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. A

    Particles on Deforming Surfaces: Theory & Analysis

    All books in analytical mechanics explain the case of a particle moving on a given static surface. But what happen if, for example, the surface is having some deformation?. I imagine that the principle of virtual work, and hence, D'Alembert are no longer valid since the normal force by the...
  2. D

    Using a Surface Integral for Mathematical Analysis of the Area of an Island

    I am not clearly understand what the question requests for, is it okay to continue doing like this ? Kindly advise, thanks
  3. LCSphysicist

    Graphical Analysis of damped oscillator

    First of all, i tried to find w, the angular frequency, by calculating the oscillations from ta to tc, there is ~ 20 oscillations coursed. so, w = 2*pi*20/(tc-ta) ta = 0, tc = 0 + 5.2 ms And tried to find the factor gama y by A(t) = A*cos(Φ + wt)*e^(-yt/2) A(0) = 2.75u = A*cos(Φ) 1u = A*cos(Φ...
  4. Adesh

    Analysis Books for learning Fourier series expansion

    Hello Everyone! I want to learn about Fourier series (not Fourier transform), that is approximating a continuous periodic function with something like this ##a_0 \sum_{n=1}^{\infty} (a_n \cos nt + b_n \sin nt)##. I tried some videos and lecture notes that I could find with a google search but...
  5. patric44

    Vector analysis problem about a gradient

    hi guys i saw this problem in my collage textbook on vector calculus , i don't know if the statement is wrong because it don't make sense to me so if anyone can help on getting a hint where to start i will appreciate it , basically it says : $$ \phi =\phi(\lambda x,\lambda y,\lambda...
  6. TytoAlba95

    Understanding MiRNA Profile Analysis: Exploring Bar Diagrams from GSE94799

    Picture source:GSE94799 Following are the two different types of bar-digram that were observed. My questions are: 1. What do bars hanging below 0 mean in the first dig. ? 2. What do bars shooting from -6 mean, also why are they below 0? 3. Like a normal gene (non-ncRNA gene) expression profile...
  7. J

    Linkage Analysis and force study

    Hi All, I am working on this linkage mechanism. Please see the attachment for images. There are 3 pivot points. Two of which are connected to the ground. The" Inside Leg 1" is telescopic to "Leg 2" and has a 120 LB compression gas spring connected at mount points as shown in the image. The leg...
  8. S

    I Exploring Deep Space: A GR Analysis

    Thank you all for clearing my doubt before. There is a question I want to ask on space and time and this time it is not about the absolute time as I have understood fairly that space and time are always relative. So Here it is according to GR It is very beautifully explained that Very massive...
  9. Boltzman Oscillation

    Engineering Variable Gain Amplifier Analysis help

    I need to find A_v, I want to relate Vin to Vout. To do this I did KVL on the major loop: $$V_{DD} = I_D*R_D + V_{SD1} - V_{SD2} - I_D*R_D$$ Since M1 = M2 then everything would cancel out and I would just get V_dd = 0 which is probably wrong. This is assuming V_sd1 = V_sd2, is that correct?
  10. T

    I What is the Purpose of Modal Analysis in Mechanical Systems?

    Consider this system, above. If I studied the mechanics of this system, I get this system of equations. At that point, I choose to study a free vibration problem and drop the damping, and conduct a modal analysis. I understand the process:vvI assume a solution such that each mass moves...
  11. jim mcnamara

    B An objective Bayesian analysis of life’s early start & late arrival

    Article: https://www.pnas.org/content/early/2020/05/12/1921655117 Phys.org link https://phys.org/news/2020-05-odds-life-intelligence-emerging-planet.html An issue I see is Mars and Venus. Mars may have had some life forms, and may still. Venus never got that far. So, in a sense, we are 1...
  12. jisbon

    Engineering Nodal Analysis of this Circuit using the Laplace Transform

    Was just practicing some problems on the Fundamentals of Electric Circuits, and came across this question. I understand I will have to transform to the s domain circuit, which looks something like this: Then doing nodal analysis, I will get the following for the first segement (10/s-V1)/1 =...
  13. R

    Ladder-like bandpass filter theoretical analysis problem

    I consider the band-pass filter of the following configuration (the ##u_m## is a voltage controlled voltage source): The transfer function is $$K_1(p)=\hat{U}_o(p) = \frac{p}{RC(p+1/RC)^2} = \frac{\omega_c p}{(p+\omega_c)^2}, \quad \omega_c=\frac{1}{RC}.\qquad (1)$$ Now I connect ##n## such...
  14. MidgetDwarf

    Lectures That Follow Pugh: Real Mathematical Analysis

    Not sure if this is the correct forum. But are there any video lectures that follow the book Pugh: Real Mathematical Analysis? Thanks.
  15. jisbon

    Engineering Mesh Analysis for time domains?

    I've tried to solve the following circuit using mesh equation, but the solution seems to differ from my attempted answer. Mesh circuit as follows: My mesh equation is: -10+3(i1)+2s(i1-i2)=0 (for the mesh on the left) and -10+12(i2)+6s(i2)+2s(i2-i1)=0 (right mesh) However the answer seems to...
  16. diegzumillo

    I Self teaching analysis and topology

    Hi, I am a physicist interested in going through a basic analysis course. The real line, open sets, that whole thing. On my own, so I need a good selection of bibliography, ranging from those that are good references but too dense to actually read to those that are very pedagogical but tend to...
  17. CaptainAmerica17

    I Help Finding the Correct Approach to this Proof (Intro Real Analysis)

    Ok, so here is what I have so far: Suppose ##T_1## is infinite and ##\varphi : T_1 \rightarrow T_2## is a bijection. Reasoning: I'm thinking I would then show that there is a bijection, which would be a contradiction since an infinite set couldn't possibly have a one-to-one correspondence...
  18. karush

    MHB -2.2.27 - Analysis of first order IVP

    well each one is a little different so,,, $$\dfrac{dy}{dt}=\dfrac{ty(4-y)}{3},\qquad y(0) =y_0$$ not sure if this is what they meant on the given expression
  19. dRic2

    I Resonant cavity and circuit analysis

    As I understand, if you solve the Maxwell's field equations for a resonant cavity, supposing a time dependence of the form ##e^{iwt}##, you get an eigenvalue problem and different modes as possible solutions. I'm reading some notes where the author states that each mode can be associated with a...
  20. M

    What should I do to specialize in material analysis techniques as a career option?

    Summary:: What should I do to specialize in material analysis techniques as a career option? What should I do to specialize in material analysis techniques as a career option?
  21. Wan Anavan

    A Simple angular momentum analysis question (check my solution please)

    is my solution correct?
  22. Cesca Roma

    I Discriminant function analysis - stepwise or otherwise?

    I’m using discriminant function analysis to determine the potential accuracy of several biometric measurements being used in conjunction for binary classification purposes for my BSc Biomed research project. Overall I've only got 110 data points so it's a stretch but hey, that's anatomy! What...
  23. CaptainAmerica17

    Would someone mind checking my proof? Intro Real Analysis

    Here is my solution. I used mathjax to type it up in Overleaf. I feel like it makes sense, but I also have a feeling I might have "jumped the gun" with my logic. If it is correct, I would appreciate feedback on how to improve it. Thanks!
  24. jisbon

    Engineering Circuit Analysis Question (Truth Table, Logic etc.)

    Hi all, Having some problems digesting on electric circuits. Below is an example of a question and I would like to ask how do I go ahead in solving this. Firstly, for these types of questions: I have understood how to write a function table, and it goes something like this: Now what I am...
  25. H

    Complex Analysis - find v given u

    Solution Attempt: \begin{align} \frac{\partial u}{\partial x} &= \frac{\partial v}{\partial y} = (x^2+y^2)^{-1} -x (x^2+y^2)^{-2} (2x) = (x^2+y^2)^{-1} - 2x^2 (x^2+y^2)^{-2} \\ \rule{0mm}{18pt} \frac{\partial u}{\partial y} &= -\frac{\partial v}{\partial x} = -x (x^2+y^2)^{-2} (2y) =...
  26. jisbon

    Circuit Analysis - Source Transformation

    My work seems to be wrong somehow since my answer is wrong, and I need your help to find out which part is going wrong for me :/ My work: 1. 2. 3. 4. 5. 6. (10/7)/(10/7+7) = 0.7627A, which is not the answer. May I consult where is the problem in solution? THanks
  27. jisbon

    Circuit Analysis Question -- 2 sources and 4 resistors

    Now, I know this question can be solved using Kirchoff Voltage rule, but the question expliciitly wants me to use power supplied = power absorbed. Hence taking V0 to be x, I can't still seem to calculate. Any ideas? Power supplied = (60)(3) + (5x)(3) = 180+15x Power absorbed = 72+ 56 +28 + 3x...
  28. michii15

    I Find the only periodic solution of an ODE

    Find the only periodic solution for 𝑦′+𝑦=𝑏(𝑥) with 𝑏:ℝ→ℝ has a period of 2𝑇 and is 1 for 𝑥(0,𝑇) and −1 for 𝑥(−𝑇,0). The ODE is easy to solve: 𝑦(𝑥)=exp(−𝑥)⋅𝑐+1 and 𝑦(𝑥)=exp(−𝑥)⋅𝑐−1. But how can I find the 𝑐 such that the solution is periodic with a period of 2𝑇? The solution is...
  29. Jonathanos

    Courses Complex Analysis Courses or Complex Variable Courses?

    Hello, My university offers a couple Complex Analysis courses, among them there is one with the following description: Introduction to complex variables: "substantial attention to applications in science and engineering. Concepts, calculations, and the ability to apply principles to physical...
  30. T

    Statics and Structural Analysis Question

    I am able to draw shear and bending moment diagrams. We were never taught how to even start with a problem like this.
  31. P

    Engineering Finite Element Analysis / Structural Analysis

    Hello engineer's community ! I got a problem. If i got a truss frame with 2 bars and an initial nodal displacement for the common node , then how can i calculate the velocity of the oscillation as function of time ? (the 2 bars have different length , same elasticity modulus , same density and...
  32. manareus

    Instrument name for water sampling and analysis

    Hello, thank you for your attention in my thread. I'm the head of Youth Science Club on one of the many High School in Indonesia, I got many members and I want to guide them for doing water sampling and analysis. In the history of my high school, no one is able to do water sampling and...
  33. M_Abubakr

    RVE Periodic Boundary Conditions in ANSYS Workbench Modal Analysis

    Hi I have a project regarding micromechanics of composites. I'm starting my analysis on the Fiber Matrix RVE. Right now I'm trying to find the natural frequency of the unit cell. The Unit cell has some unique geometry which I will keep on changing to see how natural frequency changes. I have...
  34. Adesh

    Analysis of a deformable body and Newton's 3rd Law

    I'm posting the images of "Sommerfeld's Lectures on Theoretical Physics, Vol 2, Mechanics of Deformable Bodies" I apologize for posting the images rather than writing out the whole thing. But I did it to so that nothing should be missed, as writing out the...
  35. T

    Nuclear Reactor Analysis Problem 5.34

    I'm aware that geometric buckling is equal to material buckling when k =1, any pointers on how to set up the boundary conditions for this problem?
  36. N

    Solving for λ, a, and Vmax: An Analysis of Energy Balance and SHM

    a) λ = 4/3 by considering the energy balance as P moves from A (2a) to B (1/2a). The E.E. at A changes into a gain in gravitational potential energy + build up of E.E. at B since the spring compresses. b) a = 5/3g by considering that the mass P is in dynamic equilibrium immediately after...
  37. M

    Engineering Plastic Analysis: Upper Bound Theorem

    Hi, I have a quick question about part 1 of this upper bound theorem question (in the attached image). Answer says that \lambda_c = 2.25 . First, we know that there is 1 redundancy and therefore there will be a maximum of 2 plastic hinges for failure. I have found that there needs to be...
  38. HaoBoJiang

    I want to get some books about Mechanics analysis

    Summary:: Is there somebody can help me？ The book about Mechanics analysis or classical mechanics,if you have read some good books, please recommend them to me, I will be very grateful.
  39. B

    Dimensional Analysis for Multi-Layer Flow Equations

    Hello, New to the forum. I am looking for some help with some work. It is dimensional Analysis, i have done Dimensional analysis with the analysis bridge before. But i am stuck with the question below and trying to learn it. Any help much appreciated. I have the equation q = U A dT. But i am...
  40. A

    Complex analysis: find contradiction of a relationship

    I have reached a conclusion that no such z can be found. Are there any flaws in my argument? Or are there cases that aren't covered in this? Attempt ##\log(\frac{1}{z})=\ln\frac{1}{|z|}+i\arg(\frac{1}{z})## ##-\log(z)=-\ln|z|-i\arg(z)## For the real part...
  41. Jason-Li

    Comp Sci Fourier analysis & determination of Fourier Series

    ANY AND ALL HELP IS GREATLY APPRECIATED :smile: I have found old posts for this question however after reading through them several times I am having a hard time knowing where to start. I am happy with the sketch that the function is correctly drawn and is neither odd nor even. It's title is...
  42. M_Abubakr

    Micromechanical Vibration Analysis of Composite Materials

    This project is stressing me out along with other workload and I'm in panic mode right now. The brief of the project is in the attachment. I can interpret 4 objectives out of this: (1) Analysing the relation of the physical parameters in the composite material with the characteristics of wave...
  43. P

    Studying Should I read Introduction to Calculus and Analysis by Courant?

    Should i read Introduction to Calculus and Analysis by Courant? I have calculus background I want to study multivariable and single variable in rigorous way There is a lot of books in this subject like Spivak, apstoal,Courant,... . I am not sure what to choose
  44. B

    Starship Hull Shape Analysis: Discuss the Reality of Sci-Fi

    Using real science we can extrapolate what hull shapes could be used, assuming we actually did have high thrust constant acceleration drives (we don't because it requires energy/mass ratios that tend to cancel each other out). So what shapes? Pill capsules are ideal for crewed vessels. Even...
  45. J

    Circuit Analysis of a diagram with series and parallel circuits

    I found the Req which is 13.6 and also found the It which is 0.74. I'm having trouble finding the separate current and potential difference numbers.
  46. rachelmaddiee

    Chemistry Converting 100 Yards to Centimeters: Dimensional Analysis Explained

    I’m trying to solve this question using the exact method in my book but I’m having trouble with setting this up. Here is my work** The length of a football field (100 yards) needs to be converted to centimetersLength of paperclip = 3.2 cm long36 inches = 1 yardhow many paperclips in 100 yds =...
  47. A

    Engineering Can this circuit be solved without nodal analysis?

    help will be appreciated
  48. H

    Accurate Fluid Dynamics By Video Analysis

    Continue reading...
  49. A

    Engineering Troubles with a circuit analysis situation (RLC circuit)

    thanks
  50. G

    Understanding SHM of a Mass: Exploring Energy Conservation and Elasticity

    Could I please ask for views on this question: I've answered the whole thing and agree with the answers given in the textbook. Here are those answers (where Y is the modulus of elasticity of the string = lamda in the question): Period of motion = 2 * PI * sqrt( ma/Y ) Speed passing through...
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