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).

View More On Wikipedia.org
Recent contents Top users
  1. Tirijazzmanray

    Statics problem -- Stability analysis of a slab resting on an incline

    Dear colleagues: My name is Ignacio Pérez, a mining engineering student from Spain. I am trying to analyze the stability of a slab with rounded edges against a toppling failure. The slab can be considered rectangular-prism shaped (I provide a rectangular section in the enclosed picture) but the...
  2. F

    Find the current using Nodal Analysis

    Homework Statement Find i using Nodal Analysis. Homework Equations V = I * R The Attempt at a Solution solve (1) , (2) , and (3) to find V1 , V2 ,and V3 V1 = 50/3 = 16.67 V V2 = 80/3 = 26.67 V V3 = 40 V 40 - 80/3 = 5i i = 2.667 A However , the correct answer is 1.522 A .. I don't know...
  3. G

    Prove that this function is holomorphic

    Homework Statement Prove that the function ## f(z)= 1/\sqrt{2}(\sqrt{\sqrt{x^{2}+y^{2}}+x}+i*sgn(y)\sqrt{\sqrt{x^{2}+y^{2}}-x})## is holomorphic on the domain ## \Omega = \left \{ z: z \neq 0, \left | \arg{z} \right | <\pi\right \} ## and further that in this domain ##f(z)^{2} = z. ##...
  4. Sullen_and_Sordid

    Need Advice - Six Months to Prepare for Analysis

    I have six months before I go back to school (after being out of school for over 5 years - ex engineering student). I'll be pursuing a BA in Mathematics and Philosophy - I will have to take either Abstract Algebra or Real Analysis 1 for my first quarter. Which class would you guys recommend I...
  5. boneh3ad

    A Interpreting a paper on spectral analysis

    I do a fair bit of spectral analysis of time series in my research, but to date my experience in the topic is almost exclusively from an engineering perspective rather than the more statistical approach. Of course I am aware that ultimately they are equivalent, but it means that my familiarity...
  6. D

    Energy analysis of a particle moving in a shrinking circle

    Homework Statement A particle of mass m is moving on a frictionless horizontal table and is attached to a massless string, whose other end passes through a hole in the table, where I am holding it. Initially the particle is moving in a circle of radius ##r_0## with angular velocity ##w_0##, but...
  7. Mr Davis 97

    Real Analysis: Prove Upper Bound of Sum of Bounded Sequences

    Homework Statement Suppose that ##( s_n )## and ## (t_n)## are bounded sequences. Given that ##A_k## is an upper bound for ##\{s_n : n \ge k \}## and ##B_k## is an upper bound for ##\{t_n : n \ge k \}## and that ##A_k + B_k## is an upper bound for ##\{s_n + t_n : n \ge k \}##, show that ##\sup...
  8. A

    Engineering Understanding Clamper Circuits: Analysis, Voltage Shifts, and Capacitor Behavior

    Hello everyone, I hope you could help me with the analysis of this circuit. the output voltage is supposed to be similar to the input but shifted upwards by 20V, so basically it's between 0 and 40V... but why? I mean when the input is 20V, the diode is reverse biased... and the capacitor...
  9. S

    Prove a statement using Peano's Axioms

    Homework Statement Let, m, n be natural numbers and S(n) the succesor of n. If S(n)*m = nm + m Prove that m*S(n) = nm + m Homework Equations The Attempt at a Solution
  10. M

    A Robustness of time series analysis

    I have a time series model constructed by using ordinary least square (linear). I am supposed to provide some general comments on how one would improve the robustness of the analysis of a time series model (in general). Are there any general advice apart from expanding data, making it more...
  11. Math Amateur

    MHB Understanding Difference b/w Derivative & Differential in D&K Definition 9.1.3

    I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on \mathbb{R}^n" ... ... I need some help with another aspect of Definition 9.1.3 ... Definition 9.1.3 and the relevant accompanying text read as follows...
  12. Math Amateur

    I Multivariable Analysis ....the derivative & the differential

    I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on ##\mathbb{R}^n##" ... ... I need some help with another aspect of Definition 9.1.3 ... Definition 9.1.3 and the relevant accompanying text read as follows: In the...
  13. C

    MHB Prove this proposition 2.1.13 in Induction to Real Analysis by Jiri Lebel

    Dear Everybody, I need some help with seeing if there any logical leaps or any errors in this proves. Corollary 1.2.8 to Proposition 1.2.8 states: if $S\subset\Bbb{R}$ is a non-empty set, bounded from below, then for every $\varepsilon>0$ there exists a $y\in S$ such that $\inf...
  14. C

    MHB Prove this thereom 1.2.6 v in Introduction to Real Analysis by Jiri Lebl

    Prove this Proposition 1.2.6 v in Introduction to Real Analysis by Jiri Lebl Dear Everybody, I need some help with seeing if there are any logical leaps or errors in this proof. The theorem states: $A\subset\Bbb{R}$ and $A\ne\emptyset$ If $x<0$ and A is bounded below, then...
  15. sparkie

    Nodal Voltage Analysis with dependent sources

    Homework Statement All the data is on the sheet. I named the nodes V1 to V4, however I'm primarily evaluating in terms of V3 and V4. The x=V3 and y=V4 are for the systems solving I'm using. I've looked and looked at this problem, and seem to be hung up, but I suspect it is going to be on my...
  16. Math Amateur

    MHB Multivariable Analysis .... Directional and Partial Derivatives .... D&K Propostion 2.3.3 ....

    I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with an aspect of the proof of Proposition 2.3.2 ... ... Duistermaat and Kolk's Proposition 2.3.2 and its proof read as...
  17. Math Amateur

    I Multivariable Analysis .... Directional & Partial Derivatives

    I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with an aspect of the proof of Proposition 2.3.2 ... ... Duistermaat and Kolk's Proposition 2.3.2 and its proof read as...
  18. Math Amateur

    MHB Help with D&K Lemma 2.2.7 (Hadamard) Proof: Qs on Continuity of \phi_a

    I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with another aspect of the proof of Lemma 2.2.7 (Hadamard...) ... ... Duistermaat and Kolk's Lemma 2.2.7 and its proof...
  19. Math Amateur

    I Multivariable Analysis: Another Question Re: D&K Lemma 2.2.7

    I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with another aspect of the proof of Lemma 2.2.7 (Hadamard...) ... ... Duistermaat and Kolk's Lemma 2.2.7 and its proof...
  20. Math Amateur

    MHB The Differentail and the Derivative in Multivariable Analysis .... ....

    I am reading the book "Several Real Variables" by Shmuel Kantorovitz ... ... I am currently focused on Chapter 2: Derivation ... ... I need help with an aspect of Kantorovitz's definition of "differential" ... Kantorovitz's Kantorovitz's definition of "differential" reads as follows...
  21. Math Amateur

    I The Differentail & Derivative in Multivariable Analysis ....

    I am reading the book "Several Real Variables" by Shmuel Kantorovitz ... ... I am currently focused on Chapter 2: Derivation ... ... I need help with an aspect of Kantorovitz's definition of "differential" ... Kantorovitz's Kantorovitz's definition of "differential" reads as follows: Is the...
  22. M

    Confused about choosing current direction in nodal analysis

    Homework Statement The problem states: Determine the voltage labeled v in the following circuit: https://ibb.co/hz0Q37 The variable is the voltage across the 2 ohm resistor. The ground I chose for this example is located in the center of the circuit. Homework Equations V=IR I guess. The...
  23. Oklid

    Question about Absolute Dependent Motion Analysis

    Homework Statement [/B] Find accelerations of these masses and the pulley are weightless. Homework Equations [/B] Sb+Sc=Length of the second rope (L2) The Attempt at a Solution [/B] Just like I did, I placed all variables from datum to the masses. In the second system, I write the...
  24. physea

    B Analyzing open steady flow systems with SFEE vs. Rankine cycle analysis

    Hello I have a point that I don't understand. In open steady flow systems, we use SFEE, where there's a term W in addition to a term PV, which are different things. When we analyse a cycle like Rankine, we always consider either W or PV, but not both. I also think that W=PdV always. Why that...
  25. T

    Finding the min value using the derivative

    Homework Statement Hi I'm having a trouble with finding min value of given function: f(x) = sqrt((1+x)/(1-x)) using derivative.First derivative has no solutions and it is < 0 for {-1 < x < 1} when f(x) is given for {-1 < x <= 1}. For x = - 1 there is a vertical asymptote and f(x) goes to +...
  26. L

    Proof of uniqueness of limits for a sequence of real numbers

    Homework Statement [/B] The proposition that I intend to prove is the following. (From Terence Tao "Analysis I" 3rd ed., Proposition 6.1.7, p. 128). ##Proposition##. Let ##(a_n)^\infty_{n=m}## be a real sequence starting at some integer index m, and let ##l\neq l'## be two distinct real...
  27. Photonino

    I Why do systematic uncertainties disappear using ratios?

    Hello, I often hear the phrase "Well, since you are taking a ratio bin-by-bin, you don't have to care about the luminosity syst. uncertainty and the trigger efficiency syst. uncertainty". I think I understand qualitatively why this is the case (It cancels out in the ratio, since both...
  28. J

    Applied Numerical Analysis book question

    So in my future numerical analysis class the recommended book i liked the most was Numerical mathematics by Quarteroni : https://books.google.pt/books/about/Numerical_Mathematics.html?id=m-bHBAAAQBAJ&printsec=frontcover&source=kp_read_button&redir_esc=y#v=onepage&q&f=false Since i like this...
  29. L

    MHB [Complex Analysis] Singularity in product of analytic functions

    Suppose f,g:ℂ→ℂ are analytic with singularities at z=0. I was wondering whether f(z)^2 or f(z)g(z) will have a singularity at z=0? For each, can you give me a proof or a counterexample?
  30. Baris Kalfa

    Physics Over what field I'm going to choose

    Hello dear members, I couldn't figure out whether I should post this in the academic guidance or career guidance section, yet the latter sounded more convenient for my situation. I have also seen many similar threads but I believe everybody has different thoughts& aspirations as we all know...
  31. C

    How do I fix this galactic source analysis using python?

    Homework Statement This is related to Astronomy & python . I am trying free-up sources on TS map on a galactic source with python script. But when I run the script, at the end of the process, I get the following run time error. Traceback (most recent call last): File "find_new_sources.py"...
  32. IAMJackal

    Analysis of DE Pool Filter as Steam Pressure Vessel

    Have built a 55 gallon DIY steamer from a DE pool filter. The pool filter is made from .06 inch stainless steel and was rated for an operating pressure of 50 PSI. As a pool filter, the vessel regularly operated at pressures of 10-15 PSI, and as much as 25-30 PSI when it needed cleaning. Have...
  33. M

    B Radian unit -- Why neglected in dimensional analysis?

    Why radians are usually neglected in dimensional analysis?
  34. Math Amateur

    MHB Multidimensional Real Analysis - Duistermaat and Kolk, Lemma 1.1.7 ....

    I am reading "Multidimensional Real Analysis I: Differentiation by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 1: Continuity ... ... I need help with an aspect of Lemma 1,1,7 (ii) ... Duistermaat and Kolk"s Lemma 1.1.7 reads as follows: In the above Lemma part (ii)...
  35. G

    Engineering How Does Adjusting Parameter B Affect Servo Motor Friction and System Damping?

    Homework Statement 2. Homework Equations [/B] I'm studying a mathematical behaviour of a servo motor and I need some help to understand it. The output signal is \$\beta (t)\$, representing the angle rotated by the axis at instant t, in relation to the equilibrium position. On the servomotor...
  36. mertcan

    Finite element analysis node displacement

    Hi, I would like to ask why center of element displacement is always estimated with polynomial equation involving nodes displacement (like in attachment/picture)? Also I know that if nodes' number increase for an element then displacement of center of element is estimated with higher order...
  37. M

    Ansys Workbench Static Structural Analysis

    Hello Guys I am New here on the foum Well i am simulating a static structure (Picture attached) on ansys and til now i have a result divergence when i apply different forces. i guess my loads and fixed supports aren't well defined. Please Help i know it s a bit long but please give it some time...
  38. Math Amateur

    MHB Complete Metric Spaces .... Conway, Analysis, Section 5.2 ....

    I am reading John B. Conway's book: Ä First Course in Analysis and am focused on Chapter 5: Metric and Euclidean Spaces ... and in particular I am focused on Section 5.2: Sequences and Completeness ... I need some help/clarification with Conway's defintion of completeness of a metric space ...
  39. billyray

    Help with Node Analysis Circuit Problem

    Homework Statement I have a circuit which I have a current through labelled I on circuit. I have -9.18 +j17.31. we agreed this was correct. I have a node analysis problem but cannot find the correct answer. I feel my method and my maths may be off but would like some advice if possible...
  40. T

    Intro to analysis, intro to real analysis I, numerical analysis

    Hello, Is there a difference from these courses, or are they the same course with different names? I need to know which one to choose for the upcoming semester... Intro to Analysis, Intro to Real Analysis I, and Numerical Analysis Thank you, Tracie
  41. E

    I What does the one-way analysis of variance illustrate in this case?

    Hello, I was reading an example where correlation between two features is to be measured. The two features are drive-wheels and price. The drive-wheels feature has three values: 4wd, fwd, and rwd. Then the example went on to calculate the F-score without much details using Python. Without going...
  42. billyray

    Can Mesh Analysis with Three Loops Solve a Four-Loop Circuit?

    Homework Statement I have a circuit that I am to analyse and find I. I am told to use an excel matrix sheet given to me to solve 3 unknowns. I have 4 loops so this is a problem. I have made an attempt using three loops and referred to a previous thread on here for some help. It says I can do...
  43. Noe Wong

    Algodoo and Physics Analysis of Interactions

    Homework Statement [/B] I have created a very simple Rube Goldberg device in Algodoo, and I need to analyze 3 correlating steps within it, using physics descriptives and equations. My primary focus is the ball as it hits the windmill, which I need to describe and calculate its velocity at that...
  44. T

    I Is simulation considered a type of quantitative analysis?

    Hello, I've been asked to talk about a time where I have used quantitative analysis. I once used simulation of the solar system to find out more about things like close approaches, and Gladmans criteria I was wondering if simulation is considered a quantitative method of analysis and if the...
  45. S

    I Norm of a Functional and wavefunction analysis

    Hi, I am working on a home-task to analyse the properties of a ODE and its solution in a Hilbert space, and in this context I have: 1. Generated a matrix form of the ODE, and analysed its phase-portrait, eigenvalues and eigenvectors, the limits of the solution and the condition number of the...
  46. lichenguy

    Dimensional analysis problem

    Homework Statement A block of mass ##m = 1.00 kg## is being dragged through some viscous fluid by an external force ##F = 10.0 N##. The resistive force can be written as ##R = -bv##, where ##v## is the speed and ##b = 4.00 kg/s## is a phenomenological constant. You may ignore gravity (we...
  47. mishima

    Butane Combustion Analysis Demo for a High School Chemistry Class

    Hi, I'm a high school chemistry teacher trying to develop a lab experience demonstrating combustion analysis. This is usually something we go through theoretically during discussion of percent composition and empirical formula. I'd like to actually perform one. I was wondering if this could...
  48. evinda

    MHB Questions about analysis of algorithm

    Hello! (Wave) The following algorithm is given: And it says the following: First of all, at the first line do they mean that the content of j is i? About the second line, why don't we subtract the polynomial $f[i] \cdot u \cdot h \cdot X^i $ from $(f[0], \dots, f[d'])$? Is there then...
  49. D

    MHB Sensitivity Analysis model for omnivory systems (coupled system of ode's)

    \chapter{Stage Structured Omnivory Model} %\indent For our initial computations we will be using a standard Lotka-Volterra omnivory model which was developed to analyze the population and community level dynamics. The model depicted below (figure 1.4) is a standard Lotka-Volterra model of...
  50. W

    Problem involving Source Transformation and Nodal Analysis

    Homework Statement Homework EquationsThe Attempt at a Solution I have attempted and completed all questions. However, I am now trying part (b) with transforming the voltage source into a current source. I am unable to work out the current and I am unsure what to do next. I have included my...
Back
Top