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

    I Order of "Extracted Factors" in SPSS Factor Analysis

    Hi All, I am doing some FA on SPSS. I entered 9 columns from an Excel file into SPSS. I am just not sure of how the order of the initial columns corresponds to the order of the components that have been extracted; specifically, in the "total Variance Explained" section of the outputs. Would...
  2. G

    Solving Force Analysis: Understanding Vertical and Horizontal Forces

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  3. R

    Dimensional Analysis Buckingham Pi Theorem

    This is the problem I'm currently working on: The pi groups I identified were h1, h2, d, D, g, t, and velocity, but when I looked at the solution, it selected Δh, D, t, ρ, d, ϒ, h1, with no explanation why those variables are needed. If I was solving with the Bernoulli equation, I wouldn't...
  4. Oats

    Why is a finite sub-cover necessary for proving continuity implies boundedness?

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  5. W

    A Testing Fit in Latent Class Analysis

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  6. maistral

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  7. C

    Analysis Are there any recommended Complex Analysis books for advanced students?

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  8. F

    Preparing for Vector Calculus: What Topics Should You Focus On?

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  9. O

    Schools Math Grad school with only one real analysis course?

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  10. W

    A References Request: Factor Analysis on Non-Continuous Variables

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  11. Jianphys17

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  12. Mohamed_Wael

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  13. K

    Fluid Dynamics: Dimensional Analysis and important forces

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  14. M

    Analysis Looking for a rigorous analysis textbook

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  15. binbagsss

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  16. Nikhil Rajagopalan

    Error Analysis of wall thickness

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  17. Mohamed_Wael

    Can I use symmetry in modal analysis in FEA

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  18. N

    Analysis Good books on linear algebra and real/complex analysis?

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  19. awholenumber

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  20. B

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  21. B

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  22. O

    Courses Is undergrad analysis more difficult than calculus 1&2?

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  23. NoahCygnus

    Motion analysis of an accelerating wedge and a block

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  24. Ridzuan

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  25. P

    Carnot Cycle: Analysis of Energy Exchange

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  26. S

    B Real Analysis: Expanding a Function at Different Points

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  27. A

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  28. A

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  29. jedishrfu

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  30. O

    Alternative to Mie Theory for Analysis of Homogenous Sphere

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  31. O

    Suggestions for a Power System Analysis book?

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  32. W

    Calculus Vector Analysis and Cartesian Tensors by Bourne and Kendall

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  33. Radiosan

    Uncertainty analysis of 2 port measurement

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  34. S

    I Difference between complex and real analysis

    Hello! I see that all theorems in complex analysis are talking about a function in a region of the complex plane. A region is defined as an open, connected set. If I am not wrong, the real line, based on this definition, is a region. I am a bit confused why there are so many properties of the...
  35. S

    I Proof of Harmonic Function Infinitely Differentiable

    Hello! I have this Proposition: "A harmonic function is infinitely differentiable". The book gives a proof that uses this theorem: "Suppose u is harmonic on a simply-connected region G. Then there exists a harmonic function v in G such that ##f = u + iv## is holomorphic in G. ". In the proof...
  36. C

    MHB Numerical Analysis problem Newton's method

    Can anyone help in the solution of this problem? how can i determine the zero x*??
  37. H

    Dimensional analysis: Energy Transfer

    Homework Statement There is a paper in 1973: T. Kushida, "Energy Transfer and Cooperative Optical Transitions in Rare-Earth Doped Inorganic Materials I. Transition Probability Calculation", J. Phys. Soc. Jpn. 1973, 34, 1318-1326. DOI: http://dx.doi.org/10.1143/JPSJ.34.1318 that explains the...
  38. S

    Proof of Degree <= 1 for Entire Function f

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  39. vktsn0303

    A Understand Convolution, Singularity, Kernel, etc: Math Reading Guide

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  40. C

    I Participant non-compliance: How to include data in analysis

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  41. G

    Courses Which version of Real Analysis to take?

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  42. S

    Ansys workbench transient analysis

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  43. A

    Using dimensional analysis to create dimensionless equation

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  44. davidfam

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  45. PsychonautQQ

    Prove: f_n Convergence Implies f(x)=c

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  46. T

    Another Improper Integral Using Complex Analysis

    Homework Statement $$\int_{-\infty}^\infty \space \frac{cos(2x)}{x-3i}dx$$ Homework EquationsThe Attempt at a Solution $$\int_{-R}^R \space \frac{e^{2ix}}{x-3i}dx + \int_{C_R} \space \frac{e^{2iz}}{z-3i}dz = 2\pi i\sum\space res \space f(z)$$ Then using Jordan's Lemma, as ##R\to\infty## the...
  47. T

    Improper Integral Using Complex Analysis

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  48. Cocoleia

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  49. Cocoleia

    Using Laplace to solve circuit analysis

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  50. D

    Engineering Simple DC Circuit Analysis with Transistor

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