Analysis Definition and 999 Threads

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.

Hello I have used and enjoyed the textbook: "Theory of Vibrations with Applications," by William Thomson However, many of the examples there are more civil engineering than mechanical. There are many good examples of "buildings" under vibrations (good examples, but civil, nonetheless) The few...

Hi All Someone passed onto me the following supercomputer analysis of the Covid virus: https://elemental.medium.com/a-supercomputer-analyzed-covid-19-and-an-interesting-new-theory-has-emerged-31cb8eba9d63 Very interesting. Thanks Bill

My understanding in modal analysis is very limited. All I know is it helps to find a specific mode of vibration and the natural frequency corresponding to it. While I was discussing about this with my NVH team colleague, he told me that there is no force input or excitation input given to a...

Please help me to find out if this is a feasible project. If not, what changes shall be made to make it sustainable for a long time without changing the layout? 1. Details of the stand: L 36", W 18", H 30" 2. Details of Aquarium 1: L 36", W 18", H 18", weight: 225kg 3. Details of Aquarium 2 and...

Hey! I have been thinking about different topics on mathematics, and for some reason I feel, that applied mathematics and doing numerical computations is often overlooked. When I was studying in university, more than 95 % of all examples which would require numerical methods were either omitted...

Good afternoon. As part of a personal hobby, I've been trying to design a relatively small projectile that can travel at 'bullet speed' (say, a .22 caliber bullet fired from an appropriately sized gun). I understand that the overwhelming majority of mass-produced bullets today come in a small...

Hi all, Managed to get an answer out, but unfortunately, it doesn't correspond with the answer given ( –3.09 A) Would appreciate if one could check out what I did wrongly here: ## V_{1}=2\times 5=10V ## At node 2: ## \dfrac{V_{1}-V_{2}}{2}=12+\dfrac{V_{2}}{1}+\dfrac{V_{2}-V_{3}}{2}## We can...

I am an incoming university freshman in the U.S. who wants to major in physics but also wants to add a minor that will help build some more applicable skills. As the title suggests, I am looking for some insight into a stats/data analysis minor since a close friend of mine majored in applied...

I am reading A Course in Mathematical Analysis Volume 1 by D. J. H. Garling, and I am having trouble in the following demonstration of Section 2 Differentiation. part 4 of the test, the first part of the second inequality does not make sense, I do not understand its justification. I hoped they...

I have to show that $\forall z\in B(0,0.4)$, there exists an $x\in B(0,1)$ such that $f(x)=z$ but I am not sure how to show this. From the reverse triangle inequality $$-|f(x)-f(y)|+|x-y|\leq 0.1|x-y|\implies |f(x)-f(y)|\geq 0.9|x-y|$$ im not sure if this helps.

I know that moment is distance vector x force vector x the degree between them. I understand it uses the moment about A to solve for the unknown force R. I don’t understand why it use Rx1.2m and why the perpendicular distance between A and R is 1.2m. could anyone please explain why? Many...

Hi. I am looking for a book about tensor analysis. I am aware that there have been some post about those books, but I wish to find a thin book rather than a tome but just good enough for physics, such as group theory, relativistic quantum mechanics, and quantum field theory. I am reading...

I have been reading Manton & Sutcliffe for some time now and can't quite wrap my head around something. If you take the Hopf invariant N of a topological soliton ϕ then its Skyrme-Faddeev energy (which I hope I've gotten right up to some constants) E=∫∂iϕ⋅∂iϕ+(∂iϕ×∂jϕ)⋅(∂iϕ×∂jϕ) d3x satisfies...

I am close to graduating as an EE major but I have never been able to organize a step by step method on analyzing a circuit. It seems to me that every time I am trying to analize a circuit I end up with a bunch of equations and nothing more. I know that I should: 1. Know what I am solving for...

All books in analytical mechanics explain the case of a particle moving on a given static surface. But what happen if, for example, the surface is having some deformation?. I imagine that the principle of virtual work, and hence, D'Alembert are no longer valid since the normal force by the...

I am not clearly understand what the question requests for, is it okay to continue doing like this ? Kindly advise, thanks

First of all, i tried to find w, the angular frequency, by calculating the oscillations from ta to tc, there is ~ 20 oscillations coursed. so, w = 2*pi*20/(tc-ta) ta = 0, tc = 0 + 5.2 ms And tried to find the factor gama y by A(t) = A*cos(Φ + wt)*e^(-yt/2) A(0) = 2.75u = A*cos(Φ) 1u = A*cos(Φ...

Hello Everyone! I want to learn about Fourier series (not Fourier transform), that is approximating a continuous periodic function with something like this ##a_0 \sum_{n=1}^{\infty} (a_n \cos nt + b_n \sin nt)##. I tried some videos and lecture notes that I could find with a google search but...

hi guys i saw this problem in my collage textbook on vector calculus , i don't know if the statement is wrong because it don't make sense to me so if anyone can help on getting a hint where to start i will appreciate it , basically it says : $$ \phi =\phi(\lambda x,\lambda y,\lambda...

Picture source:GSE94799 Following are the two different types of bar-digram that were observed. My questions are: 1. What do bars hanging below 0 mean in the first dig. ? 2. What do bars shooting from -6 mean, also why are they below 0? 3. Like a normal gene (non-ncRNA gene) expression profile...

Hi All, I am working on this linkage mechanism. Please see the attachment for images. There are 3 pivot points. Two of which are connected to the ground. The" Inside Leg 1" is telescopic to "Leg 2" and has a 120 LB compression gas spring connected at mount points as shown in the image. The leg...

Thank you all for clearing my doubt before. There is a question I want to ask on space and time and this time it is not about the absolute time as I have understood fairly that space and time are always relative. So Here it is according to GR It is very beautifully explained that Very massive...

I need to find A_v, I want to relate Vin to Vout. To do this I did KVL on the major loop: $$V_{DD} = I_D*R_D + V_{SD1} - V_{SD2} - I_D*R_D$$ Since M1 = M2 then everything would cancel out and I would just get V_dd = 0 which is probably wrong. This is assuming V_sd1 = V_sd2, is that correct?

Consider this system, above. If I studied the mechanics of this system, I get this system of equations. At that point, I choose to study a free vibration problem and drop the damping, and conduct a modal analysis. I understand the process:vvI assume a solution such that each mass moves...

Article: https://www.pnas.org/content/early/2020/05/12/1921655117 Phys.org link https://phys.org/news/2020-05-odds-life-intelligence-emerging-planet.html An issue I see is Mars and Venus. Mars may have had some life forms, and may still. Venus never got that far. So, in a sense, we are 1...

Was just practicing some problems on the Fundamentals of Electric Circuits, and came across this question. I understand I will have to transform to the s domain circuit, which looks something like this: Then doing nodal analysis, I will get the following for the first segement (10/s-V1)/1 =...

I consider the band-pass filter of the following configuration (the ##u_m## is a voltage controlled voltage source): The transfer function is $$K_1(p)=\hat{U}_o(p) = \frac{p}{RC(p+1/RC)^2} = \frac{\omega_c p}{(p+\omega_c)^2}, \quad \omega_c=\frac{1}{RC}.\qquad (1)$$ Now I connect ##n## such...

Not sure if this is the correct forum. But are there any video lectures that follow the book Pugh: Real Mathematical Analysis? Thanks.

I've tried to solve the following circuit using mesh equation, but the solution seems to differ from my attempted answer. Mesh circuit as follows: My mesh equation is: -10+3(i1)+2s(i1-i2)=0 (for the mesh on the left) and -10+12(i2)+6s(i2)+2s(i2-i1)=0 (right mesh) However the answer seems to...

Hi, I am a physicist interested in going through a basic analysis course. The real line, open sets, that whole thing. On my own, so I need a good selection of bibliography, ranging from those that are good references but too dense to actually read to those that are very pedagogical but tend to...

Ok, so here is what I have so far: Suppose ##T_1## is infinite and ##\varphi : T_1 \rightarrow T_2## is a bijection. Reasoning: I'm thinking I would then show that there is a bijection, which would be a contradiction since an infinite set couldn't possibly have a one-to-one correspondence...

well each one is a little different so,,, $$\dfrac{dy}{dt}=\dfrac{ty(4-y)}{3},\qquad y(0) =y_0$$ not sure if this is what they meant on the given expression

As I understand, if you solve the Maxwell's field equations for a resonant cavity, supposing a time dependence of the form ##e^{iwt}##, you get an eigenvalue problem and different modes as possible solutions. I'm reading some notes where the author states that each mode can be associated with a...

Summary:: What should I do to specialize in material analysis techniques as a career option? What should I do to specialize in material analysis techniques as a career option?

is my solution correct?

I’m using discriminant function analysis to determine the potential accuracy of several biometric measurements being used in conjunction for binary classification purposes for my BSc Biomed research project. Overall I've only got 110 data points so it's a stretch but hey, that's anatomy! What...

Here is my solution. I used mathjax to type it up in Overleaf. I feel like it makes sense, but I also have a feeling I might have "jumped the gun" with my logic. If it is correct, I would appreciate feedback on how to improve it. Thanks!

Hi all, Having some problems digesting on electric circuits. Below is an example of a question and I would like to ask how do I go ahead in solving this. Firstly, for these types of questions: I have understood how to write a function table, and it goes something like this: Now what I am...

Solution Attempt: \begin{align} \frac{\partial u}{\partial x} &= \frac{\partial v}{\partial y} = (x^2+y^2)^{-1} -x (x^2+y^2)^{-2} (2x) = (x^2+y^2)^{-1} - 2x^2 (x^2+y^2)^{-2} \\ \rule{0mm}{18pt} \frac{\partial u}{\partial y} &= -\frac{\partial v}{\partial x} = -x (x^2+y^2)^{-2} (2y) =...

My work seems to be wrong somehow since my answer is wrong, and I need your help to find out which part is going wrong for me :/ My work: 1. 2. 3. 4. 5. 6. (10/7)/(10/7+7) = 0.7627A, which is not the answer. May I consult where is the problem in solution? THanks

Now, I know this question can be solved using Kirchoff Voltage rule, but the question expliciitly wants me to use power supplied = power absorbed. Hence taking V0 to be x, I can't still seem to calculate. Any ideas? Power supplied = (60)(3) + (5x)(3) = 180+15x Power absorbed = 72+ 56 +28 + 3x...

Find the only periodic solution for 𝑦′+𝑦=𝑏(𝑥) with 𝑏:ℝ→ℝ has a period of 2𝑇 and is 1 for 𝑥(0,𝑇) and −1 for 𝑥(−𝑇,0). The ODE is easy to solve: 𝑦(𝑥)=exp(−𝑥)⋅𝑐+1 and 𝑦(𝑥)=exp(−𝑥)⋅𝑐−1. But how can I find the 𝑐 such that the solution is periodic with a period of 2𝑇? The solution is...

Hello, My university offers a couple Complex Analysis courses, among them there is one with the following description: Introduction to complex variables: "substantial attention to applications in science and engineering. Concepts, calculations, and the ability to apply principles to physical...

I am able to draw shear and bending moment diagrams. We were never taught how to even start with a problem like this.

Hello, thank you for your attention in my thread. I'm the head of Youth Science Club on one of the many High School in Indonesia, I got many members and I want to guide them for doing water sampling and analysis. In the history of my high school, no one is able to do water sampling and...

Hi I have a project regarding micromechanics of composites. I'm starting my analysis on the Fiber Matrix RVE. Right now I'm trying to find the natural frequency of the unit cell. The Unit cell has some unique geometry which I will keep on changing to see how natural frequency changes. I have...

I'm posting the images of "Sommerfeld's Lectures on Theoretical Physics, Vol 2, Mechanics of Deformable Bodies" I apologize for posting the images rather than writing out the whole thing. But I did it to so that nothing should be missed, as writing out the...