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. Rahul Shenoy

    Parameter sensitivity analysis for nonlinear system

    I am working on a problem, where I have arrived at the following nonlinear state space equation: dx1/dt = x2; dx2/dt = c11 x1 + c21x2 + c31x3 + c41x4 + c51x1x22; dx3/dt = x4; dx4/dt = c12 x1 + c22x2 + c32x3 + c42x4 + c52x1x22; c11, c21, c31, c41, c51, c12, c22, c32, c42, c52 are all a function...
  2. FallenApple

    I Does analysis form a bridge to geometry?

    So I always thought that geometry is somewhat different from the rest of math. I mean, most of math is about numbers and relations. While geometry is about space. Does analysis connect the two? For example, the hypotenuse of a triangle is just a truncated portion of the number line that has...
  3. TheBigDig

    Calculating Node Voltage using Nodal Analysis

    1. Homework Statement The circuit is driven by a voltage source, Vs(t)= 8.2 cos(1.8 t − 0.25 )V . The circuit elements are given as follows. G1= 5 S,G2= 7.6 S,G3=3.8 S (Gi is the conductance of corresponding resistor Ri) L1= 20 H,C1= 5×10−2 F If we select Node 4 as the reference node...
  4. Cocoleia

    Mesh analysis with dependent sources

    Homework Statement I need to use mesh analysis to find the three currents: Homework EquationsThe Attempt at a Solution The answers are I1= -1.25A, I2=0.125A and I3 = 1.125A I don't know where I messed up for I3
  5. F

    Load line analysis in femm4.2

    Dear Forumers, This question is about load-line analysis for loudspeaker driver magnetic circuits in FEMM 4.2 (Finite Element Method for Magnetics), I can't seem to get an answer from the mailing lists. I would like to get the permeance coefficient for random points inside the magnet. I have...
  6. A

    Force Analysis of a compressed spring

    Hi all, I am quite confused by the forces relating to a horizontlly placed spring when someone directly exerts a force to the compress it. If I exert a force F to the right to compress the spring, which, say, is placed against a wall, the spring exerts an elastic force on me but I don't see how...
  7. V

    A Relativity in Complex Analysis: Is There a Formulation?

    Is there a formulation of any of the relativity theories in terms of complex analysis? As in - I imagine - every event would be a complex number in a complex field.. or something as such..
  8. adamaero

    Engineering Analog electronics (BJT circuit analysis)

    Homework Statement For beta = 100 and assuming ro is very large, what is the DC voltage at the collector? Homework Equations IB = IE(β+1) IC = β*IB The Attempt at a Solution Since IE = 0.5mA, IB = 0.0505 A Then, IC = 5.05 A (which doesn't feel right) VC is the same potential across the 30kΩ...
  9. A

    Engineering ECG Circuit Analysis: Calculating Contribution of Eint to Vout

    What is the contribution of Eint to the output voltage Vout? Homework EquationsThe Attempt at a Solution To calculate the contribution of Eint, I removed the other two voltage sources. Then, I divided them into three potential dividers, giving me: Vbody= (ZC2/ZC2+ZC1) x Eint...
  10. D

    How to solve a nodal analysis homework question?

    Homework Statement This particular question has been raised in past posts and I have studied those posts but unable to take anything from them. Basically the question comprises 2 parts. Part A requires us to find the current through "I" using mesh analysis. By studying some of the posts on...
  11. J

    I Can the Complex Integral Problem Be Solved Using Residue Theorem?

    I have this problem with a complex integral and I'm having a lot of difficulty solving it: Show that for R and U both greater than 2a, \exists C > 0, independent of R,U,k and a, such that $$\int_{L_{-R,U}\cup L_{R,U}} \lvert f(z)\rvert\,\lvert dz\rvert \leqslant \frac{C}{kR}.$$ Where a > 0, k...
  12. J

    I Problem with this estimation lemma example

    I have been trying to show that $$\lim_{U\rightarrow\infty}\int_C \frac{ze^{ikz}}{z^2+a^2}dz = 0 $$ Where $$R>2a$$ and $$k>0$$ And C is the curve, defined by $$C = {x+iU | -R\le x\le R}$$ I have tried by using the fact that $$|\int_C \frac{ze^{ikz}}{z^2+a^2}dz| \le\int_C...
  13. Mohamed_Wael

    Large deformation in modal analysis

    Hi all, I have been simulating the following rhombus compliant mechanism using Ansys Modal analysis to have a quick understanding about its mode shapes,,,, the problem is that the deformation is extremely large you can see this as the scale is (*10^-5 ) . This result is for sure unrealistic but...
  14. Josep

    Courses Should I retake Real Analysis I?

    Hi all, I am currently in my first semester of my sophomore year, taking Real Analysis I. This class covers formal proofs, properties of the real line, sequences, series, limits, continuity and differentiation, and Riemann Integration. I apparently got stuck with the worst professor at my...
  15. F

    What hardware is needed for analyzing sound signals?

    Hello everyone, I am interested in analyzing sounds (both spectral plots and time plot). What type of hardware would I need? There are a lot of free softwares online... Are there educational hardware tools that are not too expensive? thanks!
  16. iCloud

    A Regression analysis and Time Series decomposition

    If we can use Regression analysis to forecast, why do we use “Time Series Decomposition”? What's the difference between the 2? Thanks
  17. E

    Engineering OpAmp Circuit Analysis: Finding the Differential Equation for Vo

    Homework Statement Find the differential equation for Vo Homework Equations KCL The Attempt at a Solution At node v1: ##\frac{V_1-V_{in}}{R_1}+\frac{V_1-V_p}{R_2}+C_2(\dot{V_1}-\dot{V_2})=0## At node vp: ##C_1\dot{V_P}+\frac{V_P-V_1}{R_2}=0## At node vn...
  18. Z

    I Proof check: S in C Compact implies S is closed and bounded

    I am using Lang's book on complex analysis, i am trying to reprove theorem 4.1 which is a simple theorem: Let Compact(S \in \mathbb{C}) \iff Closed(S) \land Bounded(S) I will show my attempt on one direction of the proof only, before even trying the other direction. Assume S is compact Idea...
  19. R

    What are the options for boundary conditions in ANSYS WB structural analysis?

    I am trying to perform a simple simulation in ANSYS WB Mechanical. Description is given below in image, thickness of the plate is 5 mm. Problem is I am unable to decide which type of support should I provide for this.
  20. binbagsss

    Complex analysis f'/f , f meromorphic, Laurent series

    Homework Statement consider ##f## a meromorphic function with a finite pole at ##z=a## of order ##m##. Thus ##f(z)## has a laurent expansion: ##f(z)=\sum\limits_{n=-m}^{\infty} a_{n} (z-a)^{n} ## I want to show that ##f'(z)'/f(z)= \frac{m}{z-a} + holomorphic function ## And so where a...
  21. D

    Fatigue analysis in the frequency domain

    Assuming that a TLP platform is examined and the wave forces acting on the tendons of the mooring lines are presented in RAOs (as a function of wave frequency). Using Jonswap spectra for North sea (i.e peakness factor equal to 3.3) we can obtain Hs (significant wave height); Tp (peak period) and...
  22. W

    Help needed -- Analysis of torque and force on turning vehicles

    Homework Statement Homework Equations Torque and Newton's 2nd Law Equations The Attempt at a Solution Apart from drawing a free-body diagram, I couldn't do much else. I can't seem to find the source of torque causing the car to rotate clockwise about its pivot (i defined it as the right...
  23. B

    B Unruh & Hawkins Radiation: A Comparative Analysis

    Are Unruh radiation and Hawkins radiation manifestations of the same basic phenomenon?
  24. B

    Thevenin reduction of network for fault analysis trouble.

    Homework Statement Reduction from top network to bottom network in the screen shot. I can not find the steps that have been taken to do this. Fault impedance = Zfa = Zfb = Zfc = j0.5 Homework EquationsThe Attempt at a Solution in hand written screenshot, sorry for the mess, just to show it...
  25. Minoui11

    Flowmetry Analysis (relating height to flow rate)

    Hello! 1. Homework Statement I need to find the instantaneous height of a liquid during the simultaneous filling and emptying (through a hole) of a cylinder. I have varying Qin at incremental time of 1 sec. with cylinder area=5 cm and orifice area=0.5 cm. Homework Equations Torricelli's...
  26. E

    How to do Mesh Analysis with current controlled voltage source

    Homework Statement Vs = 100cos(2000t) Homework Equations KVL, KCL The Attempt at a Solution My mesh equations are: -Vs + I1(30-12.5j)-I2(120j)=0 4Ix+I2(120j+20)-I1(120j)=0 Ix = (I1-I2) Are these correct? When I solve I get a different result than when I do nodal analysis.
  27. goonking

    Dimensional Analysis: Reference Dimensions & Repeating Variables

    lets say for example, the air drag (ϑ) that wind exerts on a tile is a function of the tile's width (w), height (h), viscosity of air (μ), density of air (ρ) and velocity of the air (V) then ϑ = f(w,h, μ, ρ, V) ϑ : MLT-2 w: L h: L μ : ML-1T-1 ρ: ML-3 V: LT-1 I understand there are 3 basic...
  28. Alvis

    I Complex Analysis Harmonic functions

    Suppose u(x,y) and v(x,y) are harmonic on G and c is an element of R. Prove u(x,y) + cv(x,y) is also harmonic. I tried using the Laplace Equation of Uxx+Uyy=0 I have: du/dx=Ux d^2u/dx^2=Uxx du/dy=Uy d^2u/dy^2=Uyy dv/dx=cVx d^2v/dx^2=cVxx dv/dy=cVy d^2v/dy^2=cVyy I'm not really sure how to...
  29. K

    Time History Fatigue Analysis - Ansys Static Structural Quer

    I'm testing a part for fatigue, and I got a time series of Forces and Moments on three different parts of the body (A wind turbine hub). From the static structural fatigue analysis, I noticed that you need a von mises stress input - that's not a problem. My problem is, how do I place different...
  30. gmm

    Engineering Circuit Analysis with Laplace Transforms

    Homework Statement Homework Equations V=IR All of them actually The Attempt at a Solution So I Started off by transforming the voltage source into the 's' domain vs(s) = (4/s) -(4/s)*e-.5t I know the initial conditions are zero, in other words at t=0, the voltage and currents at the...
  31. E

    Fault analysis -- Simplifying to Thevenin equivalent

    Homework Statement [/B] All voltages and impedances are in per unit values. After all the source transformations, why is the voltage source still 1 ? Homework EquationsThe Attempt at a Solution [/B]
  32. E

    BJT Analysis Question: Solving for Vb with Voltage Divider Method

    Homework Statement Homework Equations KVL The Attempt at a Solution This is the solution given: VB = (VCC*30k)/(70k+30k) = 3V Why is a voltage divider being used to find Vb?
  33. I

    I Sampling and analysis of variance

    Dear forumers, In advance, thank you for reading this post and helping me solving this. The problem is the following : I have a population (say, a bag) from which i take 3 samples. Each sample gets analysed once by a laboratory in order to know their concentration of a product. The result...
  34. K

    Variable Amplitude Fatigue Analysis - Super Confused on how

    Hey everyone I'd be really grateful if anyone could help me out here, been going round in circles for two weeks now and I need to get going soon. Jumping right to the point, here's my problem: We are currently working on a student project and designing a Wind Turbine for future opensource use...
  35. I

    Dynamic Analysis of a 5 DoF robot

    Homework Statement Homework Equations N/A The Attempt at a Solution I am confused as to where the ω3sin(θ)k term disappeared to? It is not included in the very last line? I asked my lecturer and he said it's ''constant'' but he kind of shrugged off the question. I understand everything...
  36. A

    Calculators Software to do latent semantic analysis

    I have a document-word matrix and I need to do latent semantic analysis to match a query document with a set of key-words to the best possible match among other documents in the matrix. The matrix is in the form of documents-words occurrence array of 1 and 0 input. What is the best software I...
  37. E

    Mesh analysis with dependent voltage source

    Homework Statement Find the: -Complex power delivered by source -Power factor of total load -Is the power factor leading, lagging, or in unity?[/B] Homework Equations KVL/KCL The Attempt at a Solution I want to solve this via mesh analysis to get currents. Mesh1: -10V + V1 + 0.75V1 = 0 V1 =...
  38. E

    Mesh Analysis w/ Supermesh and "different" current direction

    Homework Statement Find power absorbed by resistor, capacitor and inductor. Find the total complex power absorbed by all the loads.[/B] Homework Equations KVL/KCL The Attempt at a Solution I want to solve this using Mesh analysis. There is a supermesh where the 5A source is, so I start it...
  39. S

    B Modal Analysis & Mode Shapes: Real-World Applications

    What is modal analysis and what are mode shapes. Plz explain along with a real life problem for better understanding
  40. S

    A Casimir effect and dimensional analysis

    How can you use dimensional analysis to estimate the force between two plates, as a function of the area of the plates and their separation?
  41. E

    Circuit Analysis of IR transmitter/receiver

    Hi everyone, I am a complete beginner when it comes to circuit analysis that involves anything more than a few resistors and capacitors. Currently, I am working on a project that requires the transmission and reception of IR signals to control a motor. I know the requirements for the motor I...
  42. Captain1024

    SEPIC Converter Analysis: CCM Operation with VL1, VL2, IC1, and IC2 Expressions

    Homework Statement Find expressions for VL1, VL2, IC1, IC2 for each of the two intervals of a SEPIC converter under CCM operation. link: http://i.imgur.com/EY98QbC.png Homework EquationsThe Attempt at a Solution link: http://i.imgur.com/SskXRoC.jpg?1
  43. lep11

    MATLAB Data Analysis: Observation Model Problem

    The observation model will be ##z=H\theta+v##, where ##z## is column vector containing the results, ##H## is the observation matrix, ##\theta## is the parameter vector and ##v## is a vector containing random additive noise. b.) In this case ##z##=[1 1 0; 1 0 1; 0 1 1; 1 1 1]*[##m_1## ##m_2##...
  44. Saph

    Studying How to study from a Real Analysis textbook like this

    Hello, I am taking a class in RA, where we're using Bartle/Sherbert. Since I have studied few chapters from it in the summer before, I decided to take a look at a more rigorous book, like baby rudin, but since many have advised against that book, I turned to Pugh's real mathematical analysis...
  45. sammyqw

    Discovering Vc(0) using Nodal Analysis - Check out my Solution!

    Homework Statement Find Vc(0) Homework Equations Nodal analysis The Attempt at a Solution
  46. Planobilly

    What Are the Implications of Changing Component Values in a Tube Amp Circuit?

    Hi Guys, The schematic What do you think the effect of changing the value of the output tube cathode capacitor from 50uf to 250uf would be? Also the original schematic showed 500K pots and other newer schematics show 1M pots. What do you think the effect of that change would be? Next...
  47. geeth sankalpa

    Can complicated models with web openings be accurately analyzed with a 5x5 mesh?

    I am using Abacus 6.13 for development of FEM for test setup on shear capacity of cold formed steel section. it has some complicated interactions with those interaction only solid section model gives answers.but with web openings on section it has convergence problems. i tried with different...
  48. E

    Solving for Vo: Nodal Analysis Approach

    Homework Statement Determine the output voltage Vo(t) in terms of Vs Homework EquationsThe Attempt at a Solution If I were to use Nodal Analysis to solve this, would these be the proper nodal equations?\frac{V1}{-j1.6} + \frac{V1-Vs}{175} = 0 \frac{V_{I2}-Vo}{10k} + \frac{V_{I2}}{1k} = 0
  49. E

    Solving a Nodal Analysis: Find Va(t)

    Homework Statement Find Va(t) using Nodal Analysis: Homework Equations Zc = 1/(jwC) Zl = jw*L The Attempt at a Solution W = 250 Z36mH = j9 ohm Z80mH = j20 ohm Z0.25mF = -j16 ohm (is capacitor impedance always negative? It says so in my instructor's notes but I forgot why) 20cos(250t) ->...
  50. R

    Carbon dioxide in water, analysis of dissolved species HPLC?

    Does anyone here have any analytical experience with dissolved gas, particularly CO2? When CO2 is dissolved in water there can be several reactions: What I would ideally like to do is dissolve CO2 into water and then by some means of analysis, see how much of each species there is in the...
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