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. G

    Engineering Circuit analysis -- Find the complex apparent power of I(g2)

    Homework Statement Given the circuit of sinusoidal current (attachment 1) with given data: \underline{Z_3}=200(3-j4)\Omega, \underline{Z_4}=100(3+j20)\Omega, \underline{Z_5}=100(3+j4)\Omega, \underline{Z}=100(2+j5)\Omega, \underline{I_{g2}}=-10(2-j)mA After the switch is closed, the increment...
  2. George Zucas

    Lifeline Rope Strength Analysis

    Hello everybody, I am trying to analyse the lifelines we use at work, though the results I obtain are causing me headaches. The problem is, our workers often install and use what I would call homemade lifelines. My boss asked me to check whether what they do is reliable. According to what I...
  3. G

    Engineering Circuit analysis -- Find active and reactive power in the branch....

    Homework Statement Given the circuit of sinusoidal current (attachment 1) with given data: \underline{E}=100V,\underline{E_1}=40V,\underline{Z}=(10+j10)\Omega,\omega=10^5rad/s,L=1mH, C=0.1uF. Find \underline{I_L},\underline{U_{16}}, active and reactive power in the branch 2-5. 2. The...
  4. Ethan Godden

    Theorem About Binary Operations - Introductory Analysis

    Homework Statement This theorem comes from the book "The Real Numbers and Real Analysis" by Bloch. I am having a hard time understanding a particular part of the proof given in the book. Prove the following theorem: There is a unique binary operation +:ℕ×ℕ→ℕ that satisfies the following two...
  5. A

    I (old?) spectroscopy analysis notation

    Hello, I've been studying spectroscopy in organic molecule and I came across an old data from 1934. 280(5b)(k,i±e), 297(1vd)(e), 354(1vd)(k,e), 378(1vd)(k,e), 398(Ovd) (e), 426(1vd)(k,e), 766(Ovd) (k,e), 807 (Od) (k,e), 817 (lb) (k,e), 842(1vd)(k,e), 862(2)(k,e), 878(3)(k,e), This is a piece...
  6. T

    Harmonic Analysis with Ansys APDL: Obtaining Strain and Stress Solutions

    Hi everyone, I have done the Harmonic Analysis of my model with Ansys APDL 17.0 (ACADEMIC version), and I have obtained only the DOF solution of my nodes but i need the Strain and Stress solution . How can I get it? Thanks. Tonino Sepe.
  7. Soumalya

    Statics: Force Analysis of a Pipe Bender Machine

    Homework Statement .The pipe bender consists of two grooved pulleys mounted and free to turn on a fixed frame. The pipe is bent into the shape shown by a force P=300N.Calculate the forces supported by the bearings of the pulleys.[/B] Homework Equations The force equilibrium equations in two...
  8. Z

    A A discord in analysis of a closed vs. open system model

    Is there anywhere in physics textbooks , or anywhere else, a section on KINETICS OF ROTATING FLEXIBLE, CONSTRAINED BODY BY GRAVITY ( TURBINE ROTOR IN BEARINGS), NON-INVARIANT (Time -translation invariance by Noether’s theorem), WITH ECCENTRIC MASSES, TORQUE DRIVEN AT NON-CENTROIDAL AXIS...
  9. Utilite

    I Heine-Borel Theorem shouldn't work for open intervals?

    Okay, I am studying Baby Rudin and I am in a lot of trouble. I want to show that a closed interval [a,b] is compact in R. The book gives a proof for R^n but I am trying a different proof like thing. Since a is in some open set of an infinite open cover, the interval [a,a+r_1) is in that open set...
  10. L

    Force vibration analysis (ansys)

    Hi everyone, i have a question related with ansys. I request to do free vibration and force vibration for my final year project, my project title is optimum baby hammock stand. For free vibration i search from online to get the result by using modal solver (attachment below). For force vibration...
  11. K

    I Complex Analysis Radius of Convergence.

    Hello, I have two questions regarding the Radius of convergence. 1. What should we do at the interval (R-eps, R) 2. It used definition to prove radius of convergence, but I am not sure if it is necessary-sufficient condition of convergence. I get that this can be a sufficient condition but not...
  12. khaledS

    Dimensional Analysis Pendulum Equation

    Homework Statement The period of a simple pendulum, defined as the time necessary for one complete oscillation, is measured in time units and is given by T = 2π ℓ/g where ℓ is the length of the pendulum and g is the acceleration due to gravity, in units of length divided by time squared. Show...
  13. E

    I Bounding the volume distortion of a manifold

    Let $U$ be a compact set in $\mathbb{R}^k$ and let $f:U\to\mathbb{R}^n$ be a $C^1$ bijection. Consider the manifold $M=f(U)$. Its volume distortion is defined as $G=det(DftDf).$ If $n=1$, one can deduce that $G=1+|\nabla f|^2$. What happens for $n>1$? Can one bound from below this $G$? If...
  14. mikeb94

    I Mass Spectrum Analysis: Identifying Mass & Charge

    Hello everyone, I'd like to know how to identify the charge and the mass in a mass spectrum. How do I get the mass corresponding to a peak. I know how they are related p=\frac{m}{z} p_1=\frac{M_r+z_1}{z_1} p_2=\frac{M_r+(z_1-1)}{(z_1-1)} z_1 =\frac{p_2-1}{p_2-p_1} M_r =...
  15. MidgetDwarf

    Apostol Analysis vs Shilov Analysis

    I will be taking analysis in the spring next semester. I am taking intro to proof, java programming, differential equations (did not get transfer credit), and either a probability course or a second semester linear, this semester. I feel I have a good understanding of differential equations at...
  16. K

    I Complex Analysis holomorphic condition

    I understood the holomorphic condition this way. For a vector field F(x1, x2 . . ., xm) = <y1(x1, x2, x3 . . . , xm), y2(x1, x2, x3 . . . , xm), y3(x1, x2, x3 . . . , xm) . . . ,yn(x1, x2, x3 . . . , xm)> In a real analysis, its derivative is expressed as a Jacobian matrix because each...
  17. V

    Engineering Electric Circuits - Superposition and Mesh Analysis

    Homework Statement Exercise 4.15 on the image. The exercise asks for the value of the current I using superposition Homework Equations Superposition theorem, nodal and mesh analysis The Attempt at a Solution I think i am doing the mesh analysis wrong, but can't see where. Can someone...
  18. T

    Automated Air Force Lug Analysis

    Air Force Lug Analysis (section 9 here and summarized here) seems to be the best generalized method for comprehensive lug analysis. However, it relies on charts developed by the USAF in the late sixties. Every source I've found on the method uses those same images. I'm trying to make an...
  19. Jianphys17

    Which Complex Analysis Textbook Should I Use?

    Hi, i need advice, I'm studying complex analysis on which book would you recommend to do it on that of Ahlfors or T.W.Gamelin's book?
  20. M

    Air chemical analysis "homemade"?

    I have a steelworks nearby my home. Is it possible to perform an air analysis in order to know how much the air is polluted? Which instrument do I need ? Are there cheap possibilities? Thanks a lot in advance for your help!
  21. Ma Xie Er

    A Why Is the Equality in This Spectral Analysis Proof Correct?

    I'm reading "Time Series Analysis and Its Applications with R examples", 3rd edition, by Shumway and Stoffer, and I don't really understand a proof. This is not for homework, just my own edification. It goes like this: Σt=1n cos2(2πtj/n) = ¼ ∑t=1n (e2πitj/n - e2πitj/n)2 = ¼∑t=1ne4πtj/n + 1 + 1...
  22. V

    Post Buckling Analysis in ANSYS

    Hello everyone, I am trying to use ANSYS to calculate the reaction force in the edge of a buckled thin plate. (One edge is constrained and the other edge is displaced). According to what I read in the Help Documentation, the study should be done in Static Structural, and a stabilization...
  23. K

    Complete Noise Analysis: to find the minimum detectable signal

    Problem Statement: my aim is to digitalize a 10ns narrow pulse coming from a photo diode with current ranging from 10nA-70mA, as its impossible to cover this dynamic range of >60dB using a single TIA i have an option of separating it to two channels as below using two diodes ofcourse Lowest...
  24. Jianphys17

    Courses Gd of curve and surfaces or functional analysis before?

    Hello everyone, i just finished a course of analysis(2)\vector calculus.Now iI'm interested in doing Gd of curves and surfaces(Do Carmo), and functional analysis(Rudin'sbook), but do not know what may have precedence between the two, on which i should start before you think?
  25. N

    Dimensional Analysis: Subtracting Units & Unitless Numbers

    this question is about dimensional analysis involving a number with units and a number with no units, if the question is already answered in another post please redirect me if not here is a simple example, for example, : say i have 2[in]-1. the 1 is dimensionless and the 2 has units of [in]...
  26. SteliosVas

    Engineering Nodal Analysis of a combo circuit

    Homework Statement Attached is a image of the circuit that I am attempting to analyze:Homework Equations KCL The Attempt at a Solution So I know I should assign a place in the circuit where I should preform KCL after selecting a reference point. I selected the reference point as the 2ohm...
  27. I

    "AC Circuit Analysis - Find i1(t) & i2(t)

    Homework Statement Find the currents through ##R_3, i_1(t)## and ##R_2, i_2(t)##. I attached a diagram of the circuit (diagram.pdf). In the original diagram the currents I'm trying to find is marked going top to bottom, there's also no directions on the voltages in the original diagram but...
  28. goonking

    Exploring the Role of Batteries in Nodal Analysis

    Homework Statement Homework EquationsThe Attempt at a Solution If I take KCL at node V1 (I'm assuming current traveling from nodeV2 to node V1) Current in = Current out V2 - 2volts / 2 ohms = V1 / 8 ohms so my question is, how does the battery (2 volts in this case) play a role in nodal...
  29. P

    Help with a calcululs analysis problem

    Hello, I need to do a complete analysis using calculus and algebraic methods for these problems ƒ(x) = −x2 + 4x − 3 g(x) = x3 − 6x2 + 9x h(x) = x4 − 6x2 p(x) = x4 − 4x3 finding intercepts, critical points, intervals of increase and decrease, points of inflection, intervals of concavity...
  30. C

    Courses Taking Automata Theory and Analysis of Algorithms together?

    So I'm at a bit of a cross roads. For this summer semester, due to class restrictions I can only take either operating systems with Automata Theory, or Analysis of Algorithms with Automata Theory. I've heard from many people that Algorithms is a nightmare, and I'm not sure if taking Automata...
  31. B

    A Deutsch–Jozsa algorithm/Circuit Analysis

    I'm having a hard time following the analysis of the basic quantum circuit that illustrates Deutsch's Algorithm - essentially I'm not following the algebraic manipulations there making on the two input quantum bits (simple case). One analysis is given at the bottom of the page of the link I...
  32. P

    How Do You Evaluate sin(x)/x^4 Over the Unit Circle Using Complex Analysis?

    Homework Statement evaluate sinx/x^4 over the unit circle Homework Equations Cauchys Residue theorem ##sinz=1/(2i)(z+1/z)## The Attempt at a Solution So we have a branch point at z=0 but its of order 4 so I can't see any direct way of using Cauchys residue theorem. I've tried changing the...
  33. SU403RUNFAST

    Sketching a periodic function and Fourier analysis

    Homework Statement So i have a function f(x)=x^2 that is periodic -a<x<a and need to sketch this function from -3a<x<a. I know how to find the Fourier coefficients though. Homework Equations f(x)=x^2 sketch it periodically The Attempt at a Solution I know that a function is only periodic...
  34. E

    Dimensional Analysis:Relating Particle Diam, Viscosity, & Weight

    Homework Statement It is found the terminal velocity ut of a spherical particle in a fluid depends upon the diameter d of particle, the dynamic viscosity μ of fluid and the buoyancy weight W of the particle [given by the difference in density between the particle and the fluid (∆ρ) ×...
  35. Jianphys17

    I Lebesgue measure and Fourier theory

    Hi everyone, in this days i was seeing a little of Fourier series and transform, and i wondered if it was necessary to better understand before the measure and Lebesgue integral before studying it. Or it's not necessary?
  36. Titan97

    B RLC Circuit Analysis: Phase Difference & Impedance Modulus

    In an RLC series circuit let applied EMF be given ##V=V_0\sin\omega t##, $$Z=Z_C+Z_R+Z_L=R+i\left(\frac{1}{\omega C}-\omega L\right)$$ $$|Z|=\sqrt{R^2+\left(\frac{1}{\omega C}-\omega L\right)^2}$$ Then $$i(t)=\frac{V(t)}{Z}=\frac{V_0e^{i\omega t}}{R+i\left(\frac{1}{\omega C}-\omega L\right)}$$...
  37. micromass

    Insights How to Self-study Analysis. Part Ii: Intermediate Analysis - Comments

    micromass submitted a new PF Insights post How to self-study analysis. Part II: intermediate analysis Continue reading the Original PF Insights Post.
  38. SmritiB

    Resistive network point to point analysis

    In a complex resistive mesh (grid), 2 points are chosen for applying a voltage source. Now there are many paths the current can take from A to B. And there is an equivalent resistance computed as well. But how to calculate the least resistive path? I.e. The path along which when traversed, the...
  39. P

    Analysis method to describe impact of variables on parameter

    Hi, I have an optical model, fully programmably controllable with python. I want to know how much my variables (say N) of my model impact a certain parameter (i.e power, abberations). Now I have no clue how to go about this. There must be some analytical (numerical) method that I could use but...
  40. D

    Finding unknown values in DC resistor network via matrices

    Homework Statement I need to get 7 equations to make a 7x7 matrix in order to solve it. I have 4 of them, but I'm not sure how to get the voltages equations. Homework EquationsThe Attempt at a Solution I have got four equations so far. One is simply using KCL, I1 = I2 + I3 + I4. The other...
  41. happytolearn

    Transient thermal analysis in ANSYS

    I want to do a transient thermal analysis in butt welded joint.The heat flow I have given 3200 watt(Q = efficiency x current x voltage = 0.8 x 160 amp x 25 volt)to the welding zone, given 20 load step(as welding is completed in 20 sec),convection co-efficient = 11.14, emissivity = .4 and applied...
  42. RJLiberator

    Fourier Analysis for |x| and Proving a Series Convergence

    Homework Statement Consider a 2pi-periodic function f(x) = |x| for -pi ≤ x ≤ pi a) Compute the Fourier series of the function f. b) Prove that (from n=1 to n=infinity)∑ 1/(2k-1)^2 = pi^2/8.**note all "sums" from here on out will be defined from n = 1 to n=infinity Homework EquationsThe Attempt...
  43. S

    Kirchoff's method for a weird circuit

    Homework Statement In the following circuit, the battery has emf ε = 12.7 V. The resistors are R1 = 2000 Ω . R2 = 3000 Ω, and R3 = 4000 Ω. What is the current through resistor R2 ? Homework Equations Kirchoff's Rules V=IR The Attempt at a Solution i0 (into A) - i2 (current into resistor 2) -...
  44. M

    How to do failure analysis of gas turbine blade ?

    I want do thermal and structural analysis (Failure) on gas turbine blade. So what how to begin. Kindly help me.
  45. Y

    Engineering Linear Algebra - Analysis of purely resistive DC circuit

    Homework Statement I'm trying to solve this circuit when I try to simulate and run a dc sweep i get that it can't be solved. When I try to find the answer using linear algebra I get this answer after I throw it into MATLAB with the warning “[w]arning: Matrix is close to singular or...
  46. A

    What is the total variation of sin(x) on [a,b]?

    Homework Statement For a given function ##g:[a,b]→ℝ, 0 < a < b##, compute its total variation \underset{[a,b]}{\mathrm{Var}} (g) where ##g(x) = \sin(x), x\in[a,b].## Homework EquationsThe Attempt at a Solution I know that between odd multiples of ##\frac{\pi}{2}##, ##\sin(x)## is monotone, so...
  47. A

    Managing X-Ray Hardness and Low Frequency Use in Tissue Analysis

    I got question in exam, 1) How to control hardness of X-ray? 2) why low frequency of x-ray is used for investigating tissue?? so in 1) what does controlling hardness means?? and in 2) can't we use high frequency of X-ray ?so that it will penetrate more as tissue are poor absorber...
  48. P

    Complex Analysis: Contour Integration Question

    Homework Statement State, with justification, if the Fundamental Theorem of Contour Integration can be applied to the following integrals. Evaluate both integrals. \begin{eqnarray*} (i) \hspace{0.2cm} \int_\gamma \frac{1}{z} dz \\ (ii) \hspace{0.2cm} \int_\gamma \overline{z} dz \\...
  49. O

    Analysis of Atomic Absorption Spectroscopy results

    Homework Statement Hello, This week I ran an AA Spectroscopy experiment in my university, in which we had to analyze the percentage of Copper in a metal coin, and the containment of Iron in morning cereal. We used 2 standard solutions of 1 and 10 ppm (containing both Copper and Iron), and...
  50. B

    MHB Solve for a,b,c,d Solve \frac{f(-1)+f(1)}{2}=f(0) for a, b, c, d

    For a cubic function y=f(x) three points A, B and C lie on a straight line with respective coordinates (-p,f(p)),(0,f(0)) and (p,f(p)) where p is a non zero constant. a. Show that \frac{f(-p)+f(p)}{2} =f(0) I tried \frac{f(-p)+f(p)}{2} =\frac{0}{2} = 0 = f(0) That doesn't seem right b...
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