Analysis Definition and 999 Threads

Problem Statement: Finding the resistance when probed at point bc, cd and da Relevant Equations: Series and Parallel resistance equation derived from kirchhoff's law with application of ohm's law I genuinely don't know what to do on this one. The example our professor made isn't exactly clear...

Hi I am sitting with a homework problem which is to show if I can actually integrate a function. with 2D measure of lebesgue. the function is given by ##\frac{x-y}{(x+y)^2} d \lambda^2 (x,y)##. I know that a function ##f## is integrable if ##f \in L^{1}(\mu) \iff \int |f|^{1} d \mu < \infty##...

Using the given formula, meq of H2SO4 reacted= meq of salt = 5.205 The math is correct and I have verified it. Now, I am pretty sure that I am making a mistake in calculating the n- factor of the salt. According to the question, C4+6=4C+4 The n- factor is coming out to be 10, which is pretty...

My background is BS Math with Physics minor (3.5) and MA Math (3.7) from the University of Houston. My current plan is to explore the necessary background for doing research in finite element analysis. Over the next few semesters, I plan to take Numerical Methods for PDEs, Statistical Computing...

My attempt: At node 1 > 4 = 6 + I1 Node 2 > I1 + I2 = I 2 Node 3 > 6 = I 3 + I 4 I1 = (V1 - 4)/21 In node 1, Using the equation for I1, V1 = -38V. I2 = (V1 - 4 - 1)/2 So, I2 = -21.5APower supplied by the 1V battery is P=VI P=-21.5 x 1 P=-21.5W I am not sure of my method, I just started...

Above is the figure of the question. According to Kirchhoff's Rule, I have obtained three equations $$\varepsilon-iR_{10}-L_{40}\frac{di_1}{dt}=0$$ $$L_{40}\frac{di_1}{dt}-i_2R_{60}=0$$ $$i_2R_{60}-R_{30}(i-i_1-i_2)-L_{15}\frac{d(i-i_1-i_2)}{dt}=0,$$ where ##\varepsilon## stands for emf=100V...

Is there like a rule of thumb, or a simple hack for assigning current direction in circuit analysis? Even when I m consistent with the direction I choose, I still get the wrong answer most of the time. Like 1. Do current source or voltage source affect when choosing current direction? 2...

I assumed the current flows from the 20V so, 20V - 100 (i1) - Ri2 = 0 First loop 20V = 100i1 + Ri2 Second loop +Ri2 + 40V - 200(0.08) = 0 Ri2 = -24 Back to equation 1 20 v = 100i1 + (-24) therefore, i 1 = 0.44 For loop two: i1 - i2 = i3 0.44 - i2 = 0.08 therefore i2 = 0.36 ohms...

I am interested in determining more efficient ways of determining individuals' body fat percentage. To do this, I measure the circumference of a number of segments (10 of them) of the body and determine the person's percentage body fat through underwater weighing. I have done this for 252 total...

I am interested in examining how construction stilts affect walking patterns, and how experience with the stilts affects walking patterns. I recruited a group of expert construction stilt users, and a group of novice users and videoed their both walking on stilts and without stilts. I want to...

(A)My textbook states the following : (1) The example explaining the italicised statement is rather confusing. My understanding of the statement is that we need to include one extra significant figure than what the relevant rule requires us to round off to, for intermediate...

Hello, My question is what types of data analysis can I perform on a set of theoretical and experimental results? For example, I have v(x) = cos(x) and I plot my observed data to v(x). Thanks!

Hello, I am using CFD to analyse a Kaplan turbine and am unsure on how to interpret the torque values as they come as x, y and z components. My understanding is that the z component in this case will determine the rotation direction depending on whether it is positive or negative however I am...

My initial attempt had me combining the 40 and 20 ohm resistors in series, then combining the result with the 120 ohm resistor in parallel (top). However, this was incorrect. According to my answering guide, the correct method was to transform the voltage source into a current source, then...

I'm currently testing the overtone spectrum of several instruments. I haven't been able to find a freeware program that's well suited to my needs. In particular, I would like to be able to pause the playback of each overtone spectrum at specific intervals in order to compare the instruments...

Hi! I've been struggling with this. Original exercise here: Find the value of Iy when R=0. And the value of Vx when R is infinite. For the first part of the question I did this since R=0: I've tried to solve this circuit and I get that Iy and I5 are 0 A, and this can't be possible since Iy...

Hi PF! Can someone help me understand the notation here (I've looked everywhere but can't find it): given a function ##f:G\to \mathbb R## I'd like to know what ##C(G),C(\bar G),L_2(G),W_2^1(G),\dot W_1^2(G)##. I think ##C(G)## implies ##f## is continuous on ##G## and that ##C(\bar G)## implies...

Homework Statement The following may appear to be a rather strange question but I have no access to a lab to conduct experiments so I have to rely on my imagination, and questions from textbooks, to contrive questions that will hopefully improve my understanding of a topic. I have recently...

I found the formula but I can't understand how to interpret the 3 cases. Case 3 make sense. d > 0 if a > 0 because Vo^2 > 0 and Δx > 0 by default (can't have negative length). In this case t2 is negative because the numerator is a sum of two negative values and the denominator a > 0 so we...

Hi. I am currently studying the market for equity options and the use of these to predict stock return around company earnings announcements. The dependent variable in my regression analyses have been the relative change in stock price or log-return from the day before the announcement to...

Homework Statement Find the current in each resistor. (refer to uploaded diagram) Homework Equations ##Kirchhoff's Law: I_s=I_1 + I_2## Mesh analysis method The Attempt at a Solution I'm calling ##I_s## the total current before and after the current splitting up, and ##I_1## and ##I_2## are...

Hello! I have been searching the web and textbooks for a certain theorem which generalizes the value of the integral around a infinitesimal contour in the real axis, or also called indented contour over a nth order pole. It is easy to prove that if the pole is of simple order, the value of the...

Homework Statement Homework Equations I've worked out the KVL's for four meshes, I1, I2,I3, and I4. Would anyone be able to error check this for me? Also, would I be correct in thinking that I can use ohm's law by dividing V1/Z1 to find the current of the first mesh and likewise with...

I have an interest in storing, for later use, energy from excess shaft power developed by a wind turbine. Currently I am assuming that the compressor is running in a steady fashion, continually drawing 300K, 1.0 atm. air into the compression chamber and compressing it to 20 atms. before...

Lets say I am analyzing a simple AC voltage source with a resistor. In the positive voltage peak then I will use V and I say current is flowing clockwise. When I am analyzing the -Vpk iteration then do I make the current counter clockwise too or do i keep it clockwise? Thanks.

Homework Statement We've been given a set of hints to solve the problem below and I'm stuck on one of them Let f:[a,b]->R , prove, using the hints below, that if f is continuous and if f(a) < 0 < f(b), then there exists a c ∈ (a,b) such that f(c) = 0 Hint let set S = {x∈[a,b]:f(x)≤0} let c =...

I'm in my second year in college and I've taken an Operating Systems course that has a project component. I've been assigned Memory Forensics as my project topic. On approaching the professor I was told that I need to attempt to attack the Linux Kernel ( I'm guessing that means I need to write...

Hello, I was interested in learning more about complex analysis. Also, very interested in analytic continuation. Can anyone recommend a good text that focuses on complex analysis. Also, is there a good textbook on number theory that anyone recommends? Thanks! <mentor - edit thread title>>

Greetings, I'm an Undergraduate Mechanical Engineering student. I want to design bolted joints on Figure 1, I'm trying to perform a basic static analysis of the structure to understand the forces acting on its members and its current stress state. I've included dimensions and position of its...

Suppose ##(y_n)_n## is a sequence in ##\mathbb{C}## with the following property: for each sequence ##(x_n)_n## in ##\mathbb{C}## for which the series ##\sum_n x_n## converges absolutely, also the series ##\sum_n \left(x_ny_n\right)## converges absolutely. Can you then conclude that ##(y_n)_n##...

Homework Statement Find all analytic functions ƒ: ℂ→ℂ such that |ƒ(z)-1| + |ƒ(z)+1| = 4 for all z∈ℂ and ƒ(0) = √3 i The Attempt at a Solution I see that the sum of the distance is constant hence it should represent an ellipse. However, I am not able to find the exact form for ƒ(z). Any help...

Homework Statement - Given a bounded sequence ##(y_n)_n## in ##\mathbb{C}##. Show that for every sequence ##(x_n)_n## in ##\mathbb{C}## for which the series ##\sum_n x_n## converges absolutely, that also the series ##\sum_n \left(x_ny_n\right)## converges absolutely. - Suppose ##(y_n)_n## is...

Homework Statement Hi I have this question as part of my assignment but cannot get my head around part b, I have worked out part a with an answer of -9.2+17.3i amps which from a previous thread I know is correct, but can't understand why the equations given in the previous thread are different...

Problem: Let $\left(X, M, \mu\right)$ be a probability space. Suppose $f \in L^\infty\left(\mu\right)$ and $\left| \left| f \right| \right|_\infty > 0$. Prove that $lim_{n \rightarrow \infty} \frac{\int_{X}^{}\left| f \right|^{n+1} \,d\mu}{\int_{X}^{}\left| f \right|^{n} \,d\mu} = \left| \left|...

The Boston Globe reports that Prof Elias Stein has died at age 87. He was a mathematician who specialized in the mathematics of Harmonic Analysis as applied to other fields such as the stock market and gravitational waves. Prof Terence Tao of UCLA said he had a knack of asking the right...

The attached image shows a linkage mechanism with 2 parallel bars pivoted to a fixed base. The lengths of the the bars are equal. A connecting linkage and gears are used to connect it to a 3rd bar. I would like to know how to analyze this linkage system to find the forces, moments and loads for...

Homework Statement Your consulting agency, with its extensive knowledge of physics, has been subpoenaed to provide expert testimony at an automobile accident case in civil court. The case involves a crash between a Ford Escort car and a tractor-trailer truck. 1. The police department...

Homework Statement The mean field solution for the Ising model is: $$m = tanh[\beta (mJz + H)]$$ I wanted to carry out a dimensional analysis in order to verify the equation. Homework Equations $$m = tanh[\beta (mJz + H)]$$ The Attempt at a Solution Knowing that: $$[m] = \frac{A}{L}$$...

Hi all. I'm looking for a little guidance on starting out in self-studying analysis. The reason is two-fold. Firstly, I am very interested in it and want to have a deeper understanding of Calculus rather than the computational plug and chugs I learned in Calculus I last semester. Second, I've...

Homework Statement The evolution of the density in a system of attractive spheres can be described by the following dynamic equation. $$\frac{\partial}{\partial t} \rho (r,t) = D_o [\nabla^2 \rho (r,t) + \beta \nabla \rho (r,t) \int dr' [\nabla V (|r-r'|)] \rho (r',t) g(r,r',t)]$$ a)...

I studied an elementary course as an introduction to Solid State Physics. Now I have powder XRD data to practice crystal structure determination. I am going to do this alone in my computer. I want to know what software to use (free software) with manual of course. Any help please?

Homework Statement Determine whether or not the following sequences of real valued functions are Cauchy in L^{1}[0,1]: (a) f_{n}(x) = \begin{cases} \frac{1}{\sqrt{x}} & , \frac{1}{n+1}\leq x \leq 1 \\ 0 & , \text{ otherwise } \end{cases} (b) f_{n}(x) = \begin{cases} \frac{1}{x} & ...

Hi there all, I'm currently taking a course in Multivariable Calculus at my University and would appreciate any recommendations for a textbook to supplement the lectures with. Thus far the relevant material we've covered in a Single Variable course at around the level of Spivak and some Linear...

Hello, I am looking for for some good books on non-standard analysis. Hoping for something simple and not too complex. Any tips on good books appreciated.

Hello, I am interested in any introductory books to non-standard analysis. My highest level of mathematical education is Calculus II via community college. Any help appreciated.

I am trying to use PCA to classify various spectra. I measured several samples to get an estimate of the population standard deviation (here I've shown only 7 measurements): I combined all these data into a matrix where each measurement corresponded to a column. I then used the pca(...)...

1. Homework Statement the problem is my answer for question (a) is not the same as the answer provided by the question, i get 2.81 - j4.49 Ω while the answer demands 2.81 + j4.49 Ω Homework Equations simplifying the circuit, details can be seen below The Attempt at a Solution...

Homework Statement Derive the expressions for the voltage gain (Gv) of the following op amp: Homework Equations In = Ip = 0 Vp =VnThe Attempt at a Solution I can use KCL, and the fact that In and Ip are both 0, to derive the two equations, one from the top node and the other from the...

hello everyone, i have a problem related with sinusoidal steady-state analysis, the problem is like this : the circuit for the question is like this : i am still unable to find the answer for the question (b), the answer i got is not the same as the one provided by the question above, my...

Homework Statement We recently collected data on a reverse osmosis system for our unit ops lab. The report LERF (Laboratory Experiment Request Form) requests that we ascertain a value of Aw, the water permeability coefficient, for our membrane. We need to perform a T-Test on the data, however...