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. Diffie Heltrix

    Norm indueced by a matrix with eigenvalues bigger than 1

    Suppose we pick a matrix M\in M_n(ℝ) s.t. all its eigenvalues are strictly bigger than 1. In the question here the user said it induces some norm (|||⋅|||) which "expands" vector in sense that exists constant c∈ℝ s.t. ∀x∈ℝ^n |||Ax||| ≥ |||x||| . I still cannot understand why it's correct. How...
  2. R

    Mesh/Loop Analysis Question

    Homework Statement I posted the problem in the picture below.[/B] Solve for the currents I1,I2,I3,I4 Homework EquationsThe Attempt at a Solution This was my attempt at it using KVL and KCL: For I1 loop: 8I1-6I3 = -5Vx For I2 Loop: 5Vx + 15(I2+3) + 10I2 = 0 5Vx+25I2 = -45 For I3 Loop...
  3. Blargian

    Dimensional Analysis in Halliday/Resnick

    Hello world! I'm busy working through Halliday/Resnick Fundamentals of Physics chapter 1 and I'm having some difficulty with this particular question. I'll do my best to explain my reasoning and attempt at the problem 1. Homework Statement The problem: Three different clocks A, B and C run at...
  4. hdp12

    KCL Nodal Analysis & Power to Resistor (Need help)

    Homework Statement Here is the homework problem I was given: The Attempt at a Solution Above is the work that I began, however, I have an overwhelming feeling that I am incorrect and also I don't know how to continue to the next part/parts. Would someone please help me? Thank you H
  5. D

    Dimensional Analysis? Involving Temperature

    I was trying to convert a quantity in BTU/(ft*hr*F) to W/(m*C) and I can do it just fine by using a conversion factor from a table online, but what I want to know is how to come up with that conversion factor. The conversion factor I looked up and have been using is 1 BTU/(ft*hr*F) = 1.73...
  6. O

    Mesh Current Analysis: Solve & Determine Magnitudes/Voltages

    Homework Statement Solve using the Mesh-current method. Determine the current magnitudes and the voltages across all elements Homework Equations i=v/r i1+i2+i3..=0 The Attempt at a Solution loop 1: 16(i3-3)+25i1-5i2=12 loop2: 4i1-5i2=15 1) i1=5/9i2-1 substituting 1) into loop2 gives...
  7. G

    Helpful Resources for Calc. Analysis

    I have started a class on the analysis of calculus. We are three weeks in and have covered some basic set theory, fields and axioms, and now we are beginning induction. It is a very rigorous course and I hoping someone might know of some helpful resources that could aid me throughout it. Ideally...
  8. T

    Engineering Circuit Analysis (Equation) with Multiple Voltage Sources

    Homework Statement Derive the differential equation that relates the voltage (V) to the current (I) entering the circuit. Homework Equations Let: ic = C dV/dt = current traveling through the capacitor (C) ik = (V+Ek) / Rk = current traveling through the potassium (K) channel iNa = (V-ENa) /...
  9. R

    Multiple-scale analysis for 2D Hamiltonian?

    I came across a technique called "multiple-scale analysis" https://en.wikipedia.org/wiki/Multiple-scale_analysis where the equation of motion involves a small parameter and it is possible to obtain an approximate solution in the time scale of $$\epsilon t$$. I am wondering if it is possible to...
  10. phoenixthoth

    Photons and nonstandard analysis

    Hi PF contributors, Have there been attempts to apply nonstandard analysis to the behavior of photons? For instance, considering the mass of a photon to be infinitesimal. I'm guessing the answer is yes so if you could provide references, I would be much obliged. phoenixthoth
  11. thegreengineer

    Nodal analysis, choosing reference node confusion

    I know that when we have to identify the nodes for solving a circuit with nodal analysis we always have to designate a reference node (which will be the ground node) as a reference for measuring the others' voltages. However I was practicing this and I found this example on...
  12. thegreengineer

    Nodal analysis, choosing number of nodes confusion

    Good evening people. Recently I started taking the "electric network analysis" course in my school. We already saw the mesh analysis method for solving circuits. Now we are seeing the node analysis method. I understand that the first step for this method is finding the number of nodes (and one...
  13. X

    2 Port analysis of series Inductor (Simple)

    EDIT: Oops! I posted this in the wrong section! Meant to post in engineering section! I am not sure if I am doing this problem correctly or not. It is very simple. 1. Homework Statement A 2 port network consists of just a series inductor with ##Z=j 100 \Omega## in a ##50 \Omega## system...
  14. F

    Question about mesh and node analysis

    Hi, I'm trying to figure out if I haven't undestood the correct way to do a circuit analysis yet, or if I am just mistakening my calculi. Here is a scheme of the circuit: The component in the right bottom angle is a voltage dependent voltage source controlled by V0. I tried to make a mesh...
  15. M

    Dimensional Analysis: Solving E = (1/2) mv Equation

    Homework Statement Is the following equation dimensionally correct? Homework Equations E = (1/2) mv where: E = energy m = mass v = speed The Attempt at a Solution 1. I understand that the 1/2 is irrelevant. 2. I broke everything down into length, time, and mass. 3. I got ML^2/T^2 = ML/T 4. My...
  16. STEMucator

    Multiple BJT Analysis: Homework Statement

    Homework Statement Hi everyone, this is not homework, but I can't seem to see something. I have a multiple BJT circuit I've drawn, and I want to analyze it: Homework EquationsThe Attempt at a Solution Assume the transistor ##\beta##s are equal for both transistors and are known. Assume...
  17. ELB27

    Analysis Analysis textbook recommendation

    Hi everyone, I just finished self-studying linear algebra from Treil's Linear Algebra Done Wrong, and I want to continue with analysis. I don't know the requirements, so I'll just list what I know. I already know single and multi-variable calculus (to give a sense of my level, I knew everything...
  18. I

    (APDL) use two sections in an static analysis (beam/column)

    Hi, I'm just start using APDL but i have been stuck trying to make an analysis with two diferent sections, i'd like to make a frame with two column and a beam but i don't know how, thank you.
  19. S

    Exploring Mass & Velocity: A Statistical Analysis

    I was looking at a research paper the other day. In the paper they described some of the results from an experiment. They looked at two of the variables recorded in the experiment, mass and velocity. They looked at mass independently. First, they took the median of the mass. They then had two...
  20. C

    Can You Help With Finite Element Analysis in Cylindrical Coordinates?

    I am trying to numerically calculate the electric potential inside a truncated cone using the finite element method (FEM). The cone is embedded in cylindrical coordinates (r,phi,z). I am assuming phi-independence on the potential, therefore the problem is essentially 2D; I am working only with...
  21. Titan97

    Is Fourier Analysis Useful for High School Students?

    Is learning Fourier analysis useful for a high school student? If so, which book should I refer for learning the basics of Fourier analysis? This topic is not in my syllabus. But will it be useful for solving problems? (even if its not, it seems interesting to me). I have learned single variable...
  22. Remixex

    Calculus Beginners Guide to Complex Analysis

    OK, so i took a course named "Oscillations and vibrations" We began the course with an "introduction" to complex numbers, basically we raced through them in like 3 classes, we talked about how to get complex roots, adding, multiplying, Cauchy-Riemann Conditions, Cauchy's integration Theorem...
  23. T

    How do I analyze an audio amplifier circuit?

    Hi. I'm trying to analyse an audio amplifier circuit (DC, frequency response, stability, etc.). I began with the DC bias analysis but I'm having troubles finding where to start. I've attached the full circuit and a DC simplified version. I've placed an 8 ohm resistor as the load (8 ohm...
  24. N

    Dimensional Analysis of Planck Length

    Hello! So in looking at black hole thermodynamics, I came across the equation ## l_p = \sqrt{G\hbar} ## But in doing a dimensional analysis of ## \sqrt{G\hbar} ## I get ## [\sqrt{G \hbar}] = \sqrt{ \frac{Nm^2}{kg^2} \frac{m^3}{kgs} } ## This obviously doesn't amount to a length. What...
  25. L

    11kV Distribution System Fault Analysis using Symmetrical Components

    Hi could someone check my answer to the question below. Question: My Answer: I_{fA} = 3I_{1A} = 3I_{2A} = 3I_{0A} \Rightarrow I_{fA} = \frac{3E}{Z_1 + Z_2 + Z_0} = \frac{33kV}{20+20+30} = 471.43A Then using the same method I got I_{fB} = 942.86A
  26. Titan97

    Analysis Books on complex analysis and algebra

    can you recommend a good book on complex analysis? I would like a book that can sharpen my skills in solving complex number problems through graphs and also improve the algebraic part like solving problems related to roots of unity etc. (I have studied calculus myself. I have done a lot of self...
  27. S

    Offset crank slider mechanism connecting rod analysis

    Homework Statement A) Determine the value of the angle θ (measured from vertical) when the angular velocity of link AB a maximum. B) What is the maximum angular velocity of link AB. Homework EquationsThe Attempt at a Solution This is a part of a bigger question. I've managed to answer all...
  28. AXidenT

    Functional Analysis or Differential Geometry?

    I'm in my last semester of my undergraduate majoring in mathematics (focusing on mathematical physics I guess - I'm one subject short of having a physics major) and am wondering, largely from a physics perspective if it would be better to do a functional analysis course or a differential...
  29. M

    Beam statics: continous load analysis

    Homework Statement I just don't understand how to set the problem for the free body diagram (point (a) and (b)). Can someone help me with this problem? Thank you in advance.
  30. RJLiberator

    Complex Analysis Contour Circle Question

    Homework Statement I have uploaded necessary image(s) for the question I have successfully accomplished a, but I am not sure how to start b. Homework Equations The sum of the integral paths added up = the desired result. The Attempt at a Solution [/B] So we start with path CR And then go...
  31. RJLiberator

    Complex Analysis Integral Question

    Homework Statement Computer the integral: Integral from 0 to infinity of (d(theta)/(5+4sin(theta)) Homework Equations integral 0 to 2pi (d(theta)/1+asin(theta)) = 2pi/(sqrt(1-a^2)) (-1<a<1) The Attempt at a Solution I've seen this integral be computed from 0 to 2pi, where the answer is 2pi/3...
  32. K

    Dimensional analysis on equation including scattering length

    Hi all, I post a question about the dimension of wave function in position space before and people help me to identify that the unit of wave function should be in the unit of ##\text{m}^{-1/2}##. I am verifying that by doing the dimension analysis on Schrodinger equation...
  33. B

    Should I take Combinatorics with Analysis I or Algebra I?

    Hello! On this Fall Semester, I will be taking the Linear Algebra with Proofs (Friedberg), Analysis I (Rudin-PMA) or Abstract Algebra I (Dummit/Foote), and Combinatorics (Brualdi). Since I can take only one from Analysis I or AAI on Fall, I am trying to figure out if the introductory...
  34. Cobalt101

    Delayed choice measurement subsequent analysis

    This is a variant associated with the Scully and Druhl signal-idler photon delayed choice experiment, as described and discussed in Brian Greene's Fabric of the Cosmos. The commentary notes the "delay" may be configured to happen a very (years) long time after the photons pass the two...
  35. J

    Gym exercise equipment analysis

    I need some help on the direction to go with this problem. This is a workarm on a leg extension machine and there's 300 pounds (max) coming from the weight stack attached via a cable on the cam. I need to find the total force exterted on this system to double check my results on an analysis...
  36. F

    Finite Element Analysis: PE of an element

    Homework Statement The potential energy of an element in terms of local displacements q1 and q2 is given by the expression: Π = 3(q1^2) - 6q1q2 + 9(q2^2) + 9q1 Write down the expressions for element stiffness matrix k and element force f. I am at a complete loss as to what...
  37. Lagraaaange

    Full course of Vector Analysis vs Griffith Text self study?

    Senior in Fall. Is a full course on vector analysis necessary: Stockes theorem, Green Theorem, differential forms, etc. I feel like Griffith's Electrodynamics gives a sufficient overview of Vector analysis in Chapter 1 covering all you need. I've only taken the required Calc 1 - 3 sequence +...
  38. V

    On formal concept analysis (fca)

    Hi, I was using Hasse Diagram as it is great tool for data analysis but there is a confusion the thing is that I downloaded a software for fca and every time it uses a algorithm it gives a different lattice ,I do understand but suppose I am using it for some representation of concept lattice...
  39. B

    Calculus Brief calculus book to read before studying the analysis

    Dear Physics Forum personnel, I am going to start studying the analysis texts (Rudin-PMA, Apostol-MA, Pugh-RMA) on the first week of August. I have a good proof skills through working on Artin's Algebra and Hoffman/Kunze's Linear Algebra, but I unfortunately only took computational 1-variable...
  40. RJLiberator

    Complex Analysis Clarification Question

    Homework Statement Problem and solution found here: http://homepages.math.uic.edu/~dcabrera/math417/summer2008/section57_59.pdf The question I am interested in is #1. In the solution, the instructor differentiates the series to get to: 2/(1-z)^3 = the series. If I want the Maclaurin series of...
  41. J-dizzal

    Truss analysis, section method

    Homework Statement Determine the forces in members BC and CG. The forces are positive if in tension, negative if in compression.[/B] Homework Equations ΣF=0 ΣM=0 The Attempt at a Solution I don't know where I am going wrong, My equations include the applied force, since there is only one.
  42. E

    Engineering Electronic circuits analysis textbook dealing with......

    Hey all, I would like to ask your recommendation for analogue electronic circuit analysis textbooks ( diodes ,transistors and op amps etc... ) dealing with the following topics Logic gates general description and their application using analogue electronics Op-amps: 1)Non-ideal model of...
  43. RJLiberator

    Complex Analysis Series Question

    Homework Statement Let 0 < r < 1. Show that from n=1 to n=∞ of Σ(r^ncos(n*theta)) = (rcos(theta)-r^2)/(1-2rcos(theta)+r^2) Hint. This is an example of the statement that sometimes the fastest path to a “real” fact is via complex numbers. Let z = reiθ. Then, since r = |z|, and 0 < r < 1, the...
  44. M

    Roots of Negative Numbers (Complex Analysis)

    Homework Statement Express (-1)1/10 in exponential form (My first time posting - I hope I got the syntax right!) Homework Equations The Attempt at a Solution [/B] I got the solution, it's ejπ/10, but I'm not sure why. Here's my work: (-1)1/10 = (cos(π) + jsin(π))1/10 = cos(pi/10) +...
  45. N

    Engineering statics: Truss Analysis Question

    Homework Statement So I was working on this problem, and my only questions are wether BE and CE can be assumed to be no force members? Also if I am not sure a member is a no force member, will it be revealed once I do the calculations, Homework Equations ΣF = 0 The Attempt at a Solution I...
  46. G

    Engineering DC circuit analysis using Reciprocity Theorem

    Homework Statement In the following circuit I need to find current I1 if the given parameters are E1=0V,E2=15V,E3=60V In the second case, given parameters are I2=100mA,I3=40mA,E1=30V,E2=E3=0V In both cases, R2=R3=R4=R5=300 ohm Homework Equations Using reciprocity theorem for DC circuits. The...
  47. O

    Can a Non-Constant Holomorphic Function Equal Zero Everywhere?

    Homework Statement With . Give an example, if it exists, of a non constant holomorphic function that is zero everywhere and has the form 1/n, where n € N. Homework Equations So.. This was in my Complex Analysis exam, and i have no idea what to do. I always seem to get stuck at these more...
  48. D

    Do you know any book for Power Circuit Analysis?

    We have a simple book for power circuit analysis and it is so hard to pass(8-15 pass from 200+) the exams because it has not solved problems(problems are so simple) also our teacher is doing the lessons copy paste from his book I can't learn this lessons and i can't find course material. Is any...
  49. A

    ANSYS: How to interpret this remote force on a spiral disk?

    Hi! I am new to ANSYS and I am trying to understand a simulation done by some one else. I have a disk with a spiral in it, and it looks like there is a remote force being applied at the centre of the disk, but spread over the entire face. I don't understand how this force is being spread...
  50. P

    Gimbal Joint analysis (Thermal expansion)

    Good day, I am currently developing a thermal expansion analysis of a pipe line, I need to validate if the current installed Gimbal joints will withstand those conditions. These gimbal joints just allow angular movement. Is there any software or method that can help me as reference for this...
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