Approach Definition and 545 Threads

I would appreciate some advice from "old hand" heat exchanger guys regarding "good design practice" on approach temperature for tube and shell . Here's what's up: A friend works in a solar plant. Oil is heated in parabolic reflectors and used to preheat feedwater for a traditional...

Newton and Leibniz both had a method of differentiating. Newton had fluxions and Leibniz had something that resembles the modern derivative. Historically, does anyone know how they went about calculating the derivative?

Greetings! Can anyone tell me a little bit about the book Integral, Measure and Derivative: A Unified Approach by Shilov? Is it suitable for self-study? I am wishing to study the basics of measure theory. I will be using the text alongside Kreyszig's Funcational Analysis. Having already...

I am starting to deal with optomechanical systems as part of my work, and am faced with what seems to be an uncomplicated problem, however I'm ashamed to admit that I am having great difficulty getting to grips with it. I'd like some pointers and/or advice as to how to go about solving these...

Homework Statement Use the Laplace transform approach to find the renewal function for a renewal process with interrenewal p.d.f. as follows: g(x) = (c^2)xe^(-cx) , x > 0 The Attempt at a Solution M*(s) = G*(s)/(1-G*(s)) where M*(s) and G*(s) denote laplace transforms I have that G*(s) =...

1. I gave myself the task of solving the indefinite integral of an exponential function whose base is any real valued constant and whose power is a logarithm of the variable I am integrating over. Now my question is not how to solve it, but rather, whether or not my approach was efficient. I've...

My end goal is to solve for G(m) in terms of the other functions, but first I have to solve the DE : \frac{d}{dm}[F(m) G(m)] = (\frac{d}{dm}F(m)) D(m). What I've done is to say (using integration by parts) F(m) G(m) = F(m)D(m) - \int F(m) (\frac{d}{dm}D(m)) dm. This is one method I...

Homework Statement A point charge q1=5μC is held fixed in space. From a horizontal distance of 6.00 cm, a small sphere with mass 4g and charge 2μC is fired toward the fixed charge with an initial speed of 40.0 m/s. Gravity can be neglected. What is the acceleration of the sphere at the...

I have sought information about different approaches(fields) to neuroscience and how they differ in terms of understanding how the brain works. I'm interested to learn more about neurobiophysics, computational neuroscience and engineering perspectives. In engineering especially about brain...

So say I have an arbitrary function and I want to know it's limit as x,y approaches 0. I could test what happens when the x-axis approaches 0, y-axis as it approaches 0 but there are some functions where I'm told that I also need to test what happens when y=mx approaches 0, and then y=x^2 and...

There isn't a specific problem that's making me stuck, but I was hoping if someone could point me in the right direction here. I've looked up the topic online, but most of what I could find was through another approach or very unclear. The book I'm using also does not use the method my professor...

(r^2 \nabla^2 - 1) X(r,\theta,z) + 2 \frac{\partial}{\partial \theta} Y(r,\theta,z) = 0 (r^2 \nabla^2 - 1) Y(r,\theta,z) - 2 \frac{\partial}{\partial \theta} X(r,\theta,z) = 0 any suggestions are greatly appreciated :)

I'm currently teaching myself intermediate mechanics & am really struggling with the d'Alembert-based virtual differentials derivation for E-L. The whole notion of, and justification for, using 'pretend' differentials over a time interval of zero just isn't sinking in with me. And I notice...

Can someone explain to me the basic process involved in an approach to critical with a nuclear reactor. I understand that you basically start with the rods all the way in and bring them out, while taking counts - waiting for them to stabilize. I understand with the penultimate method, you...

I accidentally happened upon this photo while researching some things about the 1986 Chernobyl nuclear disaster and I freaked out! How did this worker get so close to this mass of melted nuclear fuel in the basement of Chernobyl without receiving several lethal doses of radiation? This mass of...

Advanced Calculus of Several Variables, Edwards, problem II.4.1: Find the shortest distance from the point (1, 0) to a point of the parabola y^{2} = 4x. This is the Lagrange multipliers chapter. There might be another way to solve this, but the only way I'm interested in right now is the...

Homework Statement Find the frequency of small oscillations around the minimum of the potential U(x)=1-e^(-x^2) Homework Equations Force is the negative of the gradient of the potential... The Attempt at a Solution Given the problem statement bit, "around the minimum," I take this...

Hello all, and thanks again to all the help I've been getting with this book. This is a two part problem in Advanced Calculus of Several Variables, C. H. Edwards Jr. I have the first part and the second part should be easy, but I find I'm stumped. Since the second part builds on the solution of...

Author: Jorge José and Eugene Saletan Title: Classical Dynamics: A Contemporary Approach Amazon Link: https://www.amazon.com/dp/0521636361/?tag=pfamazon01-20

Author: Morris Kline Title: Calculus: An Intuitive and Physical Approach Amazon link: https://www.amazon.com/dp/0486404536/?tag=pfamazon01-20 Prerequisities: High-School Mathematics Level: Undergrad Table of Contents: Why Calculus? The Historical Motivations for the Calculus The...

Author: Donald McQuarrie, John Simon Title: Physical Chemistry: A Molecular Approach Amazon Link: https://www.amazon.com/dp/0935702997/?tag=pfamazon01-20

Author: What Is Mathematics? An Elementary Approach to Ideas and Methods Title: Richard Courant Amazon Link: https://www.amazon.com/dp/0195105192/?tag=pfamazon01-20 Table of Contents: Preface How to use the book What is mathematics? The natural numbers Introduction Calculations with...

Author: Jerome H. Keisler Title: Elementary Calculus: An Approach Using Infinitesimals Download Link: http://www.math.wisc.edu/~keisler/calc.html Prerequisities: High School Mathematics Table of Contents: Introduction Real and Hyperreal Numbers The Real Line Functions of Real...

As the title says, why diesel engines produce less CO2 than gasoline engines and how is this related to the more torque and less power in diesel engines? PLEASE only a fluid dynamics or thermodynamics approach. Spent hours on searching to find why petrol engines produce more CO2 emissions...

This is not a re-post of my other thread in general section, so please understand. First, a brief description of myself: I'v gotten my associates degree in Automotive Technology/Repair, with perfect scores. ASE certified. But I have always been an aspiring Mechanical Engineer, with assisted...

Hello Everybody, Carroll introduces in page 106 of his book "Spacetime and Geometry" the variational method to derive the geodesic equation. I have a couple of questions regarding his derivation. First, he writes:" it makes things easier to specify the parameter to be the proper time τ...

I feel overwhelmed with something that should be capable of being explained very simply I think. Let's say you're getting thrown random questions involving surfaces/shapes creating boundries in ℝ3. Whats your step by step process in finding whether you want to do a double integral versus...

I want to solve: y'=\frac{(1+y)^2} {x(y+1)-x^2} What I tried: I have no basis to think that y' is positive or negative in some domain, but if I do, I can write: x'(y)=\frac {x(y+1)-x^2}{(1+y)^2}=\frac{x}{(1+y)} +\frac{x^2}{(1+y)^2} and then I can substitute z=\frac{x}{(1+y)} And I get the...

Thought I'd share this article w/ everyone since I found it very interesting. Imagine being able to regulate stem cells without the need for genetic manipulation or growth factors etc. Small molecules are so much easier to work with. Very interesting...

Maybe this question better belongs to programming section but I feel it has mathematics related doubt. I want an intuition on how iterative and recursive approaches are different. Just look at the simple arithmetic progression. nth term is given as a + n.d. This can be derived using both...

Hi, I developed a simple ad-hoc client/server chat program, however the design isn't exactly scalable since the addresses are hard coded and one of the clients is also the server. So i wanted to write a dedicated server, to which multiple clients could connect and chat, like irssi.. how...

I have always struggled in understanding probability theory, but since coming across the measure theoretic approach it seems so much simpler to grasp. I want to verify I have a couple basic things.So say we have a set χ. Together with a σ-algebra κ on χ, we can call (χ,κ) a measurable space...

Homework Statement Suppose H is a normal subgroup G and H has order 2. Show that H is contained in the center of G. Homework Equations Definitions. H is a normal subgroup of G if for all h in H and g in G, ghg-1 is in H. The center of a group G is Z = {z in G | zx = xz for all...

I'm reading the Wikipedia page for the Dirac equation I am not sure how one gets a new \rho and J^\mu. How does one do to derive these two? And can anyone show me why the expression for density not positive definite?

Hi. I'm taking diff eq course this semester and the text is the latest Boyce DiPrima diff eq with boundary value problems. The first test is mostly proofs on theorems about continuity, like the Heine-Borel theorem, Bolzano-Weierstrauss theorem, etc. The book doesn't go into much details about...

Homework Statement A horizontal stick of mass m has its left end attached to a pivot on a plane inclined at an angle theta, while its right end rest on top of a cylinder also of mass m which in turn rests on the plane as shown. The coefficients of friction at both points is (mu). Sorry I...

This is my first semester in graduate school and I have been looking diligently for a professor to work with. Recently, I came across a very unique opportunity and I would like to seek help from other PhD Students and/or Professors: This evening, I was talking to a professor about research...

Suvat -- Two cars approach each other on a straight road Homework Statement Two cars approach each other on a straight road. Car A is moving at 16m/s and car B at 8m/s. When they are 45m apart both drivers apply their brakes. Car A slows down at a rate of 2m/s^2 while car B slows down at...

Homework Statement I am trying to understand the equation U-L<ε as part of a proof. I have attached the original problem, [102], as well as the hints page. Homework Equations \sum\limits_{v=1}^n M_v(x_v-x_{v-1})-\sum\limits_{v=1}^n m_v(x_v-x_{v-1})<\epsilon The Attempt at a Solution...

Homework Statement The magnitude of $$B$$ is increasing at $$100T/s$$ and the solenoids (the source of the induced EMF) is infinitely long. I want to find the current through the resistors The Attempt at a Solution I basically used the same idea, but I used Mesh's method and I decided to...

I'm having trouble finding the correct approach to my (fairly simple) example. Let's say I have months of data for log-in times of a certain website. The data has been selected and cleaned such that I have a list of Date_Time for each log-in. Now, suppose I wanted to predict the log-ins...

Pluto's changes as it makes its closest approach? I've seen the photos from Hubble showing the seasonal color changes on Pluto. Just wondering if the addition of the extra atmosphere as it makes its closest approach to sun, has changed the any of the colors on Pluto, in particular the black...

A positive charge +Q is fixed at a point A on line AC. Another positively charged particle of mass m and charge +q is projected from a point B with velocity u. The point C is at large distance from A and B is situated at distance d perpendicular from point C from AC Find the minimum distance...

Where can i find something on the calculation of the emission spectrum with the semiclassical approach? Thanks

My logic is that if I am to lose weight the mass of material entering my body must be less than the mass of material exiting my body. Never mind Calories. My procedure is this, before each meal I weigh myself. If I weigh less than my immediate goal then I eat, if not then I don't. After each...

Homework Statement Question: Blue light of wavelength 485.6nm from a star is incident normally on a diffraction grating. The light is diffracted into a number of beams, as shown in Fig 5.4.(attached) The angular separation of the two second-order beams is 45.72 degrees. Calculate the...

1. What is the probability of tossing at least three 'heads' if a fair coin is tossed four times? 2. Drawing a tree Hey guys, I was just wondering...is there a mathematical approach for me solving this question without drawing an event tree? Reason I ask is so that it saves time...

Homework Statement A transverse wave on a cord is given by D(x, t) = 0.19sin(2.9x - 35t), where D and x are in m and t is in s. 1) At t = 8.6*10^-2 s, what is the displacement of the point on the cord where x = 0.62 m? 2) At t = 8.6*10^-2 s, what is the velocity of the point on the cord...

Richard Feynman's "sum-over-paths" approach to quantum mechanics? I am in terrible need of some insight or clarification. I have two questions. In the double-slit experiment, when a particle is ejected whether it be photons or electrons (I will use electrons in this question), when streams...

I was searching for the proof of \frac{d}{dx} e^x = e^x. and I found one in yahoo knowledge saying that \frac{d}{dx} e^x = \lim_{Δx\to 0} \frac {e^x(e^{Δx}-1)} {Δx} = \lim_{Δx\to 0} \frac {e^x [\lim_{n\to\infty} (1+ \frac{1}{n})^{n(Δx)}-1]} {Δx} Let h= \frac {1}{n} , So that n = \frac...