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. W

    MHB Fixed-Income Analysis: SA Bond Traders P/L & Return

    Assume there are 2 SA bond traders. Trader A has a short bond position of R50m nominal in R2048’s (selling for 9.36%) and trader B has a long position of R50m nominal in R2023’s (selling for 8.43%). Indicate (i) the likely 3 month repo rates in the current market; (ii) P/L and return they can...
  2. jdawg

    Dynamics: Relative Motion Analysis

    Homework Statement [/B] If bar AB has an angular velocity of 6 rad/s, determine the velocity of the slider block C at the instant shown. 2. Homework Equations The Attempt at a Solution vB=vA+wABxrB/A vA=0 vB= -0.8485i+0.8485j So then C relative to B: vC=vB+wBCxrC/B -vCi=...
  3. Alpharup

    I Why non-standard analysis is not used?

    In analysis, we do encounter tougher epsilon-delta proofs instead of more intuitive algebraic methods( those involving infintesimals). I have read that there is branch where infintesimals are rigorized like epsilon-deltas. My question is why people don't use that? Also, is it logically sound...
  4. M

    Static structural analysis on a solid sphere?

    Could you perform Static structural analysis on this solid sphere? No contacts to be used. I do not have any specific boundary conditions(unable to apply constraints to a complete solid spherical body) All i know is the pressure that needs to be applied. You could consider a smiley ball on...
  5. G

    Thevenin's circuit analysis. Multiple voltage sources

    Hi, i am halfway through one of my assignments and i require some assistance. I do not seek the answer to the assignment just a little boost to my knowledge. 1. Homework Statement Basically, if i am calculating the Thevenin's voltage and the resistor i have removed that is in question has a...
  6. anorlunda

    Insights AC Power Analysis – Part 2, Network Analysis - Comments

    anorlunda submitted a new PF Insights post AC Power Analysis – Part 2, Network Analysis Continue reading the Original PF Insights Post.
  7. H

    Granulometric Analysis: Radionuclide Activity, Uranium, Thorium & Potassium

    why do we need to determine the particle size while estimating the activity of radionuclides? is there any relation between the particle size (sand, silt and clay) and primordial radionuclide? will the content of uranium, thorium and potassium rely on particle sizes?
  8. B

    Analysis How are Bourbaki's book and Dieudonne's book?

    Dear Physics Forum friends, While vigorously studying Dugundji's Topology and Rudin's PMA, I found that the reference mentions the series of books written by N. Bourbaki, known as "Elements of Mathematics", and Dieudonne's Foundations of Modern Analysis. How are those books, specifically their...
  9. Y

    Can the Sequence of Upper Darboux Sums Converge to the Upper Darboux Integral?

    Homework Statement Let ##f## be a bounded function on ##[0,1]##. Let ##P_n## be a partition of ##[0,1]## such that ##P_n = (0,\frac{1}{n},\frac{2}{n},...,1)##. Finally, we define ##\alpha=\inf\{U(f,P_n):n\geq1\}##, where ##U(f,P)## is the upper Darboux sum of ##f## with partition ##P##. Show...
  10. M

    Digestion of Pb-alloy for ICP-OES analysis

    Hello everybody, I am looking for a disgestion procedure of Pb-alloy, so that we can measure the elements with ICP-OES. Pb should be removed, that it doesn't contaminate the system. So far we used HCl for digestion, but the results weren't very good. Elements of interest are: Sn Sb Bi Cu Cd As...
  11. H

    Regarding minerological analysis

    why we need to find the minerals in the sediments while estimating the amount of radionuclides. although there exist a cation exchange capacity in the minerals, do they actually concentrate the primordial radionuclides in them. further on granulometric analysis, do the clay particles retain the...
  12. anorlunda

    Insights AC Power Analysis: Part 1, Basics - Comments

    anorlunda submitted a new PF Insights post AC Power Analysis: Part 1, Basics Continue reading the Original PF Insights Post.
  13. K

    What Does a Shifted Voltage Waveform Indicate About Load Characteristics?

    https://files.slack.com/files-pri/T0GNF95E2-F0TV5JSSG/voltage_reversed_and_shifted.png This the voltage waveform across a resistor load (15W). The applied voltage is 230V AC at 50Hz. What can be inferred from this? [ the Analog to Digital conversion of Voltage happens at around 1690 Samples per...
  14. ramzerimar

    Software for learning structural analysis and FEM?

    I'm in the third semester of mechanical engineering and I'm taking classes on engineering statics right now. Our professor said the he will give us a preview of finite element methods at the end of the semester. Which softwares would you recommend for learning basic structural analysis? I mean...
  15. M

    Analysis Good book for complex analysis

    Hi friends, I am looking for a good book on complex analysis. My goal is to add some new techniques to my problem solving arsenal, learn some elegant non-intuitive proofs and finally build up to knowing enough about the Zeta function to understand it's relationship with prime numbers.
  16. L

    Analyzing the Effects of Lifting on a Wagon and Train Model in Ansys Workbench

    Hello! I wish to do a lifting analysis in Ansys workbench. Basically it is a wagon with a train on it. I wish to analyse what happens to the model when lifting the wagon which has the weigth of the wagon+train. What is the easiest way to analyse what will happen to the wagon when lifting it...
  17. V

    Find voltage across resistor using mesh current analysis

    I'd like to find Vth by mesh current analysis. Mesh A and B share a current source, so they're treated as one supermesh. What's the equation for this supermesh? Also, do I ignore the loop with the open circuit? Since there's no current flowing there... 2A = ib - ia Anyway, is this the right...
  18. A

    Ansys workbench Composite Analysis

    Hello All, I am a master student working on my thesis. am using ANSYS workbench to model the debonding between FRP and Concrete (Single Shear Test). The geometry is very simple, so meshing and sketching were easy. however I have the following quires about loading and interfaces. 1. I want to...
  19. Jianphys17

    Which Book is Best for Studying Analysis 2 and Multivariable Calculus?

    Hi at all, what is the better book for study analysis 2, if possible also with exercises...
  20. Kartik Yadav

    Proving n log n is Big-Oh of log(n!)

    To prove that n log n is big oh of log(n!), I did: n log n <= C log(n!) n log n/ log(n!) <= C Let k = 1 n > k, so for n = 2 2 log 2 / log 2 <= C 2 <= C C is an element of [2, infinity) Taking C = 2 and k = 1 can we say, n log n <= 2 log(n!) and hence n log n is big oh of log(n!) ?
  21. M

    CFD Analysis of Solidification and melting of Ice

    Hello, I was doing melting and solidification of ice kept inside a annular cylinder. The temperature of inside wall of cylinder is 80 degree. Now i want to analyse the total time consuming to melt the ice and plot temperature variation with time. Actually i did analysis but the result i found...
  22. micromass

    Insights How to self study analysis. Part I: Intro analysis - Comments

    micromass submitted a new PF Insights post How to Self Study Analysis. Part I: Intro Analysis Continue reading the Original PF Insights Post.
  23. SrVishi

    Other Proof Tips for Math Majors: Logic & Techniques for Real Analysis

    Every math major eventually learns logic and standard proof techniques. For example, to show that a rigorous statement P implies statement Q, we suppose the statement P is true and use that to show Q is true. This, along with the other general proof techniques are very broad. A math major would...
  24. S

    Relative Motion Analysis: Acceleration

    Mentor note: moved to homework forum later, therefore no template. When doing a rigid body relative motion (accel) problem using vector analysis, how do I know when it's appropriate to substitute sin/cos values vs when to use just the numbers given as the velocity?
  25. T

    Confused about solving RC circuits with nodal analysis

    Problem is in the picture below. The problem is already solved, but I am confused as to why C(dv/dt) is positive and not negative, since the current is coming out of the capacitor and towards the point v(t), which is not away from v(t) like the solution shows. But if I solve the problem with...
  26. Titan97

    Classical Book for learning AC circuit analysis

    I haven't used any book for AC circuit analysis yet. I have learned the basics of phasor diagrams which my teacher taught in the class (We were only taught series combination of LCR circuits). Can anyone suggest a book to learn more about circuit analysis (like source transformations, Norton's...
  27. rkum99

    Engineering Node/Mesh Analysis of a Circuit

    Homework Statement The following is a link to the problem diagram and my work: http://imgur.com/a/9tppH The goal is to determine the power through the 20V voltage source. Homework Equations KCL and KVL: Currents entering a node sum to zero. Voltage drops around a loop sum to zero. The...
  28. O

    Hall Effect Measurements and Analysis

    Hi all, I am reading about hall effect measurements and analysis from an old physics book, A. C. Melissinos, Experiments in Modern Physics, for a lab class I'm taking. An experiment involving hall and resistivity measurements of a p-type germanium sample is performed and discussed. He notes...
  29. S

    Treating Voltage Sources in Mesh Analysis: Clockwise Drop or Rise Positive?

    1. I have a question regarding the treatment of voltage sources in Mesh Analysis by inspection. I hope this is the correct place to post. In my course textbook (Fundamentals of Electric Circuits 4e p. 101) it says that the voltage is the algebraic sum taken clockwise of all independent voltage...
  30. Vivek Sagar

    How to perform forced vibration analysis cal using ansys

    Hi, My problem is that I have a flat rectangular plate acted by in-plane concentrated force. I want to do the forced modal analysis for 5 modes using ansys for this plate. Can anyone tell me how to do this. Regards, Sagar
  31. A

    Instructions for Video Analysis Projects

    Hi all, I'm going to have my students (algebra-based mechanics at a community college) do a video analysis project and I'm wondering if anyone knows of any resources for good sets of instructions for this type of project. I'd like something pretty open-ended so students can choose their...
  32. B

    Analysis Seeking a Rudin's PMA-level analysis book with abstract proofs

    Dear Physics Forum personnel, I recently got interested in the art of abstract proof, where the focus is writing the proof as general as possible rather than starting with a specific cases. Could anyone recommend an analysis book at the level of Rudin's PMA that treats the introductory...
  33. C

    Why does a charged Styrofoam plate attract paper but repel aluminum foil?

    Homework Statement Based on a lab we did at school, we charged a Styrofoam plate by rubbing it against wool and determined that it attracted pieces of paper but repelled pieces of aluminum foil. Can anyone clarify why this is because I believe that both the pieces of paper and aluminum foil are...
  34. Marcin H

    Solving for Vo: Graph Analysis of Vs vs t

    Homework Statement Homework Equations Vs=Vi(1-e^-t/T) The Attempt at a Solution I am stuck on B. I am not sure how I am supposed to graph Vo with so little information. Do i just use V=Vo(1-e^-t/T) and find the output voltage for each time increment that is on the original graph. So...
  35. C

    Force Analysis in Circular Pipe: How to Approach Vertical Force Balance?

    "Consider a fully developed laminar flow in a circular pipe, perform force analysis on an element of the real fluid." I've just started this type of question, and I'm a bit confused about where to go from here: I've managed to do a force balance horizontally to show that the partial derivative...
  36. I

    Order of zero (complex analysis)

    I'm confused about how this related to the roots of an equation. Here's the definition: We say that ##f## has a zero of order ##m## at ##z_0## if ##f^{(k)}(z_0)=0## for ##k=0,\dots , m-1##, but ##f^{(m)}(z_0)\ne 0## or equivalently that ##f(z) = \sum_{k=m}^\infty a_k(z-z_0)^k##, ##a_m \ne 0##...
  37. F

    How Do You Calculate Current in a Three-Phase System's Middle Capacitor?

    Homework Statement In the following three phase system, calculate the current in the middle capacitor: Homework Equations I = V/Z ZY = ZΔ / 3 The Attempt at a Solution Hello! I'm trying to figure out a method for solving any generic three phase system. In particular, I found very...
  38. D

    Nodal Analysis: Understanding KCL and Node Subtraction in Circuit Problems

    While performing nodal analysis problems, I am always unsure of which node gets subtracted from during KCL. For example, if I have (V1-V2)/2k, how do I know that it shouldn't be (V2-V1)/2k?
  39. E

    Project idea in Numeric Analysis

    hey, need an idea for a paper on differential equations, which can be implemented in two or three days work. also it will be nice if that paper has graphs on it. any help would be most welcome thx
  40. S

    Understanding Potential Dividers in Circuit Analysis

    Homework Statement how did they get this ?? it is like a potential divider, can anyone explain... Homework EquationsThe Attempt at a Solution this is what i got[/B]
  41. S

    MHB Help with functional analysis questions

    Hi, Could someone post a solution to the following questions : 1. Let R be the real numbers and A a collection of all groups that are either bound or their complement is bound. a. Show that A is an Algebra. Is it a sigma algebra? b. Define measure m by m(B) = {0 , max(on B) x <...
  42. ognik

    Fourier analysis of wave packet

    Homework Statement Assume ## \phi(k_x ) = \sqrt2 {\pi}## for ## \bar{k}_x - \delta \le k_x \le \bar{k}_x + \delta##, and ##= 0## for all other values of ##k_x##. Calculate ##\psi(x, 0)##, and show that ## \Delta x \Delta k_x \approx 1 ## holds if ## \Delta x## is taken as the width at half...
  43. evinda

    MHB Applied Functional Analysis: What You Need to Know

    Hello! (Wave) What is Applied Functional Analysis about? What knowledge is required? Which is the difference between this and Functional Analysis ?
  44. P

    Analysis Good supplementary real analysis book

    So the course I'm taking doesn't have a textbook requirement just lecture notes as the study material. While these are sufficient I would like to supplement with an outside reference that is a bit more in depth / explanatory. It's your typical undergrad real analysis course covering: The least...
  45. Andreol263

    Analysis Looking for a rigorous intro to functional analysis with practical applications?

    Hello guys, can you recommend me a good and Rigorous introduction to functional analysis?? Rigorous like E.D.Bloch book on Real analysis if possible
  46. arpon

    Geometry Textbook on Co-ordinate Geometry and Vector Analysis

    Could you suggest me any textbook on Co-ordinate Geometry and Vector Analysis?
  47. T

    Use of diagonal matrices in vibration analysis?

    why are diagonal matrices and eigen vectors useful in vibrations analysis?
  48. 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?
  49. 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...
  50. 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
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