Analysis Definition and 999 Threads

Homework Statement Hi guys I'm doing the mesh analysis of AC circuit and looking for some guidance. Here is the mesh picture and some components data: Homework Equations Kirchoff's voltage law and current law.The Attempt at a Solution I decided that mesh currents are going in clockwise...

How is symmetry used to solve electrical circuits? I have seen several problems in books in which currents in two resistors are said to be equal due to 'symmetry'. That is a concept that I fail to understand and thus cannot apply. In class, we were shown a few circuit diagrams which were...

High school student here... Recently, I've found an interest in topology and am trying to figure out the correct path for self-studying. I am familiar with set theory and some concepts of abstract algebra but have not really studied any form of analysis, which from what I've read is a...

I'm beginning to study analysis beyond real numbers, but I am a but confused. What is the relation between topology, metric spaces, and analysis? From what it seems, it's that metric space theory forms a subset of topology, and that analysis uses the metric space notion of distance to describe...

Hey, I have been stuck on this question for a while: I have tried to follow the hint, but I am not sure where to go next to get the result. Have I started correctly? I am not sure how to show that the integral is zero. If I can show it is less than zero, I also don't see how that shows it...

Homework Statement Suppose sequence x_n tends to 0 as n approaches infinity, prove that sqrt(x_n) also tends to 0 x_n is a sequence of non negative real numbers Homework EquationsThe Attempt at a Solution Proof. Let e>0. There exists an N in the naturals such that for n>N Ix_nI < e So if I...

Homework Statement Given this following circuit: What is the internal resistance of the meter movement ( R_I). This is part of a project I'm doing and I know the equation that gives you the internal resistance in this circuit. $$R_I = \frac{R_sR_p}{R_s - R_p}$$. However, I have no idea how...

Homework Statement (FYI It's from an Real Analysis class.) Show that $$\int_{0}^{\infty} (sin^2(t) / t^2) dt $$ is convergent. Homework Equations I know that for an integral to be convergent, it means that : $$\lim_{x\to\infty} \int_{0}^{x} (sin^2(t) / t^2) dt$$ is finite.I can also use the...

Homework Statement Homework Equations The relevant equation is that sqrt(z) = e^(1/2 log z) and the principal branch is from (-pi, pi] The Attempt at a Solution The solution is provided, since this isn't a homework problem (I was told to post it here anyway). I don't understand why the...

Homework Statement I can't understand an equation to LDA. The context is: Maybe the lecturer is trying to create a proof of the equation given below. I know the above that LDA projects the points along an axis so that we can have maximum separation between two classes.in addition to reducing...

Homework Statement Menthol, the substance we can smell in mentholated cough drops, is composed of C, H, and O. A 0.1005-g sample of menthol is combusted, producing 0.2829 g of CO2 and 0.1159 g of H2O. What is the empirical formula for menthol? If menthol has a molar mass of 156 g/mol, what is...

This question is about the matching the unites in an equation. The equation for an electron mobility is given by m^2/V.S. However substituting the units in the equation, doesn't yield the unit of mobility [m^2/V.S]. I have done the simplification using mks units and didn't come up to m^2/V.S...

It is mentioned in Reif's book, statistical physics, that trough dimensional analysis it can be shown that: $$\frac{1}{\beta} = kT $$ where ##\beta## equals ##\frac{\partial \ln \Omega}{\partial E}## and k is the Boltzmann constant. I don't quite see how to reach this result, can anyone give me...

This is probably a stupid question but I have Neumann BC boundary : ## \nabla u . \vec{n} =0## (same for ##v##)conditions for the following reaction-diffusion system on a [0,L_1]x[0,L_2]x...x...[0,L_n] n times in n dimensional space so ##u=u(x_1,...,x_n,t)## is a scalar I believe? so that ##...

Homework Statement The period of oscillation of a nonlinear oscillator depends on the mass m, with dimensions M; a restoring force constant k with dimensions of ML-2T-2, and the Amplitude A, with dimensions L. Use dimensional analysis to show what the period of oscillation would be proportional...

Hi. I have 2 questions regarding removable singular points. 1 - the residue at a removable singularity is always zero so by the residue theorem the integral around a closed simple contour is zero. Cauchy's theorem states the integral around a simple closed contour for an analytic function is...

Homework Statement [/B] Determine, Using the values given in TABLE A, the current I in the circuit of figure 2 by (a) Mesh analysis (b) Nodal analysis Circuit diagram and given variable attached. V1 = 120 V2 = j120 V3 = 14.142+j14.142 Z1= 2 Z2=-J5 Z3=4 Z4=-J5 Z5=J4Homework Equations [/B] KVL...

Do electrical engineers actually use stuff that is taught in Circuit Analysis classes like Node Voltage Method, Mesh Current Method, Kirchhoff Voltage/Current Law, Source Transformation. All these usually only involve resistors. Are they somewhat altered in a way to analyze circuits with other...

Node Voltage Method or Mesh Current Method.

Hi everyone. Some years ago I read about the Crower six cycle engine. Always wanted to understand it better. And now is the time to follow up on that desire. I’m trying to calculate what happens during the water injection. The goal is to determine the conditions (pressure, temperature)...

Homework Statement Let ##C \subset \mathbb{R}^n## a convex set. If ##x \in \mathbb{R}^n## and ##\overline{x} \in C## are points that satisfy ##|x-\overline{x}|=d(x,C)##, proves that ##\langle x-\overline{x},y-\overline{x} \rangle \leq 0## for all ##y \in C##. Homework Equations By definition...

Homework Statement Use unit analysis to show that the constant, 2π, is unitless. Homework Equations T=2π√L/g[/B] The Attempt at a Solution T= [T] L= [L] g= a= [L]/[T]^2= [L T^-2] [T]= 2π√[L]/[L T^-2] [/B] Is this correct? I wasn't really sure how to do this. I'm using book examples to...

I will state the problem below. I don't quite understand what I am needing to show. Could someone point me in the right direction? I would greatly appreciate it. Problem: Let p be a natural number greater than 1, and x a real number, 0<x<1. Show that there is a sequence $(a_n)$ of integers...

I am working a bunch of problems for my Real Analysis course.. so I am sure there are more to come. I feel like I may have made this proof too complicated. Is it correct? And if so, is there a simpler method? Problem: Show that $liminfa_n \leq limsupa_n$. Proof: Consider a sequence of real...

Good morning, I used the Laser beam with HR4000 spectrometer with Ocean View software when saving the files it is saved by (.ocv) format. when trying to extract information to excel I get some unreadable data like (bkg thin sheet gel.png) attached. I used the same instrument and software with...

Homework Statement It requires 10 microliters of a Cu(NO_3)_2 solution to produce a spot of 1cm in diameter. If the Cu(NO_3)_2 solution contains about 6g Cu^2+ per liter, then how many micrograms of Cu^2+ ions are there in one spot? Homework Equations simple dimensional analysis problem: 1st...

Homework Statement Basically the units of the Canonical Partition Function within the logarithms should be zero Homework Equations The Attempt at a Solution N here is a number so we ignore the left logarithms, applying a "Unit function " for the terms within the logarithm...

Homework Statement [/B] Let X be a vector space over ##\mathbb{R}## and ## f: X \rightarrow \mathbb{R} ## be a convex function and ##g: X \rightarrow \mathbb{R}## be a concave function. Show: The set {##x \in X: f(x) \leq g(x)##} is convex. Homework Equations [/B] If f is convex...

I have no idea how to do the node analysis for this circuit. I have done the mesh analysis and got the current in R3 to be 4A is this right?

Homework Statement Q1. a) In relation to Fourier analysis state the meaning and significance of 4 i) odd and even functions ii) half-wave symmetry {i.e. f(t+π)= −f(t)}. Illustrate each answer with a suitable waveform sketch. b) State by inspection (i.e. without performing any formal analysis)...

The question(s) here can be asked for many problems (and not just sorting). Let's consider the standard case of sorting an array of size ##n## containing numbers. If we consider a naive algorithm, its time would be proportional to ##n^2##. For example, the naive algorithm could be proceed with...

Anyone completed IA Maron Mathematical Analysis? Anyone like it?

Hi, Anyone out there using Megastat? The course I am in requires using it/knowing how to use it for processes. Whenever I try to get a regression analysis it insists that I need to set a confidence level - I've tried different versions of typing 95%/0.95 into no avail, and I don't know what...

Homework Statement 1. Show that for all real numbers x and y: a) |x-y| ≤ |x| + |y| Homework Equations Possibly -|x| ≤ x ≤ |x|, and -|y| ≤ y ≤ |y|? The Attempt at a Solution I tried using a direct proof here, but I keep getting stuck, especially since this is my first time ever coming...

Hi I have the following situation: (Please see attached pic) I want to know if equation (4) i have written is correct. What is confusing me is that, I remember being told in circuit analysis that each energy storage element should have its own state variable. But in this situation when I...

Hello all, I may get a contract to teach numerical analysis. I did quite a lot of numerical work during my PhD but that was a while ago. Now when I look at most books on the topic, I get the feeling that a lot is outdated, and I also feel that a lot of what I knew is outdated as well...

Homework Statement Let ##x,y \in \mathbb{R^n}## not null vectors. If for all ##z \in \mathbb{R^n}## that is orthogonal to ##x## we have that ##z## is also orthogonal to ##y##, prove that ##x## and ##y## are multiple of each other. Homework Equations We can use that fact that ##<x ...

I learned my analysis from Ruden way back when. It fell apart from overuse so I got two books to replace it - Apostol and Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by Hubbard - both very different in approach. But recently I have read Terry's two volume set...

##X_i## is an independent and identically distributed random variable drawn from a non-negative discrete distribution with known mean ##0 < \mu < 1## and finite variance. No probability is assigned to ##\infty##. Now, given ##1<M##, a sequence ##\{X_i\}## for ##i\in1...n## is said to meet...

Homework Statement The switch in the circuit in has been closed for a long time. At the switch is opened. a) Find i0 for t>=0 (b) find v0 for t>=0 I don't understand the effect of the switch in the position it is in. It's acting as a short circuit, I think, so presumably the capacitor doesn't...

Comparative genomic analysis (Free pdf download here) shows that Lokiarchaeon (the mysterious closest presumed relative to the archaeon host (known only by its genome sequence collected from an environment), which contained the endosymbiont bacteria (that became the mitochondria), had hydrogen...

A school educator is interested in determining the potential relationship between grade point average (GPA) and IQ scores among ninth graders. The educator takes a random sample of 30 ninth graders aged 14 years old and administers the Wechsler Intelligence Scale for Children-Fourth Edition...

Homework Statement The problem asks to solve for i1, i2, and i3 using the mesh method in the following circuit: I will also include the link, because I noticed I am having trouble attaching the image to the post: https://imgur.com/a/bBvuLXM I would also like to confirm the answer by solving...

Homework Statement Assume all ##s_n \neq 0## and that the limit ##L = \lim \vert \frac{s_{n+1}}{s_n} \vert ## exists. a) Show that if ##L < 1##, then ##\lim s_n = 0##. (Hint: Select ##a## so that ##L < a < 1## and obtain ##N## s.t. ##\vert s_{n+1} \vert < a \vert s_n \vert## for ##n \ge N##...

Homework Statement Identify the set of points satisfying ##1<\vert 2z-6\vert <2## such that ##z\in\Bbb{C}##. My pre-caculus is very rusty, so I am not sure if I am doing this correctly. Homework Equations ##x^2 +y^2= r^2## ##\forall z,z'\in\Bbb{C}, \vert zz'\vert =\vert z\vert\vert z'\vert##...

I have a question regarding a theoretical analysis of Ultrasonic waves : The next picture represents a system of transducers sitting on fixed boards: Datum: * there are 4 transducers ( represented by blue color , indexed by letter ' T ' ) , each outputting Ultrasonic wave (represented by...

My task is to analyze a frame's strength of a specific motorcross using different loads, and to do this i decided to focus on vertical fall from various heights, since this will probably give the largest forces on the bike. The one can also experiment with different types of landings, i.e...

Hey, I am interesting in analyzing a bicycle's frame statically from a vertical fall of x metres, this after using the energy principle i get that the force F = mv^2/r, where v = sqrt(2*g*h), r is the deformation of the bicycle at its contact point and m is total mass from the cycle and cyclist...

When we define a limit of a function at point c, we talk about an open interval. The question is, can it occur that function has a limit on a certain interval, but it's extension does not? To me it seems obvious that an extension will have the same limit at c, since there is already infinitely...

Hi fellow forum-ers :), I have a test in about two weeks where i am going to be given a dtl or ttl circuit which i have to analyse and calculate its function. The professor said that the circuit given to us will always be a useful and existing one meaning he's going to give us some NAND, NOR or...