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. SrVishi

    Analysis What are some alternatives to Rudin for learning complex analysis?

    Hello, I was wondering how well is Rudin's Real and Complex Analysis for learning complex analysis, assuming that difficulty won't be an issue. Does it cover the standard material? Is it deep enough? Should I just read from elsewhere instead?
  2. B

    Finding values of constant by using Dimensional Analysis

    Homework Statement The speed v of sound in a gas depends on the density p and pressure P of the gass. If this dependence is in the form of a power law that is, v = kpaPb where k, a and b are constants (k a dimensionless one). a. Determine by dimensional analysis the values of a and b. b...
  3. B

    How Do You Simplify Dimensional Analysis Equations?

    Homework Statement Hello, I am new to physics and i was wondering what i should do for the following equation to simplify it. Homework Equations [T]-2/[T] The Attempt at a Solution I tried 1/[T]3 Which I'm not sure is possible when dimensional analyzing. EDIT: Is it [T]-3
  4. B

    Applying Dimensional Analysis to correct the equation

    Homework Statement Check if the equation is dimensionally correct The frequency f of vibration of a pendulum of length L is given by the equation: f = L/2π √(g/L) I'm assuming 'g' is the gravitation field strength (?), which is [L]1[T]-2 The Attempt at a Solution [/B] I did not know what...
  5. C

    Schools Is Complex Analysis a must for grad school applications?

    Is taking complex analysis before graduate school apps a "make-or-break" deal if one is looking to apply for theory? I am currently deciding whether to take it junior spring or defer it to senior spring. As it has come up in my research, I have studied some of it, but I'm wondering if it must be...
  6. J

    Electrostatic analysis of cad model of protons neutrons

    Could the orbit filling order of electrons be more classical and less quantum? I attached a jpeg and need someone to do a electrostatics analysis of the CAD model version of it. Does anyone have an electrostatics software package and have time to do a finite element analysis on a 3-D part to...
  7. S

    MHB Help for test - functional analysis

    Hi - my professor in functional analysis posted 4 prior years tests just 4 days before the test without solutions. I'd appreciate if anyone can help send solutions for the following with the following questions : 1. $\mu$ is a sigma additive measure over sigma algebra $\Sigma$. A $\in...
  8. P

    Solutions to Hungerford's "Abstract Algebra" 3rd Ed.

    I'm taking an abstract algebra course that uses Hungerford's "An Introduction to Abstract Algebra" 3rd Ed. And while I feel like I'm following the material sufficiently and can do most of the proofs it's hard to learn and practice the material without a solutions guide. How am I supposed to know...
  9. DaTario

    Ambiguity in dimensional analysis

    Hi All, My question is twofold and follows: 1) Why the dimension of torque is not Joule, as it is Newton times meter? 2) Why the derivative of the velocity with respect to the distance cannot be measured in Hertz? Thank you all, Best Regards, DaTario
  10. S

    MHB What is a Semigroup and How Does it Relate to Immeasurable Sets?

    Hi, I'm taking a course in functional analysis and having some trouble with the following questions : 1. L1(R) is the space of absolutely integrable functions on R with the norm integrate(abs(f(x)) over -inf to +inf. Define a linear operator from L1(R) to L1(R) as A(f)(x)=integrate...
  11. N

    Frequency analysis of transistor amplifiers

    Hi guys, I am trying to do this question on my own but i am not confident if what i am doing is correct. please download the Question2.docx file and my workings are in blue. hope someone can help me with this. 1. Homework Statement A. For circuit (a) below, calculate: R_e and R_C to make...
  12. H

    Vector analysis, calculate path

    Homework Statement I have these vectorfields defined on the specified set. All of them are conservative on their set. Also i have three unit circles C1, C2 and C3 centered respectively on (0,0) , (-2,0) and (-1,0) I need to find the line integrals over all of them on H (beregn = calculate...
  13. mishima

    Understanding Truss Analysis: Investigating the Accuracy of a Bridge Design App

    Hi, my high school students enjoy using the applet found here (http://pages.jh.edu/~virtlab/bridge/truss.htm) to design model (basswood) bridges for our annual regional contest. It seems to require firefox these days. Recently, some designs have been causing extremely large forces to be...
  14. F

    Engineering Solving an RL Circuit Analysis Problem

    Hello! It's a pretty long time time since I did my last circuit analisys, so I feel a bit rusty. I have to calculate the evolution of current in the inductor: L is generic and u(t) is the Heaviside step function. Do note that at t = 0 the inductor behaves like a short circuit (I don't know...
  15. Titan97

    Phasor algebra in AC circuit analysis

    Homework Statement Find the peak value of current through the AC source of the following L-C-R circuit, if peak voltage is ##V_0## and angular frequency is ##\omega_0##. Homework Equations I have learned Vector algebra and calculus (single variable). I was taught how to use phasor diagrams...
  16. Q

    What is the Limit of the Sequence b_n = n - sqrt(n^2 + 2n)?

    Homework Statement Consider the sequence given by b_{n} = n - \sqrt{n^{2} + 2n}. Taking (1/n) \rightarrow 0 as given, and using both the Algebraic Limit Theorem and the result in Exercise 2.3.1 (That if (x_n) \rightarrow 0 show that (\sqrt{x_n}) \rightarrow 0), show \lim b_{n} exists and find...
  17. W

    Solving Volumetric Analysis Questions with NaOH & H3PO4

    Homework Statement A solution of sodium hydroxide(NaOH) contains 1.70g of hydroxide (OH-) ions per dm^3. 20.0 cm^3 of the solution reacts with 25.00cm^3 of 0.0400 mol/dm^3 phosphoric acid(H3PO4). How many moles of sodium hydroxide reacts with 1 mol of phosphoric acid? What will be the chemical...
  18. S

    Solving phi-fourth theory using Fourier analysis

    The equation of motion of ##\phi^4## theory is ##(\partial^{2}+m^{2})\phi = -\frac{\lambda}{3!}\phi^{3}##. Why can't this equation be solved using Fourier analysis? Can't we simply write the equation in Fourier space and take it from there?
  19. L

    Glass electrode voltage calibration and pH analysis.

    Hi, I'm stuck on part b) of the question below: Q: In order to perform pH determinations with a glass electrode, the cell potential was measured for threestandard solutions with the following pH values at 25 C: 2.04, 7.05, and 9.20. The cell voltage readout(in mV) for each of the above solutions...
  20. A

    Analysis of Train in Tunnel Problem Using an AND Gate

    This analysis uses an AND gate, the very embodiment of simultaneity, for clarity. A 1km long train travels through a 1km tunnel at a speed of 0.6c=180m/microsecond. At each end of the tunnel is a photo-electric beam sensor, which can be blocked by the train. They are connected to an AND gate...
  21. Martin V.

    Find voltage using nodal analysis

    Homework Statement Assignment: Find V_2 using Nodal Analysis Homework Equations KCL U=R*I The Attempt at a Solution - Chosen reference node - Assigned node voltages - Applied KCL to each non-reference node - Solve system of equation - Checked equations for obvious errors See circuit drawing...
  22. J

    Vector Analysis using Basis Vectors

    Hi pf, Having some trouble with basis vectors for expanding a given vector in 3-D space. Any given vector in 3-D space can be given by a sum of component vectors in the form: V = e1V1 + e2V2 + e3V3 (where e1, e2 and e3 are the same as i, j and k unit vectors). Equation 1. I am happy with...
  23. D

    Natural units and dimensional analysis

    As far as I understand, a natural system of units is one in which the numerical values of ##c## and ##\hbar## are unity. However, they still have dimensions, indeed ##[c]=LT^{-1}## and ##[\hbar]=ML^{2}T^{-1}##. How is it the case then, that certain quantities, such as the action ##S##, can be...
  24. W

    Open source for FE / Fluid Analysis?

    Hi! I'm would like to ask if there's any open source available for FE/Fluid analysis? I'm planning to use it to simulate icing and melting process in a ice storage based on different geometry.Its something like a fridge with coolant ect. I would like to simulate the icing and melting process...
  25. benzun_1999

    Over constrained least squares analysis

    Hi, I have a over constrained least squares problem. I also have the correct solution to the problem. Now I need to determine which of the vectors are contributing how much information that is close to the correct solution. I am sure there should be some methodology for this analysis, but I...
  26. B

    Analysis Which book will suit the following course syllabus (introductory analysis)?

    Dear Physics Forum personnel, I am a undergraduate student with math and CS major who is currently taking an introductory analysis course called MATH 521 (Rudin-PMA). On the next semester, I will be taking the course called MATH 522, which is a sequel to 521. My impression is that 522 will be...
  27. E

    Variables definition in Euler's introduction to analysis

    In his book, Euler gives the definition of a variable to be : "A variable quantity is an indeterminate or universal quantity, which includes within itself all completely determined values." What does he mean exactly in the last part of the sentence?
  28. S

    Crank Slider mechanism analysis

    Homework Statement For the mechanism shown, analytically find A) Velocity B) Acceleration. Of All points (B, C, D, E and G) The lengths of all links are given in the photo. It has to be solved using the analytical velocity and acceleration method. I've attempted so far deriving the equations...
  29. F

    Functional analysis, ortho basis, weakly convergent

    Homework Statement This is a problem from Haim Brezis's functional analysis book. Homework EquationsThe Attempt at a Solution I'm assuming (e)n is the vectors like (e)1 = (1,0,0), (e)2=(0,1,0) and so on. We know every hilbert space has an orthonormal basis. I also need to know the...
  30. T

    Nodal analysis with dependent voltage source

    Homework Statement In attached image. Just curious as to how their nodal analysis is correct. Homework Equations [/B] ##I_{in} = I_{out}## The Attempt at a Solution Solution in image. I am just not sure how they applied nodal analysis here to find that ##I_s = \frac{12}{12} +...
  31. B

    Analysis Where to Purchase Munkres' Analysis on Manifolds" (Hardcover

    Dear Physics Forum friends, I am currently trying to purchase Munkres' Analysis on Manifolds to replace the vector-calculus chapters of Rudin-PMA, which is quite unreadable compared to his excellent chapters 1-8. I know that there is a paperback-edition for Munkres, but I heard that the...
  32. F

    Determine speed of roulette ball through audio analysis?

    I'm trying to find a way to track the speed of a spinning roulette ball in real time through audio analysis, i.e. have a computer report the speed of the spinning ball it hears through a microphone.Here is a video of a spinning ball: I've tried watching a real time spectrum analyser (FFT), but...
  33. MacLaddy

    Engineering Phasor Circuit Analysis Homework: Understanding Incorrect Answers | MacLaddy

    Homework Statement Hello folks. I had a recent midterm where I got a problem wrong, but I'm not sure I understand why. I am hoping someone here can shed some light. Please see the attached circuit diagram.Homework Equations Phasor notation stuff... I am correct on all except one sign. Please...
  34. B

    Analysis What are the best introductory books for real analysis?

    Dear Physics Forum personnel, I am a college student with huge enthusiasm to the analysis and theoretical computer science. In order to start my journey to the real analysis. I am currently taking an introductory-analysis course (Rudin-PMA; I also use Shilov too) and linear algebra...
  35. D

    Intro Level Question -- Truss Analysis

    Homework Statement http://puu.sh/lKP9T/b6aea483b5.png http://puu.sh/lKPdk/a99777477e.png http://puu.sh/lKPkj/a9f199e959.jpg My question is the last picture/slide which says F_DB = F_DA how? why is that? Homework Equations F_DB = F_DA ? The Attempt at a Solution
  36. J

    Transistor / Photodiode Circuit Switch Analysis

    Homework Statement Firstly, this is more of a schoolwork issue, not coursework or a set task. It is more to do with understanding the circuit seen in the image provided: I am trying to understand why this circuit does what it is supposed to; activate the lamp when a certain light intensity is...
  37. ichabodgrant

    How Do You Analyze Stacked Beams Without Composite Action?

    Hi, normally when we try to analyse a structural beam with composite section, we apply transformed section method or so. But what if two beams are just put together (one onto another one) instead of having a composite relation (e.g. glued together), how am I going to analyse the forces and...
  38. Leon666

    3D Static Analysis of a Automotive Suspension

    Hello, my name is Leon and I attend to a Mechanical Engineering College. (I'm sorry for any grammar mistakes, English is not my first language) I'm trying to calculate the reactions of a Formula SAE car's suspension to the chassis, but I'm getting some strange answers. I hope someone here can...
  39. U

    Background rejection / data analysis

    Hi, How can one calculate background rejection from a background sample applying cuts ??
  40. J

    Complex Analysis: Conformal Mappings

    I am looking for conformal transformations to map: 1. Disk of radius R to equilateral triangular region with side A. 2. Disk of radius R to rectangular region with length L and width W. 3. Disk of radius R to elliptic disk with semi-major axis a and semi-minor axis b. Thanks!
  41. B

    SolidWorks worm reducer analysis tutorial needed

    I've calculated my gear ratio to be 1:27 and the most suitable reducer for it would be a worm drive. I couldn't find any descriptive tutorials to do the mesh and perform constructional analysis of the gears on SolidWorks. Can you help me?
  42. T

    Analysis Answers to questions from the book: Real Analysis by Stein

    Hi I am trying to teach myself Measure Theory and I am using the book: Real Analysis by Stein and Skakarchi from Princeton. I want to check if my answers to the questions are correct, so I am asking: Does anyone have the answers to the questions in chapter 1 ?
  43. H

    How to transfer analysis result to second analysis in Abaqus

    Hi, I have to check the buckling of a beam in fire. To do this I am following the below stages: 1. Conduct a heat transfer analysis ( transient ) for 30 minutes in fire , to find out the temperature history of the beam. Please not the temperature of the beam is not uniform 2. perform 6 runs...
  44. C

    Error Propagation in Mass Flow Rates

    I tried posting this question in this forum a couple of weeks ago, but didn't get an answer to my question. I'm going to try posting it again using the formatting template so that it is hopefully clearer. I am also not sure if this is the right forum to be posting this in. It is a problem I ran...
  45. marcus

    Chem analysis to start at best site for low-gravity industry

    Dawn spacecraft is equipped for gamma and neutron spectroscopy to analyze the chemical make-up of Ceres surface material down to a depth of 1 meter. To do this it must first descend to a low altitude--the target is 375 km. It has already descended to within 600 km and it seems likely to reach...
  46. SrVishi

    Analysis Problems and Theorems in Analysis by Polya and Szego

    Hi, apparently (as seen in my school's online library page) my school has Problems and Theorems in Analysis by Polya and Szego. I hear this book is really good, but I am wondering if this book is good for learning real analysis. I haven't looked inside the book, but is it like an inquiry based...
  47. S

    Nodal analysis with voltage source

    Homework Statement Use nodal analysis to calculate Va, Vb, and the currents IE1 and IE2 without using source conversions I have tried this many, many times, and I must be missing somethingHomework Equations [/B] The equations I came up with: VA-10/ 1.1 + VA/1.2 +VA-VB/1.4 = 0 VB+2/1.5 +...
  48. K

    Using time-step analysis to simulate Scheils equation

    Using excel, I tried to do a numerical analysis to get the same results as scheils equation. The problem is that the two concentration profiles start diverging at the end. The numerical analysis is offcourse based on time-step analysis. I have uploaded the excel file. Much Gratitude,
  49. C

    System Analysis - Determining Dampening and Natural Frequency

    Homework Statement Problem and work attached. It is mostly diagrams so I have just uploaded the pictures. I think what I did to determine the transfer function was correct. I'm not quite sure how to do the last section of part (a) where I need to determine the dampening, static gain, and...
  50. C

    System Analysis - Simplifying with Transfer Functions

    Homework Statement Sorry for the pictures, I'd normally write out the problem but it is mostly diagrams. Question and work attached. I am looking for help with part (a) right now, the transfer function I obtain is shown at the end of my work. Homework Equations Knowledge of Laplace transforms...
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