Analysis Definition and 999 Threads

[Moderator's note: This discussion has been spun off from another thread since it was getting into a more technical area only tangentially related to the original thread's topic. Some posts have been edited slightly for the new context.] They're too technical for the question here, and only...

Hello all, I am trying to understand the inputs here. Let's suppose I have a water tank at home which is made of plastic. It is filled with water. So I am confused with the inputs. At first when I gave only hydrostatic pressure, the tank was safe. But when I added atmospheric pressure by...

In the problem below, when I use nodes V1 and V2 I get the correct answer of Vo = -2.5v But when I use nodes V1 and Vo I get an incorrect answer. Please explain to me why my latter method did not work. Thanks.

Homework Statement 2. The attempt at a solution Am I doing something wrong? I know it's just voltage division with AC phasors and we have to equate the real parts and imaginary parts to find the unknown, but I feel like the question shouldn't be this hard.

Homework Statement 1) Suppose ##t## is a subsequential limit for ##(s_n)##. Write the precise definition of the meaning of this statement. 2) Explain why there exists a strictly increasing sequence ##(n_k)^\infty_{k=1}## of natural numbers such that ##\lim s_{n_k}=t##. Homework EquationsThe...

Dear colleagues: My name is Ignacio Pérez, a mining engineering student from Spain. I am trying to analyze the stability of a slab with rounded edges against a toppling failure. The slab can be considered rectangular-prism shaped (I provide a rectangular section in the enclosed picture) but the...

Homework Statement Find i using Nodal Analysis. Homework Equations V = I * R The Attempt at a Solution solve (1) , (2) , and (3) to find V1 , V2 ,and V3 V1 = 50/3 = 16.67 V V2 = 80/3 = 26.67 V V3 = 40 V 40 - 80/3 = 5i i = 2.667 A However , the correct answer is 1.522 A .. I don't know...

Homework Statement Prove that the function ## f(z)= 1/\sqrt{2}(\sqrt{\sqrt{x^{2}+y^{2}}+x}+i*sgn(y)\sqrt{\sqrt{x^{2}+y^{2}}-x})## is holomorphic on the domain ## \Omega = \left \{ z: z \neq 0, \left | \arg{z} \right | <\pi\right \} ## and further that in this domain ##f(z)^{2} = z. ##...

I have six months before I go back to school (after being out of school for over 5 years - ex engineering student). I'll be pursuing a BA in Mathematics and Philosophy - I will have to take either Abstract Algebra or Real Analysis 1 for my first quarter. Which class would you guys recommend I...

I do a fair bit of spectral analysis of time series in my research, but to date my experience in the topic is almost exclusively from an engineering perspective rather than the more statistical approach. Of course I am aware that ultimately they are equivalent, but it means that my familiarity...

Homework Statement A particle of mass m is moving on a frictionless horizontal table and is attached to a massless string, whose other end passes through a hole in the table, where I am holding it. Initially the particle is moving in a circle of radius ##r_0## with angular velocity ##w_0##, but...

Homework Statement Suppose that ##( s_n )## and ## (t_n)## are bounded sequences. Given that ##A_k## is an upper bound for ##\{s_n : n \ge k \}## and ##B_k## is an upper bound for ##\{t_n : n \ge k \}## and that ##A_k + B_k## is an upper bound for ##\{s_n + t_n : n \ge k \}##, show that ##\sup...

Hello everyone, I hope you could help me with the analysis of this circuit. the output voltage is supposed to be similar to the input but shifted upwards by 20V, so basically it's between 0 and 40V... but why? I mean when the input is 20V, the diode is reverse biased... and the capacitor...

Homework Statement Let, m, n be natural numbers and S(n) the succesor of n. If S(n)*m = nm + m Prove that m*S(n) = nm + m Homework Equations The Attempt at a Solution

I have a time series model constructed by using ordinary least square (linear). I am supposed to provide some general comments on how one would improve the robustness of the analysis of a time series model (in general). Are there any general advice apart from expanding data, making it more...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on $$\mathbb{R}^n$$" ... ... I need some help with another aspect of Definition 9.1.3 ... Definition 9.1.3 and the relevant accompanying text read as follows...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on ##\mathbb{R}^n##" ... ... I need some help with another aspect of Definition 9.1.3 ... Definition 9.1.3 and the relevant accompanying text read as follows: In the...

[FONT=verdana]Dear Everybody, I need some help with seeing if there any logical leaps or any errors in this proves. Corollary 1.2.8 to Proposition 1.2.8 states: if $S\subset\Bbb{R}$ is a non-empty set, bounded from below, then for every $\varepsilon>0$ there exists a $y\in S$ such that $\inf...

Homework Statement All the data is on the sheet. I named the nodes V1 to V4, however I'm primarily evaluating in terms of V3 and V4. The x=V3 and y=V4 are for the systems solving I'm using. I've looked and looked at this problem, and seem to be hung up, but I suspect it is going to be on my...

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with an aspect of the proof of Proposition 2.3.2 ... ... Duistermaat and Kolk's Proposition 2.3.2 and its proof read as...

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with an aspect of the proof of Proposition 2.3.2 ... ... Duistermaat and Kolk's Proposition 2.3.2 and its proof read as...

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with another aspect of the proof of Lemma 2.2.7 (Hadamard...) ... ... Duistermaat and Kolk's Lemma 2.2.7 and its proof...

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with another aspect of the proof of Lemma 2.2.7 (Hadamard...) ... ... Duistermaat and Kolk's Lemma 2.2.7 and its proof...

I am reading the book "Several Real Variables" by Shmuel Kantorovitz ... ... I am currently focused on Chapter 2: Derivation ... ... I need help with an aspect of Kantorovitz's definition of "differential" ... Kantorovitz's Kantorovitz's definition of "differential" reads as follows...

I am reading the book "Several Real Variables" by Shmuel Kantorovitz ... ... I am currently focused on Chapter 2: Derivation ... ... I need help with an aspect of Kantorovitz's definition of "differential" ... Kantorovitz's Kantorovitz's definition of "differential" reads as follows: Is the...

Homework Statement The problem states: Determine the voltage labeled v in the following circuit: https://ibb.co/hz0Q37 The variable is the voltage across the 2 ohm resistor. The ground I chose for this example is located in the center of the circuit. Homework Equations V=IR I guess. The...

Homework Statement [/B] Find accelerations of these masses and the pulley are weightless. Homework Equations [/B] Sb+Sc=Length of the second rope (L2) The Attempt at a Solution [/B] Just like I did, I placed all variables from datum to the masses. In the second system, I write the...

Hello I have a point that I don't understand. In open steady flow systems, we use SFEE, where there's a term W in addition to a term PV, which are different things. When we analyse a cycle like Rankine, we always consider either W or PV, but not both. I also think that W=PdV always. Why that...

Homework Statement Hi I'm having a trouble with finding min value of given function: f(x) = sqrt((1+x)/(1-x)) using derivative.First derivative has no solutions and it is < 0 for {-1 < x < 1} when f(x) is given for {-1 < x <= 1}. For x = - 1 there is a vertical asymptote and f(x) goes to +...

Homework Statement [/B] The proposition that I intend to prove is the following. (From Terence Tao "Analysis I" 3rd ed., Proposition 6.1.7, p. 128). ##Proposition##. Let ##(a_n)^\infty_{n=m}## be a real sequence starting at some integer index m, and let ##l\neq l'## be two distinct real...

Hello, I often hear the phrase "Well, since you are taking a ratio bin-by-bin, you don't have to care about the luminosity syst. uncertainty and the trigger efficiency syst. uncertainty". I think I understand qualitatively why this is the case (It cancels out in the ratio, since both...

So in my future numerical analysis class the recommended book i liked the most was Numerical mathematics by Quarteroni : https://books.google.pt/books/about/Numerical_Mathematics.html?id=m-bHBAAAQBAJ&printsec=frontcover&source=kp_read_button&redir_esc=y#v=onepage&q&f=false Since i like this...

Suppose f,g:ℂ→ℂ are analytic with singularities at z=0. I was wondering whether f(z)^2 or f(z)g(z) will have a singularity at z=0? For each, can you give me a proof or a counterexample?

Hello dear members, I couldn't figure out whether I should post this in the academic guidance or career guidance section, yet the latter sounded more convenient for my situation. I have also seen many similar threads but I believe everybody has different thoughts& aspirations as we all know...

Homework Statement This is related to Astronomy & python . I am trying free-up sources on TS map on a galactic source with python script. But when I run the script, at the end of the process, I get the following run time error. Traceback (most recent call last): File "find_new_sources.py"...

Have built a 55 gallon DIY steamer from a DE pool filter. The pool filter is made from .06 inch stainless steel and was rated for an operating pressure of 50 PSI. As a pool filter, the vessel regularly operated at pressures of 10-15 PSI, and as much as 25-30 PSI when it needed cleaning. Have...

Why radians are usually neglected in dimensional analysis?

I am reading "Multidimensional Real Analysis I: Differentiation by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 1: Continuity ... ... I need help with an aspect of Lemma 1,1,7 (ii) ... Duistermaat and Kolk"s Lemma 1.1.7 reads as follows: In the above Lemma part (ii)...

Homework Statement 2. Homework Equations [/B] I'm studying a mathematical behaviour of a servo motor and I need some help to understand it. The output signal is \$\beta (t)\$, representing the angle rotated by the axis at instant t, in relation to the equilibrium position. On the servomotor...

Hi, I would like to ask why center of element displacement is always estimated with polynomial equation involving nodes displacement (like in attachment/picture)? Also I know that if nodes' number increase for an element then displacement of center of element is estimated with higher order...

Hello Guys I am New here on the foum Well i am simulating a static structure (Picture attached) on ansys and til now i have a result divergence when i apply different forces. i guess my loads and fixed supports aren't well defined. Please Help i know it s a bit long but please give it some time...

I am reading John B. Conway's book: Ä First Course in Analysis and am focused on Chapter 5: Metric and Euclidean Spaces ... and in particular I am focused on Section 5.2: Sequences and Completeness ... I need some help/clarification with Conway's defintion of completeness of a metric space ...

Homework Statement I have a circuit which I have a current through labelled I on circuit. I have -9.18 +j17.31. we agreed this was correct. I have a node analysis problem but cannot find the correct answer. I feel my method and my maths may be off but would like some advice if possible...

Hello, Is there a difference from these courses, or are they the same course with different names? I need to know which one to choose for the upcoming semester... Intro to Analysis, Intro to Real Analysis I, and Numerical Analysis Thank you, Tracie

Hello, I was reading an example where correlation between two features is to be measured. The two features are drive-wheels and price. The drive-wheels feature has three values: 4wd, fwd, and rwd. Then the example went on to calculate the F-score without much details using Python. Without going...

Homework Statement I have a circuit that I am to analyse and find I. I am told to use an excel matrix sheet given to me to solve 3 unknowns. I have 4 loops so this is a problem. I have made an attempt using three loops and referred to a previous thread on here for some help. It says I can do...

Homework Statement [/B] I have created a very simple Rube Goldberg device in Algodoo, and I need to analyze 3 correlating steps within it, using physics descriptives and equations. My primary focus is the ball as it hits the windmill, which I need to describe and calculate its velocity at that...

Hello, I've been asked to talk about a time where I have used quantitative analysis. I once used simulation of the solar system to find out more about things like close approaches, and Gladmans criteria I was wondering if simulation is considered a quantitative method of analysis and if the...

Hi, I am working on a home-task to analyse the properties of a ODE and its solution in a Hilbert space, and in this context I have: 1. Generated a matrix form of the ODE, and analysed its phase-portrait, eigenvalues and eigenvectors, the limits of the solution and the condition number of the...

Homework Statement A block of mass ##m = 1.00 kg## is being dragged through some viscous fluid by an external force ##F = 10.0 N##. The resistive force can be written as ##R = -bv##, where ##v## is the speed and ##b = 4.00 kg/s## is a phenomenological constant. You may ignore gravity (we...