which he did not name).
Hello, PF!
It’s been a while since I last posted. I am looking for a critique and recommendations regarding my study plan towards Functional Analysis and applications (convex optimization, optimal control), but first, some background:
- This plan is in preparation for my master’s thesis, I...
Here is the question
a. Plot nodes in the problem and indicate how many equations will be obtained.
answer: two unknown variables
b. Use node analysis. Derive the system of equations for the voltages in the circuit.
question: Did I calculate right V_a and V_b?
C. Calculate the...
I have been conducting free decay analysis on the NREL 5-MW-wind turbine model provided by SIMPACK . I wanted to compare the free decay results with OPENFAST simulation. Hence, I applied a initial displacement of 1m on the tower top in the Y direction. While comparing the results with OPENFAST...
A non-technical opinion piece that claims there are many fatal and near-fatal events, ~23000 total, in the US every year -- with regard to supplement consumption/abuse. Additionally, it explains US labeling requirements and available remediation for problems related to supplement usage. Which...
hello,
I’m trying to figure out if I’m doing this correctly or if there’s a different way that I should be finding a missing value. I’m trending data for an automatic transformer. Every month I collect the operations counter value and at the end of the year sum the number of tap changes...
Hello,
I am currently planning on self studying math analysis with MIT ocw courses, but I cannot find the analysis course. I have found on the web that analysis and ODE are the same thing. If I want to get a good introduction to analysis, is the MIT ODE course fit for such a use?
Thanks
I was having trouble with a physics problem (string tension dynamics) In this case I have a model that simulates the phalanges of a human finger. Each phalanx is a block of mass m1, m2 or m3 respectively. And to simplify it, consider the 3 equal masses.
These phalanges are linked by joints that...
Swimming pool test kits combine a few drops of an unknown chemical with about 10 mL of pool water and then check the color of the reaction.
I would like to know the chemistry behind this. I assume that the H+ and/or the OH- ions combine with some cheemical to produce the color to be checked...
If we define Laplacian of scalar field in some curvilinear coordinates ## \Delta U## could we then just say what ##\Delta## is in that orthogonal coordinates and then act with the same operator on the vector field ## \Delta \vec{A}##?
The course description is as follows:
Description Function spaces, convergence, inner product, bounded linear operators, integral operators and integral equations, adjoint operators, expansion in eigenfunctions, resolvent, kernel
The instructor is on sabbatical, until the start of the class...
Hello everyone. I was watching the Walter Lewin lectures and I noticed in the talk he used something called dimension analysis to study the time it takes for an object to drop based on differing heights.
I'm 22:07 minutes into the video.
With some guess work on what's proportional to what...
I got something like this, but I'm not sure it is correct, because if it has the same order of convergence as trapezoidal rule which is 2, it should yield the same result as trapezoidal rule but mine doesn't (?).
For example sin(x) for [0,1], n with trapezoidal rule = 0.420735...
With my own...
In [this post][1] user William Ryman asked what would happen if we try to build "complex numbers" with shapes other than circle or hyperbola in the role of a "unit circle".
[Here][2] I proposed three shapes that could work. The common principle behind them being
that if the unit curve is...
in a discussion on the twin experiment, I read that an author (Darwin) proposed that the non-inertial traveler twin sees the transition between the redshifts and blueshifts at the very moment when he turns around, while the inertial twin sees this transition with a delay, which means that for...
Hello! Consider this circuit
Now I am susposed to solve this using nodal analysis. The first step is to "prepare the network" so that I can set up the conductance matrix.
Now I've tried it for a bit and was not really able to do it. So I went ahead and looked at the solutions and this is how...
Hi,
Both NAND and NOR are considered to be universal gates. For example, NAND gates can be used in combination to perform the AND, OR, and inverter operations. The same could be said of NOR gate.
Then, why the digital electronics section of electronics textbooks almost always start with the...
I’ve written an insight article on what I think is original material (at least I’ve not seen it in my reading nor google):
A Novel Technique of Calculating Unit Hypercube Integrals
I am looking first for someone that can follow my work, I’ve had some mathematicians look over it but none whose...
It has been 35 years since I did the math for Fourier analysis, and I have forgotten what the subtleties are. Please be kind.
So this is not a how do I calculate a DFT (though that may be my next question) but rather how do I use it, and interpret the results.
All the online and software I find...
https://www.feynmanlectures.caltech.edu/I_09.html
9-7
"From this figure we see that the horizontal component of the force is related to the complete force in the same manner as the horizontal distance x is to the complete hypotenuse r, because the two triangles are similar. Also, if x is...
So I was looking at this example problem in my textbook and I don’t understand how they got -168.1 degrees. The part I’m confused with is the first part of the 2nd picture, there’s a coma in the inverse tan, I don’t know what that means.
In many books it is just written that ##\Delta(\frac{1}{r})=0##. However it is only the case when ##r \neq 0##. In general case ##\Delta(\frac{1}{r})=-4\pi \delta(\vec{r})##. What abot ##\mbox{div}(\frac{\vec{r}}{r^3})##? What is that in case where we include also point ##0##?
https://www.feynmanlectures.caltech.edu/I_10.html
https://www.feynmanlectures.caltech.edu/I_09.html
Using Mathematical approach we can describe the motion of a falling body whose gravity is 32 m/s^2. Analysis shows that this is simply ##s-s_0=ut+1/2at^2##. Similarly we can describe the motion of...
Hello ,
I was looking into current density analysis of a PCB that handles distribution of AC power . from ansys and cadence sites , i realized by current density they refer to DC IR drop that is a pure ohmic analysis that doesn't take into consideration the AC effects . And in order to take this...
Summary:: x
Problem:
Let ##f:[0, \infty) \rightarrow \mathbb{R}## be a positive function s.t. for all ## M > 0 ## it occurs that ## f ## is integrable on ## [0,M] ##. Which of the following statements are true?
A. If ##\lim _{x \rightarrow+\infty} f(x)=0## then ##\int_{0}^{\infty} f(x) d x##...
Are you strong in analysis? I need a favor please? My go to Analysis advisor (fresh_42) is unavailable for now, I was hoping one of you might help me please:
This (it's the top sticky post in this sub-forum) is my insight article I've recently re-written and have shortened quite a bit. You...
Hello.
Can someone give m e pointers on how to find the value of vx given that it is inside a supernode(will it be the valueof the voltage inside or the difference of potential between the two nodes?): here's the exercise and what I've done so far attached.
Your time and attention are deeply...
In the news, they say that a new search for the missing MH370 airplane will begin at the location identified by Richard Godfrey.
I'm not qualified to judge the validity of this report. I'm asking others to weigh in with their judgements. I know we have several radio HAMs in PF membership...
I wanted to do an investigation about how the same musical chord can have the same pitch but sound different on different musical instruments. Like how chord C major would sound higher played in the electric guitar than a C major played on piano. How should I approach this investigation?
Hi all. I am a math major. I will be taking real analysis next Fall with an excellent professor who I know to be also quite demanding. I would like to be as well prepared for this class as possible besides going through a real analysis text or lecture series over the Summer and causing the class...
I have taken some photos (with my phone) of some optical phenomena in the lab. I'd quite like to analyse the distances between some features of the image. In school I remember using a piece of software which allowed you to choose an origin point / setup coordinate axes, select a scale (i.e. 1 cm...
I am reading Multidimensional Real Analysis II (Integration) by J.J. Duistermaat and J.A.C. Kolk ... and am focused on Chapter 6: Integration ...
I need some help with the proof of Proposition 6.1.2 ... and for this post I will focus on the first auxiliary result ... see (i) ... at the start of...
Hi,
I am doing e-field simulations and have came across two types; electrostatic and dc conduction. I know that electrostatic means there is no changing field so I'm just hoping for discussion on when one is more appropriate than the other and when one definitely should or should not be used.
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)...
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...
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?).