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. anorlunda

    Insights The What and Why of Circuit Analysis Assumptions - Comments

    Greg Bernhardt submitted a new PF Insights post The What and Why of Circuit Analysis Assumptions Continue reading the Original PF Insights Post.
  2. N

    Nodal analysis- Current directions for KCL

    In node analysis, after labeling the nodes. I don't know how to choose currents direction to apply KCL. it seems too complicated.. and I end up every time getting different answers the the solution sheet. I've an exam tomorrow. would be much appreciated if you could help me better understand the...
  3. S

    Can I Successfully Analyze Soil for N and K Without Commercial Test Kits?

    I would like to analyse soil samples myself for N and K. Tried some commercial test kits and the results are good enough in terms of precision. No idea what reagents are used in those kits. Is this something I can make myself knowing I have access to a minimal lab?
  4. A

    Meteorology: Turbulence/Dimensionless Analysis

    Good afternoon, I find it hard to understand friction velocity, shear stress, momentum and temperature scale. For a class, we are using MOST dimensionless analysis to find values of intensity for the turbulence. However, I'm struggling with the terms. What exactly is friction velocity u*? My...
  5. Euler2718

    Proof of sequence convergence via the "ε-N" definition

    Homework Statement Prove that \lim \frac{n+100}{n^{2}+1} = 0 Homework Equations (x_{n}) converges to L if \forall \hspace{0.2cm} \epsilon > 0 \hspace{0.2cm} \exists \hspace{0.2cm} N\in \mathbb{N} \hspace{0.2cm} \text{such that} \hspace{0.2cm} \forall n\geq N \hspace{0.2cm} , |x_{n}-L|<...
  6. Math Amateur

    MHB Smooth Paths in Complex Analysis .... Palka Example 1.3, Section 1.2 in Chapter 4 .... ....

    I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter 4: Complex Integration, Section 1.2 Smooth and Piecewise Smooth Paths ... I need help with some aspects of Example 1.3, Section 1.2, Chapter 4 ... Example 1.3, Section 1.2, Chapter 4...
  7. D

    Dimensional Analysis involving power

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  8. PainterGuy

    Fault analysis and symmetrical components in Power Grids

    Hi, I was trying to learn fault analysis in three phase system from conceptual point of view. I need your help to clarify few seemingly contradictory points in the following video: 1: At 32: 42, phase to ground fault in introduced. It is said that line voltage Vbc is not affected as is also...
  9. V

    Understanding Big Oh: Exploring the Best Function for a Given Equation

    Let me start by saying that this is from a 30 question assessment on Big Oh, Big Theta, and Big Omega. I understood every other question, however, even after being given the correct answer, I do not understand why my answer was wrong for this one. If you could point me in the direction of any...
  10. M

    Help with these two problems in complex analysis

    Homework Statement What is the argument of -4-3i, and -4+3i? Homework Equations tantheta=opposite/adjacent side The principle of argument is that the argument lies between -pi and pi (not including -pi). The Attempt at a Solution arg(-4-3i) = -pi + arctan(3/4) arg(-4+3i) = pi - arctan(3/4)...
  11. C

    What Could a Steeper Best Fit Line Than Maximum Line Mean in Graph Analysis?

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  12. P

    I Limitations of Dimensional Analysis in Predicting Proportional Relationships

    Our professor introduced us to dimensional analysis and told us that we can use it to predict how some variables are proportional to others, for example: I have a ball at a certain height and i want to know the time it requires to touch the grond, i can make a guess that it will depend on the...
  13. S

    Generalization of a theorem in Real Analysis

    Homework Statement If ##\{K_\alpha\}## is a collection of compact subsets of a metric space X, such that the intersection of every finite subcollection of {##K_\alpha##} is nonempty, then ##\cap K_\alpha## is nonempty. Generalize this theorem and proof the generalization. Why doesn't it make...
  14. Clara Chung

    Analysis question -- Aren't all prime numbers not a product of primes?

    Homework Statement I don't understand the lemma. Homework EquationsThe Attempt at a Solution Isn't all prime number not a product of primes? The lemma doesn't make sense to me... Moreover, if m=2, m-1 is smaller than 2, the inequality also doesn't make sense. Please help me
  15. FallenApple

    Studying How to learn Topological Data Analysis

    It's a really interesting idea. I think I want to eventually add this to my toolbox. But how? I've heard it uses ideas from algebraic topology. But how much of theoretical topology do I actually need to learn? Are proofs important? I don't care about developing the algorithms from scratch. I...
  16. F

    I A question about Vector Analysis problems

    Why is it difficult to find really challenging vector analysis problems (problems about Green's, Stokes' and Gauss' theorems in a Calculus 3 course) in Calculus books? Most of the problems are elementary, at least that's the impression I have(I could be wrong). Is it really difficult to...
  17. B

    Pressure gradient along a streamline using CV analysis

    Homework Statement Use a CV analysis to show that an element of fluid along a streamline gives \[\partial p/\partial x=-\rho u\partial u/\partial x\] Homework Equations \[\sum F=\oint_{CS}^{ } \rho \overrightarrow{V}(\overrightarrow{V_{rel}}\cdot \overrightarrow{n})\] The Attempt at a...
  18. H

    I Uncertainty Analysis: Understanding Errors in Quantity Measurements

    Hey, I have a question about uncertainty analysis. So my university told me that, usually a quantity has 3 types of errors, reading error, standard deviation (which comes from some repeated measurements of that quantity), and equipment accuracy (which is usually stated on the equipment). My...
  19. Mr Davis 97

    I How can we characterize mathematical analysis?

    If algebra can be characterized as the study of algebraic structures and the structure-preserving maps between them, how could characterize mathematical analysis? In analysis, can we break it down into certain mathematical structures, maybe topologies or metric spaces, and the continuous maps...
  20. G

    Arbitrary current with mesh analysis

    Given the circuit in the diagram I was wondering would I be able to make ib equal to the mesh i3. I have the equation for my Super Mesh at i1 and i3 which is: -25+30i3+5Va+20(i3-i2)+10(i1-i2)=0 (1). The mesh i2 is equal to -2A (2). subbing (2) into (1) gives: -25+50i3+5Va-30i2+10i1=0 (3)...
  21. Cocoleia

    Analyzing a Current Mirror: Finding Rref for Vcc=8V and Icopy=0.38mA

    Homework Statement I am working on this problem. They start out by giving me: I am asked to find Rref such that Vcc=8V and Icopy=0.38mA. Homework Equations Transistor equations The Attempt at a Solution In this case, they never specify if IB=0A (sometimes it does ?) but I would assume that...
  22. M

    What alternative methods can be used for solving nodal analysis equations?

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  23. S

    Ideal conditions in which circuit analysis is done

    What are the ideal conditions in which circuit analysis or analysis of an electrical system is done?I know that the air friction,friction between materials is ignored in ideal systems, such as for ohms law applications.What else is ignored in analysis of ideal electrical systems?
  24. T

    Analysis of the entropy S of an arbritary system can be written as a power series?

    Is it ok to assume that the entropy ##S## of an arbritary system can be written as a power series as a function of the system's internal energy ##U##? Like $$S(U) = \sum_{i=1}^{\infty}a_iU^i = a_1 U + a_2 U^2 + \ ...$$ with ##a_i \in \mathbb{R}##. What results could be obtained from such...
  25. A

    Gas analysis system design issue

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  26. mertcan

    Studying Finite element analysis for Electromagnetism

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  27. PhotonSSBM

    Other What Are the Best Books for Learning Data Analysis in Physics with Python?

    I'm looking for a good reference book on data analysis techniques for science (namely physics) that has a lot of programming applications and some decent error analysis coverage. Right now I'm analyzing large datasets of telescope arrays and would like something to learn from as this is my...
  28. A

    Engineering Can someone explain me this problem? (Circuit analysis using superposition)

    I do not really understand why we don't include 7Ω resistor in step 1, and I need some explanation with step 2.
  29. marsupial

    Nodal Analysis with Dependent Voltage Source

    Homework Statement Here is a diagram of the circuit and my redrawing with currents drawn: We are to find the power delivered by the dependent voltage source. I found a solution online, but I am not sure why they had the KCL line as: $$ \frac{v_1 - 160} {10} + \frac{v_1} {100} + \frac{v_1...
  30. Mr Davis 97

    Functions and Analysis with a fixed-point

    Homework Statement A fixed-point of a function f : A → A is a point a ∈ A such that f(a) = a. The diagonal of A × A is the set of all pairs (a, a) in A × A. (a) Show that f : A → A has a fixed-point if and only if the graph of f intersects the diagonal. (b) Prove that every continuous function...
  31. G

    Engineering DC circuit analysis: conceptual mistake?

    Homework Statement Homework Equations[/B] I have a circuit that consists on 3 components in parallel: a current source Ia, a resistor R and a capacitor C. Ia is directed upwards, while the currents through the capacitor and the resistor are both directed downwards. Select the correct option in...
  32. Oats

    Show that this function is differentiable

    Homework Statement [/B] 2. The attempt at a solution I'm not really sure where to start. We just want to show that ##\lim_{x \to c} \frac{f(x) - f(c)}{x - c} = 0##. I see that ##\lim_{x \to c} (x - c)^2 = 0##. I feel that this may be a simple trick of inequalities, but I am having a complete...
  33. franciobr

    Python workflow for experimental data analysis

    Hello! I have been using python for my data analysis and processing needs as an experimental physicist for an year now. I have used MATLAB and originpro before and python provides me everything I need. But I am not satisfacted with my worflow specifically for plotting needs. I often find myself...
  34. S

    What is the best software for the analysis of chaos in electric circuits?

    What is the best software for the analysis of chaos in electric circuits.
  35. L

    I Can a Circular Function with Complex Variable Represent a 3D Graph?

    Does a circular function with complex variable represent a three-dimensional graph? For example cosiz
  36. M

    Real time analysis of mains frequency

    All, I could use some help. I would like to measure mains frequency in real-time and pass the data through a high-level programming language (preference of Python). I am not sure where to start with this project, I assume commercial mains frequency analyzer exist, however, my google searches...
  37. Math Amateur

    MHB What Is the Top Recommended Book on Complex Analysis for Beginners on MHB?

    What book do MHB members regard as the best for a rigorous but clear and (moderately) easily understood introduction to complex analysis? (Note - would be good if the book had hints to solutions of exercise.) Peter
  38. Jason Louison

    Automotive Help with finite heat release analysis

    https://www.engr.colostate.edu/~allan/thermo/page8/page8.html The link above takes you to a site I have found to be very helpful in my studies of the Otto cycle, but on this particular page, it depicts an equation for the rate of change of cylinder Pressure vs. crank angle, and in this...
  39. B

    A Statistical analysis for comparing trends among multiple variables

    In our study, we measured the seasonal abundance of selected genes from two sites. We want to make a comparison between the seasonal trends between the genes (i.e. which genes had similar trends and which didn't). What would be the best statistical analysis for this purpose? Thanks!
  40. davidge

    I Spherical Harmonics from operator analysis

    I found an interesting thing when trying to derive the spherical harmonics of QM by doing what I describe below. I would like to know whether this can be considered a valid derivation or it was just a coincidence getting the correct result at the end. Starting making a Fundamental Assumption...
  41. ISamson

    I How to Perform Spectral Analysis at Home: Tips and Tricks

    What can spectra tell us? They can tell us the speed of the object, its temperature, size and some more, but how can we do this at home with a glass prism? Do you know?
  42. Abdul Wali

    MATLAB Matlab Derivative block analysis and filter design

    Hi, May someone helps me regarding this!? i have a controller which will control AC motor as attached. in this controller, a stage comes where I need to use a Derivative Block before point 'B' as shown in the attached picture " controller block diagram" [...
  43. D

    Other Books for Geometry, Real Analysis and EM

    Hi, all. I would like to read books about the topics - Geometry, Real Analysis and Electricity and Magnetism. And I find the followings. Are they decent and rigorous? Geometry The Real Numbers and Real Analysis Introduction to Electrodynamics Classical Electricity and Magnetism Electricity...
  44. Oats

    I Must functions really have interval domains for derivatives?

    Nearly every analysis reference I come across defines the derivative for functions on an open interval ##f:(a, b) \rightarrow \mathbb{R}##. I understand that, in constructing the definition of ##f## being differentiable on a point ##c##, we of course want it to first be a point it's domain, so...
  45. N

    Modal analysis - results exported - need to compute deflecti

    Hello, I have got results for a modal analysis (mesh of 150 shell elements) in ascii format. I have also got (from another process) forces to apply at each element; how do it compute the deflection? I get that it's a form of summation of all the modes, but I am stuck. Thanks! BB
  46. G

    Quantitative analysis -- manufacturing Furfural from bagasse

    Hello everyone.. Here is the thing I am working on a project where I am manufacturing Furfural from bagasse. The reaction is thermodynamically possible. I took some amount of bagasse and added it to a reactor at atmospheric pressure. I then added diluted Sulphuric acid which acts as catalyst...
  47. S

    Analysis Best books and papers for classical "hard" analysis tricks

    It seems that most recently published analysis textbooks are written from a more abstract perspective, e.g., dealing with functions on general metric spaces or with spaces of functions. However, often solving a problem requires some "get your hands dirty" classical or "hard" analysis -- for...
  48. W

    I Order of "Extracted Factors" in SPSS Factor Analysis

    Hi All, I am doing some FA on SPSS. I entered 9 columns from an Excel file into SPSS. I am just not sure of how the order of the initial columns corresponds to the order of the components that have been extracted; specifically, in the "total Variance Explained" section of the outputs. Would...
  49. G

    Solving Force Analysis: Understanding Vertical and Horizontal Forces

    Hi, I'm trying to figure out the forces Fx in the drawing I have uploaded. If I have a vertical force Fy acting on the bracket I have drawn. I know from experience that this force is going to pull my bracket horizontally but I can't figure out how I work out a horizontal force from a vertical...
  50. R

    Dimensional Analysis Buckingham Pi Theorem

    This is the problem I'm currently working on: The pi groups I identified were h1, h2, d, D, g, t, and velocity, but when I looked at the solution, it selected Δh, D, t, ρ, d, ϒ, h1, with no explanation why those variables are needed. If I was solving with the Bernoulli equation, I wouldn't...
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