What is Analysis: Definition and 999 Discussions

Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development.The word comes from the Ancient Greek ἀνάλυσις (analysis, "a breaking-up" or "an untying;" from ana- "up, throughout" and lysis "a loosening"). From it also comes the word's plural, analyses.
As a formal concept, the method has variously been ascribed to Alhazen, René Descartes (Discourse on the Method), and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery (which he did not name).

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  1. Jeviah

    CFD analysis of a turbine, interpreting torque values

    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...
  2. D

    Engineering Question on basic circuit analysis

    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...
  3. N

    Overtone Spectrum Analysis Software

    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...
  4. F

    Engineering Help me finding the current in here please (Circuit analysis)

    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...
  5. M

    A What do the notations in functional analysis mean for a given function?

    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...
  6. Claric1

    Error analysis: propagation of error

    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...
  7. babaliaris

    Mathematical Analysis Of V^2 = Vo^2 + 2a(X-Xo)

    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...
  8. M

    A Regression analysis: logarithm or relative change?

    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...
  9. Zack K

    Mesh Analysis Method for Finding Current in a Circuit with Dependent Source

    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...
  10. Santilopez10

    I What is the value of the integral for higher order poles in the real axis?

    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...
  11. Toolkit

    Engineering Circuit Mesh analysis question

    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...
  12. D

    Air Compressor Model Analysis

    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...
  13. Boltzman Oscillation

    In AC analysis do I alternate the current and voltage?

    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.
  14. NihalRi

    Function Continuity Proof in Real Analysis

    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 =...
  15. T

    Forensic analysis using Memory Dump

    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...
  16. D

    Textbook Recommendations: Complex Analysis

    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>>
  17. S

    Static Analysis Of Bolted Joints

    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...
  18. JD_PM

    I Understanding why ##(y_n)_n## is a bounded sequence

    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##...
  19. MakVish

    Complex Analysis: Find Analytic Functions w/ |ƒ(z)-1| + |ƒ(z)+1| = 4

    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...
  20. JD_PM

    Analysis of an absolutely convergence of series

    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...
  21. M

    Engineering Nodal analysis of an AC circuit

    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...
  22. Ackbach

    MHB Book Recommendation, Please: Time Series Analysis

    I am looking for a book recommendation. I've been looking for something like this on Amazon without success. I want a book on Time Series analysis that includes the following topics: ARMA/ARIMA, ARCH/GARCH, LSTM and deep learning, filters, state spaces, and any other main categories of...
  23. J

    MHB Real Analysis - Convergence to Essential Supremum

    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|...
  24. jedishrfu

    Elias Stein, Mathematician Of Harmonic Analysis has Died

    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...
  25. J

    Linkage analysis of forces and stresses?

    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...
  26. B

    Car Crash Analysis: Analyzing Friction & Speed

    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...
  27. JD_PM

    Dimensional analysis on an Ising model solution

    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: $$[m] = \frac{A}{L}$$...
  28. opus

    Introductory Analysis -- Self Studying

    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...
  29. JD_PM

    Dimensional analysis of an equation of motion

    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)...
  30. A

    A What is the best free software for analyzing powder XRD data?

    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?
  31. Euler2718

    Showing a sequence of functions is Cauchy/not Cauchy in L1

    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} & ...
  32. A

    Calculus Multivariable calculus without forms or manifolds

    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...
  33. Q

    Calculus Books on non-standard analysis?

    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.
  34. Q

    Books on non-standard analysis?

    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.
  35. R

    I Principal component analysis (PCA) coefficients

    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(...)...
  36. e0ne199

    Engineering Problems about Zin in complex circuit analysis

    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...
  37. Boltzman Oscillation

    Engineering Derive expressions for the voltage gain of this opamp circuit

    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...
  38. e0ne199

    Question about sinusoidal steady-state analysis

    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...
  39. runningman19

    Statistical Analysis on Results Obtained from a Model

    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...
  40. K

    Mesh Analysis AC, solving simultaneous equations....

    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...
  41. C

    Symmetry in Electrical Circuit Analysis

    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...
  42. CaptainAmerica17

    B Spivak's Calculus as a Prerequisite for General Topology

    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...
  43. Mr Davis 97

    I Metric Spaces and Topology in Analysis

    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...
  44. G

    Is the Integral Zero for Closed Paths in Complex Analysis?

    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...
  45. M

    Analysis Proof: prove that sqrt(x_n) also tends to 0

    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...
  46. Safder Aree

    Engineering Finding Internal Resistance through Circuit Analysis

    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...
  47. A

    Show that the integral converges

    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...
  48. Measle

    Complex Analysis - sqrt(z^2 + 1) function behavior

    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...
  49. Z

    Equation related to Linear Discriminant Analysis (LDA)?

    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...
  50. Dustyneo

    Chemistry Combustion Analysis- Empirical and molecular formula

    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...
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