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. 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
  2. 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) ->...
  3. 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...
  4. benarceneaux

    Proving n^2 + 3n^3 is Θ(n^3) for n >= 0

    First off I'm studying for an exam tomorrow, this isn't homework. Also, I've already written the proof and verified I've gotten the correct answer. I'm here to ask some questions about the solution that I am not completely confident I understand. Here's the problem: Prove that n2 + 3n2 is Θ(n3)...
  5. E

    Mesh Analysis: Converting from Time to Frequency Domain with Correct Equations

    Homework Statement [/B] 1. Convert from time to freq domain 2. Use mesh analysis to find I1, I2, I3 3. Find Ve and convert it to time domain Homework Equations KVL V=IR The Attempt at a Solution Are these mesh equations correct? 45cos(500t) -> 45V 80mH -> 40j 50mH -> 25j 25uF -> -80j 12.5uF...
  6. E

    Find Node A and B Voltage with Mesh Analysis

    Homework Statement Use Mesh analysis to find voltage of Node A and B Homework Equations V=IR KVL The Attempt at a Solution Are my mesh equations correct? Mesh1: -j30V + (-j50 + 10)I1 - 10I2 = 0 Mesh2: (10-j20)I2 - 10I1 - j50V - I3(-j20) = 0 Mesh3: (-j20+30+j10)I3 - (-j20)I2 = 0
  7. E

    Nodal Analysis Help: Solving System of Equations

    Homework Statement Attempted Solution: For my two nodal equations, I got: 40j + 20 - 12Va*j + 2Vb *j +4Va - 4Vb = 0 and 2Vb - 2Va - 6Vb*j - 4Va*j-10-20j Are these right? How do I solve this system of equations?
  8. V

    Contact analysis in Flexible gear

    Hi everybody, I'm working on an analysis model of flexible gear in ANSYS workbench. This model has 3 components: flexible gear(FG), wave generator(WG) and rigid gear(RG) Applied force have two case: WG makes FG deforming from circular shape to ellipse shape, the FG contacts and engages to RG...
  9. whatphysics

    Engineering Solving Circuit Analysis Problem: Finding R and V(t) for Given Conditions

    There is a question I am not sure of how I should start/approach. Any help would be appreciated, thanks. Vc(0)=3V and ic(t)=e^-50t for t>0 and t=0. Find the value of R and voltage v(t) for t>0 and t=0
  10. O

    Sample preparation of powders for trace metal analysis

    When preparing a fine powder for trace metal analysis, is ashing prior to digesting unnecessary? If not, or not necessarily, where could I learn more about important considerations to determine whether of not any preparation prior to digestion is required? The one instance I have come across...
  11. caffeinemachine

    MHB Stein-Shakarchi 'Complex Analysis' Chapter 3 Exercise 15 b.

    I am stuck on a problem given in Stein and Shakarchi's Complex Analysis. (Chapter 3, Exercise 15b) Use the maximum modulus principle or Cauchy inequalities to solve the following: Let $f$ be a bounded holomorphic function on the open unit disc, and suppose that $f$ converges uniformly to $0$ in...
  12. G

    Significant Figures & Error Analysis

    Hi, I've just had my first lab in physics and I'm having a bit of trouble understanding how to determine the significant figures of my final answers and transforming them in scientific notation. For example: Homework Statement [/B] I had to measure three sides of a parallelepiped with a...
  13. D

    Modal and Harmonic Analysis of composite

    Can someone help me with the procedures for Modal Analysis and Harmonic Analysis of Composites using ANSYS APDL?
  14. Z

    Engineering Find the Thevenin Equivalent Circuit

    Homework Statement Homework Equations Node Voltage Method V=IR The Attempt at a Solution KCL at Node 1: KCL at Node 2: i is the current moving towards "a" I've simplified the two equations down but the problem I run into is that normally I'm able to write a third equation to define i0...
  15. Biker

    B Dimensional analysis and units

    Hello, I have been doing high school physics for about 3 years now and I am perfectly fine with it. However, Something tricked me off few days ago. It is how we treat units. I was kind of hesitant to post this thread because I have seen multiple threads about it before and some member really...
  16. K

    What Is the Ideal Resistor Value for a Diode Circuit Using Load-Line Analysis?

    Homework Statement Determining the best resistance for my simple circuit consisting of a diode, battery, and resistor. Doing this using Load- Line Analysis Homework Equations ID = VD - V / R - Given by KVL[/B] (I can disregard n-pretend ) The Attempt at a Solution [/B] Here I have...
  17. H

    Calculating Entrained Flow in Injector Design: Challenges and Considerations

    Hello, I am trying to analyze an injector and having trouble coming up with the final equation for the calculation. The apparatus can be seen below. Assuming we know the inlet flow rate and pressure (A) from the pump/fan and the pipe geometry. The pressure out of the outlet of the nozzle is...
  18. jaskamiin

    Analysis Have a math degree, need to refamiliarize with advanced math

    I've been out of school for a while and working as a programmer. I want to start taking some masters courses for applied math (PDEs, numerical analysis, etc) and need to become familiar again with the advanced math I used to use in undergrad. I took two semesters of real analysis as an...
  19. RoboNerd

    Question on graphing potential

    Homework Statement Homework Equations I know that potential from a point charge equals kq/r and that potential difference equals - (integral of)(E dot dl) The Attempt at a SolutionI tried to approach this problem using the point charge approach by comparing the relative values of kq/r for...
  20. N

    Mesh and nodal analysis don't quite match, but why?

    Homework Statement [/B] Find I by mesh and nodal analysis Homework EquationsThe Attempt at a Solution ##V_{10}## is defined at the junction of ##Z_1##, ##Z_2## and ##Z_4##. ##V_{20}## is defined at the junction of ##Z_2##, ##Z_3## and ##Z_5##. ##0V## is defined at the junction of ##V_1##...
  21. RoboNerd

    Question on lightbulb brightness in circuit analysis

    Homework Statement Homework Equations I know that power of a lightbulb/resister is I^2 * R The Attempt at a Solution OK. Here's my attempt: Let's consider the situation where we do not close the lightbulb and assume that the wires and switch are ideal because they have no resistance. I...
  22. Marcin H

    Loop Current Method/Loop Analysis Confusion

    Homework Statement Homework Equations Loob Analysis V=IR The Attempt at a Solution So I think I have the right equation here, but I am a bit confused on some parts. I am not too sure why i2=i1-ix. The way my professor explains it doesn't make much sense. Also (TYPO) in the second...
  23. I

    A What are the bounds of a ratio with a given set of numbers and variables?

    Sorry in advance if I've posted in the wrong section. given the set ##\{r_i, r_{ii}, r_{iii}, ... , r_R\}## where ##r \ \epsilon \ \mathbb{Z}_+ \ , \ r_i \geq r_{i+1}##How would you go about finding the bounds of something like this, or determining if it even has any? ##( \...
  24. F

    Space vector analysis of 3 phase -- stuck on a concept

    I am trying to understand space vectors in 3 phase machines. If you have a balanced 3 phase system, the 3 phasors of voltage, current or whatever... should sum to 0. i<0 + i<-120 + i<-240 = 0. But in this image of a rotating space vector ...
  25. Svein

    Insights An Analysis of Road Capacity - Comments

    Svein submitted a new PF Insights post An Analysis of Road Capacity Continue reading the Original PF Insights Post.
  26. thegreengineer

    BJT transistor analysis: common emitter confusion

    Recently I started studying semiconductors and analogue electronics. First I studied the diode and its I-V characteristics and analysis in DC circuits, as well as in AC circuits. Now I started with BJT transistors. I was explained that transistors act as electronic switches. My problem is not...
  27. Destroxia

    Complex Analysis - Exponential Form

    Homework Statement Write the given numbers in the polar form ##re^{i\theta}##. ## \frac {2i} {(3e^{4+i})} ## Homework Equations ## z = re^(i\theta) ## ## \theta = Arg(z) ## ## r = |z| = \sqrt { x^2 + y^2 } ## The Attempt at a Solution I'm not really sure how to go about the exponential...
  28. L

    A Why Can't the Continuum Hypothesis Be Decided Using Standard Real Number Models?

    I know that there are several models of the real numbers, some where the Continuum Hypothesis holds, others where it does not. I would like to understand why the usual definition of the reals, limits of Cauchy sequences of rational numbers under the usual absolute value norm, isn't one of these...
  29. N

    A Data Analysis: consistency of e.g. two measurements

    How do we check consistency of measured data, e.g. x1 = 1 ± 0.1 x2 = 1.4 ± 0.3 I can do this for two different samples to check for significance in terms of different means, but how to check internal consistency of a single set. How can we do this using: a) standard normal probability table...
  30. Simon T

    MHB What will the profit be if 1500 units are sold next year?

    the first year of operation for a small company yielded a loss of \$5000. The company has \$15,000 per year tied up in fixed costs and spent 40,000 on raw materials and labour. Since the company was not well known, they were only able to sell 500 units of their product that year. It is hoped...
  31. gmDevi

    Job Skills Career in finance/data analysis?

    Hi guys! I have a B.Sc. in physics in Italy and I'm about to choose my Master of science. I realized, while working on My B.Sc., that I don't really want to work in a lab, so I'm looking for other possibilities other than the usual theoretical/condensed matter/medical physics. A University in...
  32. B

    Analysis Readability of Rudin's Real and Complex Analysis

    So I decide to self-study the real analysis (measure theory, Banach space, etc.). Surprisingly, I found that Rudin-RCA is quite readable; it is less terse than his PMA. Although the required text for my introductory analysis course was PMA, I mostly studied from Hairer/Wanner's Analysis by Its...
  33. Diego Berdeja

    I Lorentz Transformations in the context of tensor analysis

    Hello everyone, There is something that has been bugging me for a long time about the meaning of Lorentz Transformations when looked at in the context of tensor analysis. I will try to be as clear as possible while at the same time remaining faithful to the train of thought that brought me...
  34. ibkev

    B Tensor Calculus vs Tensor Analysis?

    I've seen the terms tensor calculus and tensor analysis both being used - what is the difference?
  35. W

    Rayleigh method Dimensional Analysis

    Homework Statement ii)Rayleigh method gives me inverse of expected result.Would really appreciate your help. Homework Equations show that ##f(gamma)##=##(\frac {ro*R^5} {E*t^2})## where ro=density R=radius E=energy The Attempt at a Solution We will do dimensional analysis on the elements...
  36. MidgetDwarf

    Courses Good Books for Numerical Analysis & Mathematica for Learning

    I am currently working through Spivak, and have finished Geometry by Moise. I wanted to learn numerical analysis on my own. I could take it at the university, but I rather use the elective for differential geometry. What are good books on Numerical Analysis? I have completed 2 books in Linear...
  37. ESMAT 1995

    Lumped system analysis in transient heat conduction

    Homework Statement so, i had this question where i had a sphere and a cylinder with given dimensions and propreties ( roh, C and k) he also gave me initial temperatures, then both of them dipped in a bath of water of given temperature but unknown h ( convective coefficient) then he gave me the...
  38. B

    Analysis Seeking books that cover my upcoming math course

    Hello! I am currently searching for some alternative books I can use for the analysis course starting on this Fall Semester. The course will cover the compactness, contraction principles, approximation theory, and some applications like special functions and Fourier series. The required...
  39. M

    I Dimensional Analysis: Torque, Moment of Inertia & Angular Acceleration

    Hi The relation between torque, moment of inertia and angular acceleration is: T=Ia Have a look to it's units: (N.m)=(kg.m^2).(Rad/s^2) >>>> N=kg.m.Rad/s^2 Please explain the equation Dimensionally. How (kg.m.Rad/s^2) is equal to N? Thanks.
  40. G

    Engineering AC circuit with a switch -- analysis

    Homework Statement Given the circuit of sinusoidal current (attachment1) 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 of...
  41. S

    Torque and RPM Analysis: Understanding Power Transmission with Pulleys

    Please I need some help. I'm thinking that if I have a driving shaft with a torque of 10Nm and an RPM of 1000. If I add two 3 inches pulley on the shaft to transmit power to another shaft with a pair 6 inches pulley mounted on it and connected to the initial 3 inches via a belt. Will I have...
  42. B

    Analysis Supplements to Complex Analysis of Rudin-RCA?

    Dear Physics Forum friends, I will be doing a reading course in the complex analysis starting on this Fall Semester. The assigned book is Rudin's Real and Complex Analysis. From my understanding, Rudin treats complex analysis very elegantly, but very terse. I am curious if you could suggest...
  43. P

    How Is the Complex Integral Evaluated Using Contour Integration and Residues?

    Homework Statement calculate ## \int_{-\infty}^{\infty}{\frac{2}{1+x^2} e^{-ikx}dx}##, where k is any positive number Homework EquationsThe Attempt at a Solution So first consider the closed contour ##I= \int{\frac{2}{1+z^2} e^{-ikz}dx}## We can choose the contour to be along the real axis ##...
  44. M

    Small signal analysis of a cascode amplifier

    Hello there. I am stuck trying to figure out the voltage gain of a cascode amplifier from a small signal analysis. The circuit seems to be under-determined for reasons I do not understand or maybe I am missing the perfectly obvious. Here's my small signal model: The only relation I can...
  45. B

    Analysis Leonard Euler's Books in Analysis and Algebra

    Dear Physics Forums friends, I am an aspiring mathematician who is deeply interested in the analysis, topology, and their applications to the microbiology. Recently, I started to become very curious about why concepts and theorems in the real analysis and topics come as they are; the...
  46. K

    I Complex Analysis, holomorphic in circle.

    Hi, I have a question regarding corollary 2.3. in the uploaded image. it looks very trivial to me becauese Cauchy's theorem states "if f(z) is holomorphic, its closed loop integral will be always 0". Is this what the author is trying to say? what's the necesseity of the larger disk D' at here...
  47. J

    Geometry is important for vector analysis?

    Hello from Italy I'm switching from CS to Physics BS because i personally find it more various and interesting (and in Rome there is one of the best physics school in the world). Mathematical analysis is a common subject and my credits will be recognised but i didn't study Linear algebra yet...
  48. chwala

    Is the sum of a rational number and an irrational number always irrational?

    Homework Statement show that if ##x## is rational and ##y## is irrational, then ## x+y## is irrational. Assume that ##x## is irrational and that ##y## is also irrational. Is ##xy## irrational?Homework EquationsThe Attempt at a Solution lol ##{1/2} +{√2}## [/B]is irrational. ##{{1/√2}}×{√2}=2...
  49. martinbandung

    B Analysis Of Stilts Movement Research

    Hello all, I'm planning to do a research about stilts movement. I chose it because stilt is a traditional game in my country. In my plan, i want to analyze the velocity of the walker, the frequency of stilts, and the length of steps. I need some other idea to be added to my research. Such as the...
  50. P

    A Frequency analysis of signal with unknown period

    I was reading up on (discrete) Fourier transform when my mind started to think of an what-if scenario: Assumed I'm sampling a signal of the form a1*sin(b1+c1) + a2*sin(b2+c2) + a3*sin(b3+c3) + ... + aN*sin(bN+cN) + some noise where the a's represents magnitudes, b's represents frequencies and...
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