Analysis Definition and 999 Threads

Summary:: The image shows two circuits, in the first one, using Nodal Analysis we find that V1=4.8V, but in the second circuit V1=10 because using KCL - 10+V1=0. I understand what happened in the first circuit, but I don't understand what happened in the second one, they look the same to me...

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Summary:: So I found Vth=1.19 using Nodal analysis and I'm not sure if that's right, I'm trying to find Rth now but I'm confused as to what to do, any tip that tells me at least from where to start is appreciated. Edit: so I did 12||60 so Rth=10 ohm, is that correct? Is Vth correct too?

Hi, I'm a physicist so I have a basic knowledge of probability and hypothesis testing etc. I would like to more sophistically calculate from available data in my country whether ones Covid infected people have a statistically significant different probability of reinfection than people who are...

Hi, I was attempting another turbomachinery question and am struggling with a few concepts. The question is: "A single stage gas turbine for power generation is designed for the following overall duty: - Power output is 4.2 MW, and mass flow rate is 70 kg/s - Inlet stagnation pressure = 3 bar...

the only way i can think of changing the method is by using 2 light gates instead of 1, calculating the velocity through each and using this to get an average velocity, but not sure how this would help

Hello, this is my working. My professor did not give any answer key, and thus can I check if I approach the question correctly, and also check if my answer is correct at the same time. When t < 0, capacitor acts as open circuit, $$V(0-) = V(0+) = 9V$$ When t = infinity, $$V( ∞) = 5V$$ (because...

Hi, I'd to work with a model which represents a contact problem. I want to suppose that f_0=0 and f_2=0 where f_0 is a density of body forces and f_2 is a density of surface tractions . I am mathematician so I don't know if the hypothesis that I'd to suppose will make the problem have a sense in...

*A is the node all the way to the left above the 30V but I didn’t end up using it because I don’t think you need it since the same as 30V, right? * I know I messed up somewhere because shouldn’t V1-4 = 30? After finding my V1 I used that value to find the other Vs and it ended up being close to...

I was walking around with my head in the clouds and suddenly I wondered if a smart person, say, a philosopher, could start at the full monster of real analysis instead of elementary calculus. Would there be any hope for this unfortunate soul? What are your opinions and why? Or if you feel this...

Say you have measured several quantities and you can calculate the value of a physical quantity as a sum/product of the several measured quantities, and you are interested to calculate the uncertainty of that physical quantity. I have just learned about the Monte Carlo method applied to error...

My work is attached. I did get the answer right using the formula V=√(G*me/r). Im just confused as to why I can't use V=2pi*r/T to also get the right answer? With this equation I would assume T=86400s. I was able to use both equations to get the correct answer for a problem relating to...

Attempt at solution: I wanted to try and solve this with dimensional analysis. I reasoned that I would chose the following dependent variables: - [V] : Volume ( of the block) - [Q] : Heat ( the radioactive decay would cause some heating of the water) - [R]: Radiation - [Cv]: Heat capacity...

Hi, I'm reading the volume 1 of "Introduction to calculus and analysis" by Courant and Fritz but the problems are hard for me, i understand what he say but i can't solve many problems of the chapter one. It's normal or should i try with other book?

time = x(min) distance = 1(y) y = unknown unitsI think the answer should be 1(y)/ Min. This is not correct becase 1(y) is unknown. Any help? I have the answer but am confused

Ans: 0.123A Tried mesh analysis and got it but didnt for nodal analysis

Let us suppose we have one constant variable ##b \pm \delta b = 20 \pm 1 ## and one function that depends on ##x ##, such as, ##a(x) \pm \delta a ## The problem is I want the difference between ##a(x) ## and ##b ## to be ##0 ##. Let me denote this difference as ##c \pm \delta c ##. To...

Hey! :giggle: Question 1: If $f\in O(\Delta (0,1,15))$ then does it hold that $$\int_{C(0,10)}\frac{f(z)}{(z-6+4i)^5}\, dz=2\pi i\text{Res}\left (\frac{f(z)}{(z-6+4i)^5}, 6-4i\right )+\int_{C(0,6)}\frac{f(z)}{(z-6+4i)^5}\, dz$$ Do we maybe use here Cauchy theorem and then we get...

I have a problem: in the same anime I saw that Senku estimated the time to start burning the paper in sixty seconds, one minute and with a lens. The data is as follows: The lens he used has a diameter of 5 centimeters. The solar constant, assuming it is the same as 3700 years ago, is 1362 watts...

#### If ##b \leq x_n \leq c## for all but a finite number of n, show that ##b \leq \operatorname{lim inf}_{n \to \infty} x_n## and ##\operatorname{lim sup}_{n \to \infty} x_n \leq c_n## (Buck, Advanced Calculus, Section 1.6, Exercise 24) Let ##\beta =\operatorname{lim inf}_{n \to \infty} x_n##...

Clearly, ##x_{n+1}>x_n \because x_n + \sqrt{x_n} > x_n## $$ \begin{align*} x_{n+1} &= x_n+ \sqrt{x_n} \\ &= x_1 + \sqrt{x_1} + \sqrt{x_2} + \cdots \sqrt{x_n} \\ &>n+1 \end{align*} $$ ##\because \sqrt{x_n}>\sqrt{x_1}=1## In fact, $$x_{n+1} > 1+ \sqrt{1} + \sqrt{2}+ \sqrt{3} + \cdots \sqrt{n}$$...

I'm reading this chapter in Electrical Engineering book regarding AC circuit analysis where there is a solved example which I've attached, but there are some concepts that are confusing me. First, why and how do we know that the phasor value of voltage is: -pi/2 Note: I do understand that...

I find the following definition in my complex analysis book : Definition : ## F(z)## is said to be a branch of a multiple-valued function ##f(z)## in a domain ##D## if ##F(z)## is single-valued and continuous in ##D## and has the property that, for each ##z## in ##D##, the value ##F(z)## is one...

Hi folks, I'm looking for a solid introductory book on electronics and circuit analysis. I have seen The Art of Electronics highly recommended. I will likely get it but as a supplement. Does anyone know of any other good electronics textbooks? I don't mind old textbooks. Some of the newer...

Problem: Source: Halliday et al Physics 4e, p9, sample problem 4. Why is it valid to assume that $$F\alpha v^b$$ as the author does here, and not some more complex equation e.g. $$F=av^{e_1}+bm^{e_2}+cr^{e_3}$$, or $$F=av^{e_1}+bv^{e_2}+\cdots $$ (or some other equation)? A very similar...

Hi, I wonder how to approach stress analysis of quick return mechanism used in shaper machines (see the diagram below): The first issue is: which moment in the working process of this mechanism should be used for analysis (when will the mechanism experience largest loads)? So far I assumed...

I have done a bit of googling but cannot find anything in this regard at all. It seems to all be "thought of" (rather than explained) by the Huygens–Fresnel principle and other spin offs. Can anyone point me to a particle explanation of diffraction for sound waves? Or does anyone here have...

What is meant by the constant background and how would one deduce the half-life IF not from the fit?

This author seems to say so: https://blogs.scientificamerican.com/roots-of-unity/one-weird-trick-to-make-calculus-more-beautiful/

Can anyone suggest a good lecture series on Complex Analysis on YouTube? I have already searched on YouTube myself, and there are a few. But I wanted to know if any of you would recommend some particular lecture series which you consider to be good.

Hello all, I have been asking this question, here, and gaining more insight. I think I can finally ask it the way I need. I can: Conduct an eigenvalue analysis Code the Lanczos algorithm. Understand mode shapes Build the solution of set of coupled differential equations from mode shapes...

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Hello I have tried asking this different ways, here. I do not know exactly what I am asking. So I am hoping to try again. Say we have a differential equation for a multi-body system. We cannot solve it because of the coupling (too difficult). So, we turn to a modal analysis (eigen value...

I think there are 4 essential node. So we can write 3 KCL independent equations.

Hello. Could we approximate a tensor of (p,q) rank with matrices of their elements? I am talking also about the general case of a tensor not only special cases. For example a (2,0) tensor with i, j indices is a matrix of ixj indices. A (3,0) tensor with i,j,k indices I think is k matrices with...

Could you tell me which one of these, but also why because I want to understand. Thank you!

Hello The figure below is that of a two body problem in oscillation. Whether by Free Body Diagrams or Hamilton's Principle, we can obtain the two coupled differential equations that describe the oscillation. At this point, one could obtain the closed form solution for the displacement...

For this one circuit, I've applied Kirchhoff's laws as following: $$\left\{\begin{matrix} V-6\Omega I_{6}-24V-2\Omega I_{2}=0\\ 24V-6\Omega I_{6}-12V-24V=0\\ I_{2}+I_{6}=6A \end{matrix}\right.$$ but the values I get for ##I## and ##V## aren't correct... what's wrong?

I've just studied simple pendulum: The simple pendulum (for small oscillations) differential equation is first image. I've no problem to arrive this result and formula. My problem is to get to the second formula by passing through another formula (Image 3) that my book mentions. I can't...

$$cos\theta = \frac {s}{1-s} = \frac{p-1}{p}$$ in this equation ##\theta## is the bond angle and ##s## and ##p## are the fractional s-character of the orbital and p-character of the orbital. This is equation is used rigorously in showing that the s-character of the axial orbitals in a ##sp^3d##...

So I found a paper, https://www.sciencedirect.com/science/article/pii/S0022231314006048?via%3Dihub which concerns a property of a compound called "Quantum Yield", which is a result of various factors (independent variables). The authors are trying to figure out what factors affect the quantum...

Hi there, attached were the results: https://prnt.sc/v3yg1f Both are negative and need to be added together to get the torque force. Calculations are from a model of specified radius and input air speed, its a turbine. Just need help in understanding what the negative results mean and how they...

Hello everyone, My question for this thread concerns the application of (mainly) mathematical analysis to fields such as signal processing and machine learning. More specifically, I was wondering if you happen to know of some interesting application of things like measure theory or functional...

So, I have calculated that to dimmensional analyse this equation;

Dear all, We learn students to work with significant figures. I guess we all know those rules of thumb. Now imagine I have an expression like L = 2x, where x is a length a the 2 is an amount, i.e. the value of a discrete 'function'. If x=0,72 m (2 significant figures), then L = 1,44 --> 1,4 (2...

Do you think a first course in analysis should focus entirely on inequalities and leave set-theoretic topology for another occasion? Should this depend on whether or not the student had a first rigorous calculus course first? If I'm not mistaken, Victor Bryant (Yet Another Introduction to...

I've attempted this questions after understanding the theory from my lecture notes, but my equation is looking bizarre here. Is this correct so far? Are my mesh equations correct here? Thanks.

My homework is on mathematical physics and I want to know the concept behind Laurent series. I want to know clearly know the process behind attaining the series representation for the expansion in sigma notation using the formula that can be found on the attached files. There are three questions...

I know that dimensional analysis is a rough way to check the correctness of the solution to a homework problem. However, what exactly is it and what are the other applications of it? Why does it work? Thanks.