Analytical Definition and 260 Threads

Hi, I have been trying to find analytical solutions for a finite rectangular sheet, say, in the xy plane, with dimensions a and b. Assume it is uniformly charged. An excellent (and short) description of the problem is here. The three integrals for Ex(x,y,z), Ey(x,y,z) and Ez(x,y,z) given on...

How to find the value of an infinite series. for e.g.Ʃ_{n=1}^{\infty} (β^{n-1}y^{R^{n}}e^{A(1-R^{2n})}) where β<1, R<1, y>1, and A>0? Note that this series is covergent by Ratio test. I already have the numerical solution of the above. However, I am interested in analytical solution...

I want to know the analytical formulation for a beam or bar without crack and with crack subjected to tensile loading through mechanics approach.

The average particle energy of a Fermi-Dirac gas, with zero chemical potential, is about 3.15T, where T is the temperture of this gas. To get the average energy, one needs to do an integration. The integrand is something like \frac{x^3}{e^{x/k_BT}+1}. I could get the result numerically. But...

My friend was doing an analytical geometry problem and a shape appeared that I wanted to find the area of with my new knowledge of integrals. I found the area and I'm now working to find an equation for the nth area as the size of the shape changes for all integers. After doing the math I come...

Homework Statement Joe pushes on the handle of a 10 kg lawn spreader. The handle makes a 45° angle with the horizontal. Joe wishes to accelerate the spreader from rest to 1.39 m/s in 1.5s. What force must Joe apply to the handle? Neglect friction. Homework Equations A=Vf-Vi/t. F=ma...

Hi. Since these equations are approaching three hundred years old I'm pretty sure someone must have solved them somewhere before. However I have not been able to find any text-books or papers that actually show me how to solve these equations. So I'm wondering if anyone here know where I can...

Hello everyone, So I've stumped uppon some problems during my project. It is not my homework or anything, so I didn't post it there. I've built a magnetic levitation system, which could lift up to 2kg. The problem is, that we cannot regulate the vertical position of the item. But that can...

Homework Statement In a four bar linkage r0=30mm, r1=10mm, r2=35mm, r3=20mm and theta1=45 degrees. Calculate theta2, theta3, Vc, W2, and W3 assuming that W1=30 rad/s ccw. Homework Equations R1*costheta1 + R2*costheta2 - R3*costheta3 - R0*costheta0 = 0 (3-x) R1*sintheta1 +...

What are the rules of analytical – not numerical (matrix) entry of bra-ket convertion – operations on bra-ket, in particular – tensor product ? For example – how in analytical form to do this: U|\Psi\rangle where: U=I\otimesI I=|0\rangle\langle0|+|1\rangle\langle1|...

What is the analytical method for solving log. eqs., like x=2^x/14 ? In high school they only teach us the graphical approach =/ joo

Author: Grant Fowles and George Cassiday Title: Analytical Mechanics Amazon Link: https://www.amazon.com/dp/0534494927/?tag=pfamazon01-20 Prerequisities: Calculus-based intro physics and a year of calculus; differential equations and matrix algebra highly recommended before or concurrently...

I am writing my first paper in applied mathematics.I would like to know how important is it to write a analytical proof for the numerical solutions arrived?I always thought these sort of things were left to the 'pure mathematicians' and one didn't need to bother.As a engineer,I was always used...

I have read many threads concerning many excellent books on calculus but not for analytical geometry. I can't seem to find any thread about good references for analytical geometry. I am taking the course analytical geometry and calculus in college and I need good book in both fields. I have...

Hello everybody, I am solving a 2D problem of thermal stresses in a rectangular plate in which temperature is changing only y direction. Plate has fixed displacement conditions. Could anyone help me to find out analytical solution of thermal stresses for my problem? Does anyone suggest me...

Homework Statement Calculate the molar solubility of Ag2C2O4 (silver oxalate) in a solution that has a fixed H3O+ concentration of 1.0 x 10^-6 M. Homework Equations The Attempt at a Solution I found the pertinent reactions, the charge balance and the mass balance so far, but I...

Homework Statement Find the concentration of Pb2+ in 0.0010 M KI with PbI2. Include activity coefficients in your solubility-product expression. The Ksp of PbI2 is 9.8*10^-9 Homework Equations Ksp= [Pb2+]\gammaPb2+[I-]2\gamma2I- Assume that [I-]=0.0010 M. The ionic strength of 0.0010 M Ki...

So I've several huge integrals to solve by hands and I would like to check my result with Mathematica. However I don't really know how to do so. Here is one of the several integrals I must solve: \int \frac{1}{2\pi \sigma _x \sigma _y \sqrt{1-\rho ^2 }} \exp \{ \frac{-1}{2(1-\rho ^2)} \left (...

Homework Statement Calculate the voltage at each of the extraordinary nodes (V1 – V3), and the current through each of the six resistors. http://i.imgur.com/VbZQH.png Homework Equations KCL: ƩIn = 0 V=ir I=A^{-1}B \Delta = a11C11 + a12C12 + a13C13 A^{-1} = \frac{adjA}{\Delta}...

I am an engineering student. I am an average student. I don't think my methods of analysis and thinking are proper. I did take steps to improve my thinking abilities by becoming a left-handed person, solving sudoku and lateral thinking puzzles. I want to be a scientist in my life. But i...

Someone has an analytical balance Adam AAA please send me its user guide. My balance has a serious error, Any weight displayed in double. I can't re-calibrate it without user guide :( Help me :)

Hi all, I need to solve this problem for my environmental chemistry class. It is supposed to be a "review" problem of concepts from analytical and gen. chem. but I certainly do not know how to do it. Homework Statement If you work at the wastewater treatment plant, you are exposed to...

hallo I ams earching analytical solution for system of two ODE in next form x*(dy/dr) - (y*y/r) = constant1*r*r*x*x*x x*(dy/dr)+(x*y/r)=constant2*r*r*x*x*(r*constant3-y) where x(r) and y(r). conditions are x=constant4 at r=constant5 and y=0 at r=constant5 thnx r.

Hello All, I am new to this community but by reviwwing the questions and answers posted in this forum I was encouraged to share my question with you and I hope you can help me. I have a system of 4th order ordinary differential equations for several functions which I call them: y_1,y_2...

Hello! First post, over here, hopefully it'll pique some interest, and awesome answers, but any and all answers are welcome! So, point is, we were given a guest lecture over how to 'jokingly' find answers to specific problems using methods that appear to not be justified; now, after the...

i need lectures in analytical mechanics, please help

Hello, In my study i came across to solve the analytical solution for coupled equation y(x,t) and z(x,t).The equations contains" f " function which is a function of the first variable exponentially. The first equation is : ∂y/∂t=∂^2(y)/∂x^2- 2*f(y)*z; The second equation ...

What's the difference between analytical and continuum mechanics?

Hi all, I'm trying to find an analytical solution to the following integro-differential equation: a f'(x)\int_0^x f(x)dx + b f'(x) + a [f(x)]^2 - a f(x) = 0 with initial condition: f(0)=1 This is a simplified problem for which I know the solution: f(x)=1. I'm trying to find...

I just started a numerical analysis class and I'm curious: what are the advantages and disadvantages of the two methods? Do we use numerical methods in situations where getting analytical solutions is possible? If so, why? I just want a better understanding of when each method is used in...

Question 20 from our final I just took (Analytical Chemistry UF). "You may recall that the wavelength of the sodium D1 line in vacuum is 589.7558nm. In air it becomes 589.5924nm. What is the difference in frequency for these two wavelengths." I said 0. All the other people did the...

Analytical form of an "Interpolated" function Hallo, I have a question on the use of "Interpolation" function in Mathematica. I am wondering whether it is possible to extract an analytical expression for a function built using the "Interpolation" option. Say, I have the following function...

Homework Statement Demonstrate Analytically: If \lim_{x\to a}f(x)=L and L<0, there exists a δ>0 so that x\inDom(f), 0<|x-a|<δ \Rightarrow f(x)<0 2. The attempt at a solution I start identifying what I want to demonstrate and what are my assumptions. x\inDom(f), 0<|x-a|<δ \Rightarrow f(x)<0 I'm...

Homework Statement Lets say we have a 2D rectangular plate with a point heat source and some boundary conditions. I would like to solve and understand step by step the solution to this second order differential equation. Let's say dimensions of rectangular are a and b. 2 opposite sides are at...

Hi, I'm trying to find an analytical solution (if one exists) to the 1d diffusion equation with variable diffusivity κ(x); \partial_t u(x,t) = \partial_x[\kappa(x) \partial_x u(x,t)] Could someone point me in the right direction to solve this if its possible to do so analytically. I've...

This is the book I used for classical mechanics in College. I'm looking through it again, trying to study and really deeply learn the things I winged in my undergrad years, hopefully to take a GRE and go into graduate school. I'm having some issues with this text. Often, it will use things...

A cannon launches a 10cm diameter cannonball w/ a muzzle velocity of 100 m/s horizontally from the top of a 40m high wall under STP. The cannon has a mas of 40 kg and is free to recoil. a. What is the initial v of the cannonball wrt the ground b.calculate the landing position neglecting air...

What method can I use to analytically solve the following 2nd order PDE? u=u(x,t) ∂u/∂t - a*x*∂u/∂x-D*∂^{2}u/∂t^{2} = 0 I.C.: u(x,t=0)=u_i B.C.: u(x=+∞)=0 u(x=-∞)=1 Is self-similar the only way to solve it, or is there any other method can be used to solve it? How to set the...

Hey, so I am just working on a second year Analytical Mechanics assignment, and right now dealing with oscillations. I have two questions I am stumped on and don't know if I have it right. It is probably basic, but just checking. 6. The frequency fd of a damped oscillator is 100 Hz, and the...

Hi there. I have to study the analyticity for the complex function: f(z)=\frac{y-ix}{x^2+y^2} The exercise suggest me to use polar coordinates. So, I do this kind of exercise using a theorem that says that if the function acomplishes the Cauchy-Riemann conditions, and the partial...

Homework Statement The following data were obtained for the analysis of soil for vanadium content in mg/g using two different methods. Do the two methods yield essentially the same results? Method 1 Method 2 26.30 26.22 26.43 26.32 26.28 26.20 26.19...

Homework Statement The following set of analyses represent concentrations of chloride in blood serum (meq/L): 103,106,107,114. One value appears suspect. Determine if it can be rejected at the 95% confidence level. Homework Equations Mean Standard Deviation...

Homework Statement A wheel of radius b rolls along the ground with constant forward acceleration a0. Show that at any given instant, the magnitude of the acceleration of any point on the wheel is (a0^2 + (v^4 / b^2))^(1/2) relative to the center of the wheel. Here v is the...

I'm currently reading Apostol's Calculus. I'm now on the part where I need to prove sin and cos values for specific values. Right now I'm working on sin and cos of pi/6. However, I always get at 1/2 and √3/2 for the final value. Here's my solution so far: Homework Statement Use the properties...

I found this question in HRW (sixth edition), one of the 'checkpoints' (checkpoint 2, to be precise) in chapter 12 on 'rolling, torque, and angular momentum': Homework Statement Disks A and Bare identical and roll across a floor with equal speeds. The disk A roll up an incline, reaching a...

I've been told that their exists no perfect mathematical method of obtaining a line of best fit from a population of data. This doesn't make a whole lot of sense to me, so I have made an attempt at doing such (see google docs link)...

Find the sum of : [2^{}0/3] + [2^{}1/3] + [2^{}2/3] + [2^{}3/3] + [2^{}4/3] + ... + [2^{}2008/3] where [] is the greatest integer function symbol... if the question is not clear here is the question.. Find the sum of : [(2^0)/3] + [(2^1)/3] + [(2^2)/3] + [(2^3)/3] + ... [(2^2008)/3]

I have purposely made this topic of analytical concepts . The questions are quite difficult . I cannot solve them . Lets see whether you people can do it . 1.Paper 1 - IIT Junior Squad . 2. Paper 2 -...

Hello all, I'm currently working on some magnetic shielding, and my supervisor wants me to try and find an analytical solution to the magnetic field inside the shielding. The shielding is basically bucket shaped (a hollow cylinder with the top cut out), and its meant to shield its interior...

Homework Statement I don't know how to type math equations of I have included a image file. Take initial conditiona as [0 1] Homework Equations The Attempt at a Solution No idea