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).

View More On Wikipedia.org
Recent contents Top users
  1. 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...
  2. 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...
  3. 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...
  4. G

    I A question about units in equation: Dimensional analysis

    This question is about the matching the unites in an equation. The equation for an electron mobility is given by m^2/V.S. However substituting the units in the equation, doesn't yield the unit of mobility [m^2/V.S]. I have done the simplification using mks units and didn't come up to m^2/V.S...
  5. W

    I Dimensional analysis involving partial derivatives

    It is mentioned in Reif's book, statistical physics, that trough dimensional analysis it can be shown that: $$\frac{1}{\beta} = kT $$ where ##\beta## equals ##\frac{\partial \ln \Omega}{\partial E}## and k is the Boltzmann constant. I don't quite see how to reach this result, can anyone give me...
  6. binbagsss

    Mathematical Biology- Neumann BCs, Turing Analysis

    This is probably a stupid question but I have Neumann BC boundary : ## \nabla u . \vec{n} =0## (same for ##v##)conditions for the following reaction-diffusion system on a [0,L_1]x[0,L_2]x...x...[0,L_n] n times in n dimensional space so ##u=u(x_1,...,x_n,t)## is a scalar I believe? so that ##...
  7. Zack K

    Dimensional Analysis of an oscillation

    Homework Statement The period of oscillation of a nonlinear oscillator depends on the mass m, with dimensions M; a restoring force constant k with dimensions of ML-2T-2, and the Amplitude A, with dimensions L. Use dimensional analysis to show what the period of oscillation would be proportional...
  8. D

    I Complex analysis - removable singular points

    Hi. I have 2 questions regarding removable singular points. 1 - the residue at a removable singularity is always zero so by the residue theorem the integral around a closed simple contour is zero. Cauchy's theorem states the integral around a simple closed contour for an analytic function is...
  9. P

    Engineering Solve this Circuit using both Nodal Analysis and Mesh Analysis

    Homework Statement [/B] Determine, Using the values given in TABLE A, the current I in the circuit of figure 2 by (a) Mesh analysis (b) Nodal analysis Circuit diagram and given variable attached. V1 = 120 V2 = j120 V3 = 14.142+j14.142 Z1= 2 Z2=-J5 Z3=4 Z4=-J5 Z5=J4Homework Equations [/B] KVL...
  10. AchillesWrathfulLove

    Engineering Do electrical engineers actually use Circuit Analysis skills?

    Do electrical engineers actually use stuff that is taught in Circuit Analysis classes like Node Voltage Method, Mesh Current Method, Kirchhoff Voltage/Current Law, Source Transformation. All these usually only involve resistors. Are they somewhat altered in a way to analyze circuits with other...
  11. AchillesWrathfulLove

    Which is a better method for Circuit Analysis?

    Node Voltage Method or Mesh Current Method.
  12. L

    Partial Thermo analysis of a Crower engine

    Hi everyone. Some years ago I read about the Crower six cycle engine. Always wanted to understand it better. And now is the time to follow up on that desire. I’m trying to calculate what happens during the water injection. The goal is to determine the conditions (pressure, temperature)...
  13. Onezimo Cardoso

    How to Prove Inequality for Convex Sets in R^n?

    Homework Statement Let ##C \subset \mathbb{R}^n## a convex set. If ##x \in \mathbb{R}^n## and ##\overline{x} \in C## are points that satisfy ##|x-\overline{x}|=d(x,C)##, proves that ##\langle x-\overline{x},y-\overline{x} \rangle \leq 0## for all ##y \in C##. Homework Equations By definition...
  14. DracoMalfoy

    Dimensional Analysis: Period of a Pendulum to the length

    Homework Statement Use unit analysis to show that the constant, 2π, is unitless. Homework Equations T=2π√L/g[/B] The Attempt at a Solution T= [T] L= [L] g= a= [L]/[T]^2= [L T^-2] [T]= 2π√[L]/[L T^-2] [/B] Is this correct? I wasn't really sure how to do this. I'm using book examples to...
  15. J

    MHB Real Analysis, Sequences in relation to Geometric Series and their sums

    I will state the problem below. I don't quite understand what I am needing to show. Could someone point me in the right direction? I would greatly appreciate it. Problem: Let p be a natural number greater than 1, and x a real number, 0<x<1. Show that there is a sequence $(a_n)$ of integers...
  16. J

    MHB Real Analysis, liminf/limsup Equality and Multiplication

    Here are a couple more problems I am working on! Problem 1: Prove that, $limsupa_n+liminfb_n \leq limsup(a_n+b_n) \leq limsupa_n+limsupb_n$ Provided that the right and the left sides are not of the form $\infty - \infty$. Proof: Consider $(a_n)$ and $(b_n)$, sequences of real numbers...
  17. J

    MHB Real Analysis, liminf/limsup inequality

    I am working a bunch of problems for my Real Analysis course.. so I am sure there are more to come. I feel like I may have made this proof too complicated. Is it correct? And if so, is there a simpler method? Problem: Show that $liminfa_n \leq limsupa_n$. Proof: Consider a sequence of real...
  18. H

    Extracting data from a spectrometer to Excel

    Good morning, I used the Laser beam with HR4000 spectrometer with Ocean View software when saving the files it is saved by (.ocv) format. when trying to extract information to excel I get some unreadable data like (bkg thin sheet gel.png) attached. I used the same instrument and software with...
  19. S

    Simple dimensional analysis problem, thanks for any help

    Homework Statement It requires 10 microliters of a Cu(NO_3)_2 solution to produce a spot of 1cm in diameter. If the Cu(NO_3)_2 solution contains about 6g Cu^2+ per liter, then how many micrograms of Cu^2+ ions are there in one spot? Homework Equations simple dimensional analysis problem: 1st...
  20. S

    Canonical partition function of an ideal gas (unit analysis)

    Homework Statement Basically the units of the Canonical Partition Function within the logarithms should be zero Homework Equations The Attempt at a Solution N here is a number so we ignore the left logarithms, applying a "Unit function " for the terms within the logarithm...
  21. TyroneTheDino

    Proof involving convex function and concave function

    Homework Statement [/B] Let X be a vector space over ##\mathbb{R}## and ## f: X \rightarrow \mathbb{R} ## be a convex function and ##g: X \rightarrow \mathbb{R}## be a concave function. Show: The set {##x \in X: f(x) \leq g(x)##} is convex. Homework Equations [/B] If f is convex...
  22. R

    Node Analysis on Circuit: Solving for R3 Current

    I have no idea how to do the node analysis for this circuit. I have done the mesh analysis and got the current in R3 to be 4A is this right?
  23. C

    Fourier Analysis and the Significance of Odd and Even Functions

    Homework Statement Q1. a) In relation to Fourier analysis state the meaning and significance of 4 i) odd and even functions ii) half-wave symmetry {i.e. f(t+π)= −f(t)}. Illustrate each answer with a suitable waveform sketch. b) State by inspection (i.e. without performing any formal analysis)...
  24. SSequence

    Can Sorting Ever Be Done in Time Proportional to n?

    The question(s) here can be asked for many problems (and not just sorting). Let's consider the standard case of sorting an array of size ##n## containing numbers. If we consider a naive algorithm, its time would be proportional to ##n^2##. For example, the naive algorithm could be proceed with...
  25. E

    Opinions on I.A. Maron's Mathematical Analysis textbook?

    Anyone completed IA Maron Mathematical Analysis? Anyone like it?
  26. O

    B Megastat's Regression Analysis keeps asking confidence level

    Hi, Anyone out there using Megastat? The course I am in requires using it/knowing how to use it for processes. Whenever I try to get a regression analysis it insists that I need to set a confidence level - I've tried different versions of typing 95%/0.95 into no avail, and I don't know what...
  27. B

    Mathematical Analysis Proof: |x-y|<= |x|+|y|

    Homework Statement 1. Show that for all real numbers x and y: a) |x-y| ≤ |x| + |y| Homework Equations Possibly -|x| ≤ x ≤ |x|, and -|y| ≤ y ≤ |y|? The Attempt at a Solution I tried using a direct proof here, but I keep getting stuck, especially since this is my first time ever coming...
  28. A

    Engineering Confusing circuit analysis question

    Hi I have the following situation: (Please see attached pic) I want to know if equation (4) i have written is correct. What is confusing me is that, I remember being told in circuit analysis that each energy storage element should have its own state variable. But in this situation when I...
  29. N

    Your thoughts on numerical analysis teaching

    Hello all, I may get a contract to teach numerical analysis. I did quite a lot of numerical work during my PhD but that was a while ago. Now when I look at most books on the topic, I get the feeling that a lot is outdated, and I also feel that a lot of what I knew is outdated as well...
  30. Onezimo Cardoso

    Inner product - Analysis in Rn problem

    Homework Statement Let ##x,y \in \mathbb{R^n}## not null vectors. If for all ##z \in \mathbb{R^n}## that is orthogonal to ##x## we have that ##z## is also orthogonal to ##y##, prove that ##x## and ##y## are multiple of each other. Homework Equations We can use that fact that ##<x ...
  31. bhobba

    Analysis Are Terry Tao's Books On Analysis Worth Getting?

    I learned my analysis from Ruden way back when. It fell apart from overuse so I got two books to replace it - Apostol and Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by Hubbard - both very different in approach. But recently I have read Terry's two volume set...
  32. L

    A Convergence of a subsequence of a sum of iid r.v.s

    ##X_i## is an independent and identically distributed random variable drawn from a non-negative discrete distribution with known mean ##0 < \mu < 1## and finite variance. No probability is assigned to ##\infty##. Now, given ##1<M##, a sequence ##\{X_i\}## for ##i\in1...n## is said to meet...
  33. marsupial

    Engineering The effect of a switch in a Laplace circuit analysis

    Homework Statement The switch in the circuit in has been closed for a long time. At the switch is opened. a) Find i0 for t>=0 (b) find v0 for t>=0 I don't understand the effect of the switch in the position it is in. It's acting as a short circuit, I think, so presumably the capacitor doesn't...
  34. Barath Kr

    How to apply moments in ANSYS Explicit Dynamic Analysis?

    Hello All, I want to apply moments to Revolute Joints in Explicit Dynamic Analysis. But i could not find any option to apply moments. I saw an youtube video, from which it is cleary know that it is possible to apply moments to revolute joints under initial conditions. But i don't know how they...
  35. BillTre

    Lokiarchaeon Genome Analysis Supports Hydrogen Hypothesis

    Comparative genomic analysis (Free pdf download here) shows that Lokiarchaeon (the mysterious closest presumed relative to the archaeon host (known only by its genome sequence collected from an environment), which contained the endosymbiont bacteria (that became the mitochondria), had hydrogen...
  36. D

    MHB Analyzing Correlation between IQ Scores and GPA in Ninth Graders

    A school educator is interested in determining the potential relationship between grade point average (GPA) and IQ scores among ninth graders. The educator takes a random sample of 30 ninth graders aged 14 years old and administers the Wechsler Intelligence Scale for Children-Fourth Edition...
  37. kstorm19

    Solving a circuit using both the mesh and node analysis

    Homework Statement The problem asks to solve for i1, i2, and i3 using the mesh method in the following circuit: I will also include the link, because I noticed I am having trouble attaching the image to the post: https://imgur.com/a/bBvuLXM I would also like to confirm the answer by solving...
  38. F

    [Intro analysis] Prove lim s_n = 0

    Homework Statement Assume all ##s_n \neq 0## and that the limit ##L = \lim \vert \frac{s_{n+1}}{s_n} \vert ## exists. a) Show that if ##L < 1##, then ##\lim s_n = 0##. (Hint: Select ##a## so that ##L < a < 1## and obtain ##N## s.t. ##\vert s_{n+1} \vert < a \vert s_n \vert## for ##n \ge N##...
  39. T

    Complex Analysis prerequisite material review

    Homework Statement Identify the set of points satisfying ##1<\vert 2z-6\vert <2## such that ##z\in\Bbb{C}##. My pre-caculus is very rusty, so I am not sure if I am doing this correctly. Homework Equations ##x^2 +y^2= r^2## ##\forall z,z'\in\Bbb{C}, \vert zz'\vert =\vert z\vert\vert z'\vert##...
  40. Z

    Questions about static analysis in Ansys

    In ansys , i want to do static analysis of a section of steel pipe supported on piers . the only loads are internal pressure of water and the weight of water and steel . 1. For the weight of the structural element, on Ansys I find that there is among the loads proposed in the list of loads...
  41. C

    I Analysis of Ultrasonic Waves at a point

    I have a question regarding a theoretical analysis of Ultrasonic waves : The next picture represents a system of transducers sitting on fixed boards: Datum: * there are 4 transducers ( represented by blue color , indexed by letter ' T ' ) , each outputting Ultrasonic wave (represented by...
  42. D

    Load analysis on a motorcross bike - need some advice

    My task is to analyze a frame's strength of a specific motorcross using different loads, and to do this i decided to focus on vertical fall from various heights, since this will probably give the largest forces on the bike. The one can also experiment with different types of landings, i.e...
  43. D

    I Static analysis of bicycle frame - Need some clarification

    Hey, I am interesting in analyzing a bicycle's frame statically from a vertical fall of x metres, this after using the energy principle i get that the force F = mv^2/r, where v = sqrt(2*g*h), r is the deformation of the bicycle at its contact point and m is total mass from the cycle and cyclist...
  44. D

    I Limit of Extension: Can Function Have Different Limit?

    When we define a limit of a function at point c, we talk about an open interval. The question is, can it occur that function has a limit on a certain interval, but it's extension does not? To me it seems obvious that an extension will have the same limit at c, since there is already infinitely...
  45. D

    Materials for DTL, TTL circuit analysis

    Hi fellow forum-ers :), I have a test in about two weeks where i am going to be given a dtl or ttl circuit which i have to analyse and calculate its function. The professor said that the circuit given to us will always be a useful and existing one meaning he's going to give us some NAND, NOR or...
  46. Peter Morgan

    A Stochastic signal analysis in QM

    [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...
  47. jmex

    Lame question on tank analysis

    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...
  48. paulmdrdo

    Engineering Op-Amp Circuit Analysis: Troubleshooting Incorrect Node Usage

    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.
  49. Valour549

    AC Circuit Analysis- Find Impedance

    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.
  50. Mr Davis 97

    Real Analysis Definition and Explanation

    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...
Back
Top