understanding

  1. A

    Understanding the rigorous meaning of fluid.

    I'm taking my first course on Fluid Mechanics. My book (my books means the book which I'm reading not the one I have written:) ) says that the definitions of fluids like Fluid is something that flows or Anything apart form solid is a fluid are somewhat vague and therefore the rigorous...
  2. B

    Understanding a specific Chebyshev integral

    I have a situation where I'm trying to understand the physics of a cooling tower. Part of the solution for the model I'm working with involves an integral: C = \int_{T_{low}}^{T_{high}} \frac{1}{\left(h' - h_a\right)} dT where h' is a slowly varying, monotonically increasing function with...
  3. A

    can anyone help me with this understanding of quintic equations?

    this is the context: I don't get this part: Can anyone help me with understanding this part of the sentence? I really need it. I don't get the writer's intention. what is it mean that solutions for every single coefficient? can you rewrite this in another word so I can understand it? I...
  4. M

    Check my understanding (line integrals)

    Ok so if I'm understanding correctly, line integrals integrate over a curve (C) unlike over a region on the x or y axis like a regular integral would. So you have a curve represented by the vector function r(t) = C = x(t) i + y(t) j let's take a region along that curve that can be defined by...
  5. N

    Need help understanding Locus

    Recently, there's been a lot of suspended classes so topics were rushed, and I'm a 100% sure this wasn't discussed. Basically, the question is "Find the locus of points three times as far from (0,4) as from (2,0)". I tried searching up a similar question online, but couldn't find any. From...
  6. W

    I want a deep understanding of Limits, Differentiation and integration

    Hello :) I'm a teacher in electronics department, I did a light basics of limits, differentiation and integration last semester in just solving problems. But I want a deep understanding of what these topics actually are? Where can I use limits? Is limits still valuable these days? What...
  7. R

    Computational nonlinear system equations understanding.

    Here is a snippet of some mathematical article: For a general, nonlinear dynamic system with parameters $\boldsymbol c$, running from time $0$ to time $T$ $\boldsymbol z\left(t+1\right)\boldsymbol=\boldsymbol s\left(\boldsymbol z\left(t\right),\boldsymbol u\left(t\right),\boldsymbol...
  8. D

    Not understanding simple factorization

    I'm not understanding how this simple factorization works...I know how to solve it, but it is making no sense to me. 3p+3 -------- 3 I know the answer is p+1, but I don't understand how factoring 3p+3 works. My instructions say to rewrite as 3p + 1(3), then factor out the common...
  9. B

    Vector Spaces (Understanding the Basics)

    Hello everyone, I'm studying for the Math GRE subject test and I'm currently going over Linear Algebra. I'm carefully rereading my course book "Linear Algebra Done Right" By Sheldon Axler (Third Edition). I have a few questions in regards to the fundamental concepts: Going over the...
  10. H

    understanding quotient topology

    Let $h$ be a (real-valued) continuous function on some closed interval $[c,d].$ Let, $\lambda =\min_{[c,d]}h$ and $\gamma = \max_{[c,d]}h$ . Also, $h$ can be considered as a surjective map (onto) from $[c,d] \rightarrow [\lambda,\gamma]$. **Question** How can one show that if $[c,d]$ has the...
  11. A

    Deeper Understanding of Limit Proofs

    In an "N epsilon proof of sequence convergence", we tend to assume the limit. For example: If we were proving that the sequence 1/n as n goes from 1 to infinity, converges to 0, we would start with |1/n−0|<ϵ. As you can see we initially assume that the limit is 0. However, what if we thought...
  12. H

    Understanding ring homomorphisms

    So trying to study chapters on ring homomophisms and integral domains, and there is this one problem in the book where I just don't get how to show the kind of problems yet (as I'm not yet used to it); the problem is: Show that the matrices $R=\begin{pmatrix} a & b \\ 0 & a \\...
  13. J

    need help understanding proof

    Let v1,...,vn be vectors in Rn. Then {v1,...,vn} spans Rn if and only if, for the matrix A = v1 v2 ··· vn , the linear system Ax = v is consistent for every v ∈ Rn. I understand the proof but I'm unsure with how the word "consistent" is used, does it mean v should be the same for each...
  14. M

    Understanding of capacitance of parallel transmission wire

    Hi, Can someone have a look through my solution and give me some feedback about my understanding of the problem attached. Thanks
  15. C

    Understanding of the Perlin Noise

    Hi there! I'm trying to understand how does the Perlin Noise work and having a problem with it. I have found this kind of tutorial Building Up Perlin Noise and can't understand the next paragraph I'm not sure whether the problem is in my poor English knowledge or in my poor math...
  16. W

    Intuitive understanding of how slope is the inverse of area under the curve

    Hello, I'm trying to gain an intuitive understanding regarding how the area under a function is the opposite/inverse of the slope of that function. I am familiar with the ideas that differentiating a function determines the slope and integrating a function determines the area under the...
  17. S

    Predictive modelling and understanding how important your last data point is

    Hi all. Using this as a simple example – There is a fairly basically computer game called Mr Jump. The aim of the game is to complete the level by finishing the course. Your game performance is measured in percentage terms, if you complete the level you get to 100%. If you “die”...
  18. T

    Trouble understanding inverse of fractional functions

    I've developed a model for finding inverse functions, as demonstrated in the image enclosed below: https://i.stack.imgur.com/flqlO.png I know there's a method for working out an inverse function by swapping out x and ys, but the model I've developed makes more sense to me from a visual...
  19. S

    Understanding Absolute Viscosity - shearing stress

    Hi everyone, I have found information about Absolute viscosity: Coefficient of absolute viscosity is a measure of internal resistance. Dynamic (absolute) viscosity is the tangential force per unit area required to move one horizontal plane with respect to an other plane at an unit velocity...
  20. S

    Help with Understanding/Solving floor function #1

    Hey, So I'm in pre-calculus class in my B.Sc. Computer Science degree, and I have to say that I am not the brightest sun-shine in the world when it comes to math, so I would love for you guys to help me out in times of need! So we started with floor / ceiling functions, and the professor...