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. L

    Calculus and analysis at the same time

    Hello, I dropped out of high school a year ago where I did up to calculus II as it's called in USA. This was done using the computational method so we didn't learn any proof. But I feel like I matured as a mathematician and tried reading Zorich's Analysis I (found online) which I'm not finding...
  2. J

    How to Derive Equation 2 for Stress Analysis in Flywheels

    Hello, I'm trying to follow along with the stress analysis derivation for flywheels given here, but I'm stuck at the point where it says:2⋅σ t⋅δrsin(1/2⋅δθ) + σrδθ - (σr + δσr) (r + σr )θδθ = ρr2ω2δr ⋅δθ in the limit reduces to: σ_t- σ_r - r⋅\frac{dσ_r}{dr}= \rho⋅r^2 ω^2 I'm a little rusty...
  3. chaitugk

    Experimental Modal Analysis using FDD?

    I am a beginner to Experimental Modal Analysis and I have a scaled miniature frame and my objective is to conduct modal identification under the structure's operating condition using Frequency Domain Decomposition (FDD). However, after I expose the structure and take the reading, the results...
  4. C

    Do I need Spivak/Apostol before analysis?

    Hello, I'm currently studying math and want to become a mathematician. So far I know up to computational single variable calculus, i.e. Calculus I and II, but not III. Since I found the school textbooks easy I decided to follow the MIT course for Calculus III, so I have started watching the...
  5. RJLiberator

    General Understanding of Terms [ Complex Analysis ]

    Hi all, I was unsure where to put this thread as I read the main topic title in the topology/analysis forums and decided to post it here. I am looking for a chart/graph/website that helps me understand the basic terms such as: -neighborhoods -Boundary points -Singularity points - "Function is...
  6. S

    How to do basic statistical analysis?

    My job requires me to update excel reports and also send out analysis and summaries. My concern is, I don't really have a lot of experience with statistics, numbers analysis, or have enough background to know what type of tools are available for me. For example, let's say I send out a weekly...
  7. RJLiberator

    Simple Complex Analysis Clarification

    I am currently learning how to work with Cauchy-Riemann equations. The equation is f(z) = 2x+ixy^2. My question: is u(x,y) = 2x or just x? At this link: http://www.math.mun.ca/~mkondra/coan/as3a.pdf in letter e) they say u(x,y) is equal to x. But I don't understand how that is possible. Is...
  8. B

    How to Calculate Stresses and Deflections in a Complicated Lever System

    Hi guys, I'm new here and this is my first post so apologies if its in the wrong location or anything. My post is not in regards to a direct question as such but i am more looking for general advice and guidance on how to tackle a problem. I am working on a project that involves lifting...
  9. RJLiberator

    Complex Analysis simple Mapping question

    Homework Statement Find the image of the rectangle with four vertices A=0, B= pi*i, C= -1+pi*i, D = -1 under the function f(z)=e^x 2. The attempt at a solution So, the graph of the original points is obvious. Now I have to map them to the new function. Seems easy enough, but I am not getting...
  10. RJLiberator

    Complex Analysis Properties Question 2

    The problem states, Show that: a) |e^(i*theta)| = 1. Now, the definition of e^(i*theta) makes this |cos(theta)+isin(theta)| If we choose any theta then this should be equal to 1. What can help me prove this? If I choose, say, pi/6 then it simplifies to |(sqrt(3))/2+i/2)| which doesn't seem to...
  11. RJLiberator

    Complex Analysis Properties Question

    Use properties to show that: (question is in the attached picture) Now, it is my understanding that due to properties you can express (sqrt(5)-i) as the sqrt((sqrt(5))^2+(-1)^2) which equals sqrt(6). And (2zbar+5) can be represented as (2z+5). But this would be sqrt(6)*(2z+5) which is NOT...
  12. M

    Solving a Connection Problem: Bolted Joint Stress Analysis

    Hi dear friends. I have a big problem and I need your help, I've realized that the joint connection I've drawn (and it is made already) was (most probably) wrong. There is a plate that is bolted to two U beams and the plate is welded to a horizontal I beam at the top. Please take a look at the...
  13. Callmejoe

    Learn Analysis: Math Skills & Textbook Guide

    Hello, I would like to start learning mathematical analysis. I have a basic year of calc( on course in differential, one integral) and a course in multivariable calculus. Will I be able to learn analysis or do I need to learn formal proofs of some sort? Is linear algebra necessary? Also any...
  14. J

    FEA Analysis, verification of values

    Homework Statement Hi there. I have to do this excercise for my exam and I am kinda lost with the verification of data, more precisely calculations. Can you guys help me out? I set 100N load right above the hole... the distance between centers of the hole and nut is 190mm. the max distance...
  15. T

    Engineering Kirchhoff's Law & Circuit Analysis: Q&A

    Homework Statement Using Kirchhoff's current law, determine: 1) The nodal equations 2) The expression and solution for the inductor voltage 3) The expression and solution for the inductor current 4) Determine the initial and final inductor current Circuit diagram: Homework EquationsThe...
  16. AzarulNaim

    Structural analysis in ANSYS

    i'm new in ANSYS software. So, i want helps from others. that is my part. i need to do structural analysis on it but i don't know what supports and loads i need and how to do in ansys. supposely, my part will rotate with 50rpm, torque = 120Nm. diameter of cylinder is 80cm, height of spike is...
  17. fobsnation

    Mechanical analysis of a simple object

    Homework Statement presentation of a component and its mechanical concerns along with some mathematics behind it. Homework EquationsThe Attempt at a Solution I really have no idea how to even start this but I thought of doing the spring in mechanical pens. I would appreciate any help :)
  18. L

    Where to Find Challenging Complex Analysis Problems Online?

    Sorry if this is the wrong forum to post this- Can anyone suggest a good (ideally online) resource for challenging complex analysis problems? The ones I have found so far have been mainly computational- I'm looking for conceptually harder problems, preferably requiring lots of proofs, which...
  19. D

    Modal Analysis of a Rotor Blade Using Simpack

    Hi everyone, I am relatively new to Simpack and would appreciate some help with getting started. Basically I am trying to obtain the displacement of a rotor blade as it rotates (I already have the model). I want to have the displacements of each modal shape along the entire blade radius. Now...
  20. ANON222

    Analysis of Aircraft Container Collision w/ AH & PL

    Homework Statement There is an aircraft container, platform lift (PL) and aircraft hold (AH). I need to know the range of dimension, G and Z that will cause the aircraft container to collide with the aircraft hold. Homework EquationsThe Attempt at a Solution...
  21. D

    What is the correct way to compute physical displacement in FEM modal analysis?

    Hi all, I have an FEM model that I am doing a modal analysis of. I wanted to check that how I am computing the physical displacement is the correct way, as I've read a lot of about normalising modes, participation factors, effective masses, etc. and I'm not 100% sure on it. I've got the...
  22. G

    Vibration analysis - thin circular plate

    I'm moving on to a new area of focus at work and have found myself analysing a vibration issue. I've had the basics a BSME gets you at an accredited university (20 yrs ago), but am rusty to say the least. I'm looking for guidance on good reading materials to knock the rust off. My problem is...
  23. A

    Article with good analysis of different models?

    I reading article "The Cosmological Constant and Dark Energy" P. J. E. Peebles, Bharat Ratra http://arxiv.org/abs/astro-ph/0207347 They use following sources of density: ## \Omega_{M0}+\Omega_{R0}+\Omega_{\Lambda0}+\Omega_{K0}=1## Next I see " The measurements agree with the relativistic...
  24. D

    What are the best textbooks for learning Fourier analysis and its applications?

    Hello all, I'm a third year university physics major. I haven't read much on Fourier analysis however I have had been introduced to it through an oscillations and waves class. My professor was saying that it can be applied to many different areas and is extremely helpful tool to have under your...
  25. B

    Taking Real Analysis, Abstract Algebra, and Linear Algebra

    Dear Physics Forum advisers, I am a college sophomore in US with a major in mathematics, and an aspiring algebraic number theorist and cryptographer. I wrote this email to seek your advice about taking the Analysis I (Real Analysis I), Abstract Algebra I, and Linear Algebra with Proofs. At...
  26. D

    Plate applying force to a tube - nonlinear analysis ansys

    I am trying to apply a force to the tube structure via the plate. I am struggling to get this to solve. Current set up is as follows: Frictionless contact between the two compenents displacement constraing the plate in the x direction force applied to the plate Could anyone offer some...
  27. S

    Fatigue Life of 0.10mm SS304 Sheet | Sathish Rosario

    Dear All, I would like to calculate fatigue life for the following: A SS430F metal component is repeatedly hitting at 0.10mm SS304 sheet with 1 Kg load from 0.20 mm distance. Assume, Area of hitting: 5.5mm X 16mm = 88 Sq.mm. Hitting load = 1 Kg Tensile strength of 0.10mm SS304 sheet is 515...
  28. S

    Dimensional analysis and minima of a potential

    Homework Statement Consider the Euclidean classical action ##S_{cl}[\phi] = \int d^{4}x (\frac{1}{2}(\partial_{\mu} \phi)^{2} + U(\phi))##, with ##U(\phi) = \frac{\lambda}{8}(\phi^{2}-a^{2})^{2}-\frac{\epsilon}{2a}(\phi - a)##. (a) Show that, in four-dimensional space-time, the mass...
  29. J

    Beam Analysis for Indeterminate Beam with Overhang

    1. The problem, I have a beam 9000 mm in length. assuming a x-coordinate system: supports are at the x= 1500, x= 4500, and x= 7500 positions. there's a uniformly distributed load (let's call it w) through the length of the beam (from 0 to 9000mm) Solve for the MAXIMUM moment. This would be much...
  30. Vorrawit

    System analysis of a centrifuge

    Homework Statement Initial training involves a slow onset rate (1 g/s) run up to a maximum of 9 g’s. After these initial runs, a rapid onset rate (ROR) of 6 g/s is typically performed; this is for high performance fighters. Finally, a Tactical Aircraft Combat Maneuver (TACM) may be performed...
  31. T

    Pressure drop analysis on water pipe system w/pump

    Hey everyone. Four days ago I didn't know anything about fluids but I started my internship and got assigned a project that is all about fluids! And I need some help, this topic can get really complicated but I'm trying to take it one step at a time. Problem Description: There is a pump...
  32. QuantumCurt

    Complex before real analysis? How's my fall schedule look?

    Hey everyone, I'm transferring into UIUC this fall, and I just registered for my classes earlier today. I'm completing dual degrees in physics and math. I've completed the introductory physics sequence, and the introductory calculus sequence, plus a 200 level introductory differential equations...
  33. C

    Twin Paradox - Question on Space Time Diagram Analysis Resolution

    I started a thread previously (https://www.physicsforums.com/threads/time-dilation-happens-on-moving-frame-but-which-one.814622/) around this concept but it got closed by one of the staff after helpfully pointing me to...
  34. A

    Factor analysis versus Baye`s estimates?

    I am doing a retrospective research on breast cancer using multivariate estimates. The aim of the research is to calculate the probabilty of findng the breast cancer given the multiple independent variables (IVs). So the outcome should be binary in nature (cancer versus benign). Some of IVs are...
  35. M

    MHB Numerical Analysis: Project 01 | CPP

    http://www.cpp.edu/~jlcannons/mat_201_2015_spring/Project_01.pdf I don't know if this counts as cheating, but I hope someone could look this over and see what my professor is ask.
  36. RJLiberator

    Should I take Complex Analysis? Am I ready?

    Here's my situation: Summer 2015, I am majoring in math and physics. I am taking a 4-week course on DIFF EQ right now, and completely loving it and doing extremely well. Just finished my set of Calc 1, 2, and 3, and an intro to advanced math course (proof-writing basics). Diff EQ is a 220...
  37. ShayanJ

    Forming Spherically Symmetric Metric: Math Analysis & Omitted Steps

    In most GR textbooks, the general form of a spherically symmetric metric is obtained by inspection which is acceptable. But in the textbook I'm reading, the author does that with a mathematical analysis just to illustrate the method. But I can't follow his calculations. In fact he omits much of...
  38. ranju

    Analysis of Filters: Calculating Characteristic Impedance Z0T

    Homework Statement In the given filter network , we have to find the characteristic impedance Z0T And the author found it as Z0T= √Z12/4 + Z1Z2 But I didn't get this , how this expression came up..! I found Z0 by considering Z1/2 in parallel with Z2 & the resultant is in series with Z1/2... & a...
  39. evinda

    MHB Finding a Local Minimum of $G$: Algorithm & Analysis

    Hello! (Wave) A $m \times m$ grid is a graph of which the vertices are ordered pairs of natural numbers $(n_1, n_2)$ with $1 \leq n_1 \leq m$ and $1 \leq n_2 \leq m$. Two vertices $(k_1,k_2)$ and $(k_3,k_4)$ are neighbors iff $|k_1-k_2|+|k_3-k_4|=1$. We suppose that a unique number $y_w$ is...
  40. R

    Wavelets vs disadvantages of Fourier Analysis and Synthesis?

    I am a beginner. The Fourier series, Fourier Transform and it's inverse play very important role in Fourier Analysis and Fourier Synthesis. I have read that Fourier transform is localised in only frequency domain.Also,it contains information about the signal in phase and frequency spectrum...
  41. B

    Abaqus 6.14 CAE - Imperfection Study

    The title of the project is as follows: A study of the effect of imperfections on the buckling capability of a soda can under axial loading. My group and I are aiming to carry out the following: Linear buckling analysis of soda can to gain first 5 eigenvalues Riks buckling analysis with...
  42. S

    Complexity Analysis problem of an Algorithm.

    ##A,B## are symmetric matrices of graphs ##G,H## respectively. For ##x \in G##,consider the graph ##(G-x)##, it has vertices adjacent to ##x## and vertices non adjacent to ##x##.## A_x## is the symmetric matrix of the graph ##(G-x)##, where ##C## is the symmetric matrix of the graph created by...
  43. P

    How can dimensional analysis be carried out correctly?

    Hello! May I first please direct your attention to Walter Lewin's first Classical Mechanics lecture on Units, Dimensions and Scaling Arguments? He first carried out a dimensional analysis to determine the relation between the time taken for a ball to fall from a particular height to the height...
  44. D

    Circuit analysis and general study tips

    The more work I do in the field of EE, the more I realizing that my general circuit analysis skills are usually the root of my confusion and could use improvement. Even after putting on my break-a-big-problem-into-smaller-pieces hat, I still find myself confused about the relationships between...
  45. N

    Complex Analysis: Use of Cauchy

    http://www.math.hawaii.edu/~williamdemeo/Analysis-href.pdf Please look at problem 2 on page 39 of the problems/solutions linked above. I know I'm going to kick myself when someone explains this to me but how was equation "(31)" of the solution obtained? The first term of the RHS of (31) is...
  46. A

    Singular spectral analysis of periodic series with period L

    Let's have a time series with a period=L. Suppose we arbitrarily choose the window length of the trajectory matrix to be equal to L which is also equal to the period of a time series. Then the second column of the matrix will also start with the same entry as the first column, because all...
  47. R

    Tesla Powerwall: Engineering Analysis

    Just thought I'd post this on here to see what comments people have: http://www.teslamotors.com/powerwall Tesla has announced a Li-ion battery "Powerwall" priced at $3500 for 10 kWhr storage. What payback to people perceive? Gimmick, niche market or disruptive technology?
  48. S

    How to selfstudy to learn (electronics) network analysis (Thevenin, Norton)?

    I am learning network theorem,my syllabus includes application of kcl,kvl,thevenin and norton theorem,superposition theorem,maximum power transfer I studied it from malvino,its quite good! But lack of solved problems! Actually I am finding difficulty while solving networks with double voltage...
  49. E

    Complex analysis book recommendation for electrical engineering

    I need recommendation about complex analysis book. As I'm electrical eng. student, it should cover everything one engineer need to know about that mathematical field, but without strict mathematical formalism :)
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