Analysis Definition and 999 Threads

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?

Two point-like particles of mass m. The particles are rigidly connected to each other with a mass-less rod of length L. The particles are initially at rest in such a way that one particle is at the origin and the other is at the point (0, L). A point-like particle of mass M collides with a...

TL;DR Summary: I'm looking for a book on statistical/data analysis. Hey all. I've been doing statistical analysis in my research (such as using PCA and LDA), but I have never received a formal education on statistical analysis or data mining, and what I know about analysis is quite scattered...

Hi first time using this forum, I have some homework that I am entirely stuck on, can anyone help me with this question? I understand the placement of nodes, and that I need to convert complex numbers, but apart from that I have no idea what direction that I'm supposed to take in this. I don't...

Figure: My attempt at a solution: Once the capacitors have been applied, we see directly that ##\boxed{v_c=v_0=0\, \textrm{V}}## Wouldn't this one be done like this? I know the following: in a circuit with capacitors and coils, if we have Capacitor: we change for an open circuit. Coil: we...

The following properties of big-O notation follow from the definition: (i) if ##f(x)=O(u(x))## as ##x\rightarrow{a}##, then ##Cf(x)=O(u(x))## as ##x\rightarrow{a}## for any value of the constant ##C##. (ii) If ##f(x)=O(u(x))## as ##x\rightarrow{a}## and ##g(x)=O(u(x))## as ##x\rightarrow{a}##...

Figure: My attempt at a Solution: We calculate REACTIONS: $$\sum F_x=0\rightarrow \boxed{Bx=0}\qquad \sum F_y=0\rightarrow By+A=50$$ $$\sum M_B=0\rightarrow \boxed{A=25\, \textrm{kN}}\quad \boxed{B=25\, \textrm{kN}}$$ KNOT B: $$\alpha \rightarrow \alpha =90-40=50\, \textrm{º}$$ $$\beta...

Figure: My attempt at a Solution: $$\overrightarrow{TFD}=TFD\dfrac{(-0,16\widehat{i}+0,11\widehat{j}-0,08\widehat{k})}{0,21}$$ View from above: We calculate ##D##: $$\sigma =90-\arctan \left( \dfrac{0,07}{0,240}\right)=73,74\, \textrm{º}$$ $$d=0,16\cdot \sin (\sigma)=0,1536\, \textrm{m}$$...

Diagram of the problem below. I have 45 minutes to finish all parts of this question without reference material. The Mechanics of Materials section of these tests are largely Structural Analysis, which I was not taught to this level in my undergrad degree so I am teaching myself via Youtube...

In this thread I attempt to find a closed form solution to the gradient descent problem for a single sigmoid neuron using basic calculus. If you would like to give pointers feel free, if you see me make a mistake please let me know! Thank you!

Hi. I'm nearing retirement so I thought I would take some math classes. This fall I took a Real Analysis class at a good school and dropped it because I did so bad on the first exam. I did great on the homework and quizzes. I also took Real Analysis about 47 years ago at a very good school...

So, I use Ansys (well known FEM software) and get the next output for a modal analysis toy problem (If you happen to know Ansys that's a pre, but I promise it shouldn't matter). The problem is a simple beam, clamped at one end. I used 160 20-node brick elements to solve it (so no Timoshenko...

I know that if there is only one conductor providing the current density, then the current density can be used. But if you apply Maxwell's equation when there are multiple current sources, I don't know which value to use. This is not an analysis using a tool, but a problem when I develop the...

In Lecture 7, Prof. Arthur Mattuck (MIT OCW 18.03) taught that the following equation $$ y’ +ky = k \cos(\omega t)$$ can be solved by replacing cos⁡(ωt) by ##e^{\omega t}## and, rewriting thus, $$ \tilde{y’} + k\tilde{y}= ke^{i \omega t} $$ Where ##\tilde{y} = y_1 + i y_2##. And the solution of...

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...

##P_m(r + 1, n)= n^{-r}\cdot E_m(r + 1, n), E_m(r + 1, n)= \binom{n}{m} A(r+1, n-m) = \binom{n}{m} \displaystyle\sum_{v=0}^{n-m}(-1)^v \binom{n-m}{v}(n-m-v)^r ## ##P_{m+1}(r, n) = \binom{n}{m} A(r, n-m-1) =\binom{n}{m+1} \displaystyle\sum_{v=0}^{n-m-1}(-1)^v \binom{n-m-1}{v}(n-m-1-v)^r...

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...