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

    Dimensional Analysis and units of time

    time = x(min) distance = 1(y) y = unknown unitsI think the answer should be 1(y)/ Min. This is not correct becase 1(y) is unknown. Any help? I have the answer but am confused
  2. wcjy

    Circuit problem with two sources and three resistors (Nodal Analysis)

    Ans: 0.123A Tried mesh analysis and got it but didnt for nodal analysis
  3. Arman777

    I Question about data analysis and error

    Let us suppose we have one constant variable ##b \pm \delta b = 20 \pm 1 ## and one function that depends on ##x ##, such as, ##a(x) \pm \delta a ## The problem is I want the difference between ##a(x) ## and ##b ## to be ##0 ##. Let me denote this difference as ##c \pm \delta c ##. To...
  4. M

    MHB Complex Analysis: Does $\int_{C(0,10)} f(z)$ Equal 0?

    Hey! :giggle: Question 1: If $f\in O(\Delta (0,1,15))$ then does it hold that $$\int_{C(0,10)}\frac{f(z)}{(z-6+4i)^5}\, dz=2\pi i\text{Res}\left (\frac{f(z)}{(z-6+4i)^5}, 6-4i\right )+\int_{C(0,6)}\frac{f(z)}{(z-6+4i)^5}\, dz$$ Do we maybe use here Cauchy theorem and then we get...
  5. Carlos_Ishigami07

    Scientific analysis -- How many seconds does it take for the paper to burn?

    I have a problem: in the same anime I saw that Senku estimated the time to start burning the paper in sixty seconds, one minute and with a lens. The data is as follows: The lens he used has a diameter of 5 centimeters. The solar constant, assuming it is the same as 3700 years ago, is 1362 watts...
  6. yucheng

    Inequalities Since ε is arbitrarily small, do the inequalities hold?

    #### If ##b \leq x_n \leq c## for all but a finite number of n, show that ##b \leq \operatorname{lim inf}_{n \to \infty} x_n## and ##\operatorname{lim sup}_{n \to \infty} x_n \leq c_n## (Buck, Advanced Calculus, Section 1.6, Exercise 24) Let ##\beta =\operatorname{lim inf}_{n \to \infty} x_n##...
  7. yucheng

    Prove the lower bound for a sequence (Buck, Advanced Calculus)

    Clearly, ##x_{n+1}>x_n \because x_n + \sqrt{x_n} > x_n## $$ \begin{align*} x_{n+1} &= x_n+ \sqrt{x_n} \\ &= x_1 + \sqrt{x_1} + \sqrt{x_2} + \cdots \sqrt{x_n} \\ &>n+1 \end{align*} $$ ##\because \sqrt{x_n}>\sqrt{x_1}=1## In fact, $$x_{n+1} > 1+ \sqrt{1} + \sqrt{2}+ \sqrt{3} + \cdots \sqrt{n}$$...
  8. bardia sepehrnia

    AC Circuit Analysis: Solving Example with Confusing Concepts

    I'm reading this chapter in Electrical Engineering book regarding AC circuit analysis where there is a solved example which I've attached, but there are some concepts that are confusing me. First, why and how do we know that the phasor value of voltage is: -pi/2 Note: I do understand that...
  9. F

    [Complex analysis] Contradiction in the definition of a branch

    I find the following definition in my complex analysis book : Definition : ## F(z)## is said to be a branch of a multiple-valued function ##f(z)## in a domain ##D## if ##F(z)## is single-valued and continuous in ##D## and has the property that, for each ##z## in ##D##, the value ##F(z)## is one...
  10. Mondayman

    Intro Physics Textbook on Electronics and Circuit Analysis

    Hi folks, I'm looking for a solid introductory book on electronics and circuit analysis. I have seen The Art of Electronics highly recommended. I will likely get it but as a supplement. Does anyone know of any other good electronics textbooks? I don't mind old textbooks. Some of the newer...
  11. W

    Dimensional analysis assumption

    Problem: Source: Halliday et al Physics 4e, p9, sample problem 4. Why is it valid to assume that $$F\alpha v^b$$ as the author does here, and not some more complex equation e.g. $$F=av^{e_1}+bm^{e_2}+cr^{e_3}$$, or $$F=av^{e_1}+bv^{e_2}+\cdots $$ (or some other equation)? A very similar...
  12. FEAnalyst

    Quick return mechanism stress analysis

    Hi, I wonder how to approach stress analysis of quick return mechanism used in shaper machines (see the diagram below): The first issue is: which moment in the working process of this mechanism should be used for analysis (when will the mechanism experience largest loads)? So far I assumed...
  13. Byron Forbes

    Particle analysis of diffraction

    I have done a bit of googling but cannot find anything in this regard at all. It seems to all be "thought of" (rather than explained) by the Huygens–Fresnel principle and other spin offs. Can anyone point me to a particle explanation of diffraction for sound waves? Or does anyone here have...
  14. S

    How Is the Variance Used as Weight in Half-Life Error Analysis?

    What is meant by the constant background and how would one deduce the half-life IF not from the fit?
  15. S

    B Is complex analysis really much easier than real analysis?

    This author seems to say so: https://blogs.scientificamerican.com/roots-of-unity/one-weird-trick-to-make-calculus-more-beautiful/
  16. murshid_islam

    I Any Good Lecture Series on Complex Analysis?

    Can anyone suggest a good lecture series on Complex Analysis on YouTube? I have already searched on YouTube myself, and there are a few. But I wanted to know if any of you would recommend some particular lecture series which you consider to be good.
  17. T

    A What is the purpose of modal analysis?

    Hello all, I have been asking this question, here, and gaining more insight. I think I can finally ask it the way I need. I can: Conduct an eigenvalue analysis Code the Lanczos algorithm. Understand mode shapes Build the solution of set of coupled differential equations from mode shapes...
  18. asd852

    Circuit analysis involving parallel and series conditions

    par
  19. T

    I Justification (or philosophy) of modal analysis

    Hello I have tried asking this different ways, here. I do not know exactly what I am asking. So I am hoping to try again. Say we have a differential equation for a multi-body system. We cannot solve it because of the coupling (too difficult). So, we turn to a modal analysis (eigen value...
  20. A

    Engineering Circuit Analysis -- How many independent equations can be written using KCL?

    I think there are 4 essential node. So we can write 3 KCL independent equations.
  21. T

    I Can Tensors of Any Rank Be Approximated by Matrices?

    Hello. Could we approximate a tensor of (p,q) rank with matrices of their elements? I am talking also about the general case of a tensor not only special cases. For example a (2,0) tensor with i, j indices is a matrix of ixj indices. A (3,0) tensor with i,j,k indices I think is k matrices with...
  22. Andrei0408

    Choosing Between Options: Reasons & Analysis

    Could you tell me which one of these, but also why because I want to understand. Thank you!
  23. T

    A Modal Analysis vs. the Solution to the Diff.Eqs.

    Hello The figure below is that of a two body problem in oscillation. Whether by Free Body Diagrams or Hamilton's Principle, we can obtain the two coupled differential equations that describe the oscillation. At this point, one could obtain the closed form solution for the displacement...
  24. greg_rack

    Applying Kirchhoff's laws for a loop analysis

    For this one circuit, I've applied Kirchhoff's laws as following: $$\left\{\begin{matrix} V-6\Omega I_{6}-24V-2\Omega I_{2}=0\\ 24V-6\Omega I_{6}-12V-24V=0\\ I_{2}+I_{6}=6A \end{matrix}\right.$$ but the values I get for ##I## and ##V## aren't correct... what's wrong?
  25. F

    Equation Demonstration -- Simple Pendulum Analysis

    I've just studied simple pendulum: The simple pendulum (for small oscillations) differential equation is first image. I've no problem to arrive this result and formula. My problem is to get to the second formula by passing through another formula (Image 3) that my book mentions. I can't...
  26. Yokoko

    Chemistry Please confirm my Activity Coefficient Calculations

  27. Hamiltonian

    Derivation of the orbital analysis equation and its physical significance

    $$cos\theta = \frac {s}{1-s} = \frac{p-1}{p}$$ in this equation ##\theta## is the bond angle and ##s## and ##p## are the fractional s-character of the orbital and p-character of the orbital. This is equation is used rigorously in showing that the s-character of the axial orbitals in a ##sp^3d##...
  28. H

    I Principal Component Analysis with dependent variable?

    So I found a paper, https://www.sciencedirect.com/science/article/pii/S0022231314006048?via%3Dihub which concerns a property of a compound called "Quantum Yield", which is a result of various factors (independent variables). The authors are trying to figure out what factors affect the quantum...
  29. K

    Calculating torque from moment results in CFD analysis

    Hi there, attached were the results: https://prnt.sc/v3yg1f Both are negative and need to be added together to get the torque force. Calculations are from a model of specified radius and input air speed, its a turbine. Just need help in understanding what the negative results mean and how they...
  30. D

    A Applications of analysis in signal processing/machine learning?

    Hello everyone, My question for this thread concerns the application of (mainly) mathematical analysis to fields such as signal processing and machine learning. More specifically, I was wondering if you happen to know of some interesting application of things like measure theory or functional...
  31. T

    Dimensional analysis of the Froude Number

    So, I have calculated that to dimmensional analyse this equation;
  32. haushofer

    I Error analysis: simple but confusing matter

    Dear all, We learn students to work with significant figures. I guess we all know those rules of thumb. Now imagine I have an expression like L = 2x, where x is a length a the 2 is an amount, i.e. the value of a discrete 'function'. If x=0,72 m (2 significant figures), then L = 1,44 --> 1,4 (2...
  33. I

    Calculus Analysis with or without set-theoretic topology?

    Do you think a first course in analysis should focus entirely on inequalities and leave set-theoretic topology for another occasion? Should this depend on whether or not the student had a first rigorous calculus course first? If I'm not mistaken, Victor Bryant (Yet Another Introduction to...
  34. jisbon

    Engineering S-domain analysis with initial conditions

    I've attempted this questions after understanding the theory from my lecture notes, but my equation is looking bizarre here. Is this correct so far? Are my mesh equations correct here? Thanks.
  35. HansBu

    Laurent Series (Complex Analysis)

    My homework is on mathematical physics and I want to know the concept behind Laurent series. I want to know clearly know the process behind attaining the series representation for the expansion in sigma notation using the formula that can be found on the attached files. There are three questions...
  36. Leo Liu

    I What are the applications of dimensional analysis and why does it work?

    I know that dimensional analysis is a rough way to check the correctness of the solution to a homework problem. However, what exactly is it and what are the other applications of it? Why does it work? Thanks.
  37. T

    Vibrations, Modal Analysis and Mechanical Systems

    Hello I have used and enjoyed the textbook: "Theory of Vibrations with Applications," by William Thomson However, many of the examples there are more civil engineering than mechanical. There are many good examples of "buildings" under vibrations (good examples, but civil, nonetheless) The few...
  38. bhobba

    COVID Supercomputer Analysis Of Covid Virus

    Hi All Someone passed onto me the following supercomputer analysis of the Covid virus: https://elemental.medium.com/a-supercomputer-analyzed-covid-19-and-an-interesting-new-theory-has-emerged-31cb8eba9d63 Very interesting. Thanks Bill
  39. K

    Automotive Modal analysis - Input and boundary conditions given?

    My understanding in modal analysis is very limited. All I know is it helps to find a specific mode of vibration and the natural frequency corresponding to it. While I was discussing about this with my NVH team colleague, he told me that there is no force input or excitation input given to a...
  40. Vutum

    Wood/Glass/Metal 3-in-1 DIY Aquarium Stand Feasibility Analysis

    Please help me to find out if this is a feasible project. If not, what changes shall be made to make it sustainable for a long time without changing the layout? 1. Details of the stand: L 36", W 18", H 30" 2. Details of Aquarium 1: L 36", W 18", H 18", weight: 225kg 3. Details of Aquarium 2 and...
  41. Theia

    MHB Would you read a blog about numerical analysis?

    Hey! I have been thinking about different topics on mathematics, and for some reason I feel, that applied mathematics and doing numerical computations is often overlooked. When I was studying in university, more than 95 % of all examples which would require numerical methods were either omitted...
  42. CommissarCold

    Exhaustive Projectile Analysis

    Good afternoon. As part of a personal hobby, I've been trying to design a relatively small projectile that can travel at 'bullet speed' (say, a .22 caliber bullet fired from an appropriately sized gun). I understand that the overwhelming majority of mass-produced bullets today come in a small...
  43. jisbon

    Using nodal analysis to solve for current

    Hi all, Managed to get an answer out, but unfortunately, it doesn't correspond with the answer given ( –3.09 A) Would appreciate if one could check out what I did wrongly here: ## V_{1}=2\times 5=10V ## At node 2: ## \dfrac{V_{1}-V_{2}}{2}=12+\dfrac{V_{2}}{1}+\dfrac{V_{2}-V_{3}}{2}## We can...
  44. I

    Programs Physics Major with Stats/Data Analysis Minor (Is this a good combo?)

    I am an incoming university freshman in the U.S. who wants to major in physics but also wants to add a minor that will help build some more applicable skills. As the title suggests, I am looking for some insight into a stats/data analysis minor since a close friend of mine majored in applied...
  45. madafo3435

    I Differential analysis: convex functions

    I am reading A Course in Mathematical Analysis Volume 1 by D. J. H. Garling, and I am having trouble in the following demonstration of Section 2 Differentiation. part 4 of the test, the first part of the second inequality does not make sense, I do not understand its justification. I hoped they...
  46. M

    Showing that a function is surjective onto a set

    I have to show that $\forall z\in B(0,0.4)$, there exists an $x\in B(0,1)$ such that $f(x)=z$ but I am not sure how to show this. From the reverse triangle inequality $$-|f(x)-f(y)|+|x-y|\leq 0.1|x-y|\implies |f(x)-f(y)|\geq 0.9|x-y|$$ im not sure if this helps.
  47. mingyz0403

    Engineering Machine Analysis -- gripping pliers

    I know that moment is distance vector x force vector x the degree between them. I understand it uses the moment about A to solve for the unknown force R. I don’t understand why it use Rx1.2m and why the perpendicular distance between A and R is 1.2m. could anyone please explain why? Many...
  48. Haorong Wu

    Classical Books about tensor analysis just good enough for physics

    Hi. I am looking for a book about tensor analysis. I am aware that there have been some post about those books, but I wish to find a thin book rather than a tome but just good enough for physics, such as group theory, relativistic quantum mechanics, and quantum field theory. I am reading...
  49. JackHolmes

    A Help with the Derrick scaling argument and topological solitons

    I have been reading Manton & Sutcliffe for some time now and can't quite wrap my head around something. If you take the Hopf invariant N of a topological soliton ϕ then its Skyrme-Faddeev energy (which I hope I've gotten right up to some constants) E=∫∂iϕ⋅∂iϕ+(∂iϕ×∂jϕ)⋅(∂iϕ×∂jϕ) d3x satisfies...
  50. Boltzman Oscillation

    What approach should be used when solving a circuit?

    I am close to graduating as an EE major but I have never been able to organize a step by step method on analyzing a circuit. It seems to me that every time I am trying to analize a circuit I end up with a bunch of equations and nothing more. I know that I should: 1. Know what I am solving for...
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