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Finite Element Method

Finite element method is a numerical technique for finding approximate solutions to boundary value problems. It uses variation methods to minimize an error function and produce a stale solution. Finite element method encompasses all the methods for connecting many simple element equations over many small subdomains, named finite elements, to approximate a more complex equation over a larger domain.

A typical work out of the method involves dividing the domain of the problem into a collection of subdomains, with each subdomain represented by a set of element equations to the original problem, followed by systematically recombining all sets of element equations into a global system of equations for the final calculation.

The element equations are simple equations that locally approximate the original complex equations to be studied, where the original equations are often partial differential equations. The finite element method is commonly introduced as a special case of Galerkin method. The process is to construct an integral of the inner product of the residual and the weight functions and set the integral to zero.

Finite element methods are a good choice for analyzing problems over complicated domains, when the domain changes, when the desired precision varies over the entire domain, or when the solution lacks smoothness. An example of this would be in numerical weather prediction where it is more important to have accurate predictions over developing highly nonlinear phenomena rather than relatively calm areas. 

Matrix and Linear Equations

Please provide assistance in understanding how to prove whether or not finite mathematical equations are true or false. I have attached the questions that I am experiencing difficulty on. In your solution, please explain how to prove, i.e., your recommendation on the specific formula I should use. My textbook does not provide th

Continuous Method for Time Recording

See the attached file. When performing time study process insurance claims adjusting company doctors Triple R, Barney Rubble analyst applies the continuous method for time recording. The activity is divided into four work items. In Figure 7.3 (attached) are the rating factors (RF) performance and the times recorded by the con

Different positive factors of an integer

Find the smallest positive integer with exactly n different positive factors when n is: 3,4,5,6,10 I am not sure if I should do it like this: For 3 the answer would be: 1 * 2 * 3 = 6 (or is 1 not counted? in that case 2 * 3 * 5 = 30) By this approach for 6 the answer would be: 2 * 3 * 5 * 7 * 11 * 13? Or maybe 1,2,3,4,6,1

Quantitative method for solving equations

Solve the following equations and find the values of x and y. 2x + y = 4 4x - 2y = 24 Please graph the equation, choose your own range, but make sure the two graphs intersect.

Using Newton-Raphson Method to Find Roots

I need some help on the Newton-Raphson method. The question goes as follows: The velocity, v mm/sec. of a point on an eccentric cam at a certain instant is given by V= 0.3 x-ln x, where x is the displacement in mm. 1 a) Show that when the velocity is zero the displacement lies between 1 and 2 mm. b) Use the Newton

Discrete Math: Quantitative Method

You are working on a project that has 12 activities and wand to perform aCPM analysis on a project. You determine the critical path consists of only five actives. You then compute the variances for the five critical path activities and these variances 3, 4, 2, 1, and 6 days. If the desired completion date for the project is 50 d

Quantitative Method: Word Problem

You ask subordinates how it will take to complete the job they are working on. The subordinates say, "if everything goes right it will take 6 hours, most likely it will take 8 hours, and if everything goes wrong it will until the end of tomorrow or another 16 hours." Since this job is a part of a larger project you must estimate

Discuss finite measure space.

Let (X, M, u) be a finite measure space. Show that a. if E, F, in M and u (the symmetric difference of E and F) = 0, then u(E) = u(F) b. Say that E ~ F if u ( the symmetric difference of E and F) = 0; then ~ is an equivalence relation on M c. For E, F in M, define rho (E, F) = u ( the symmetric difference of E and F). Th

Find area and estimate with finite sums.

Consider the function f(x) = x^2 + 2 on the closed interval [1, 6]. Using rectangles, use n = 10 and calculate the approximate area between the function f and the x axis on the interval [1, 5]. Use left endpoints in the following. 1. Find the change in x for each sub-interval. 2. Find f(1); f(1.5); f(2); f(2.5); f(3) . .

Order of the product of two elements in a group

Let G be a group (finite or infinite) and let a and b in G. Let o(a) represent the order of a. Suppose G is abelian and both a and b are of finite order. Show that ab is of finite order and o(ab) divides o(a)o(b).

Mathematics - Modified Distribution Method

Solve the problem using Modified Distribution Method 1. The ABC Umbrella Factory has received a letter from a regular customer ordering umbrellas for his 3 department stores: Store Monthly Requirement Plaza Fair 250 Fair Mart

Ratio to Moving Average Method

An analyst wants to use the ratio-to-moving average method to forecast a company's sales for the next few quarters. Beginning in Quarter 2 of 2005 , the analyst collects the following sales data (in millions of dollars). Estimate the seasonal index associated with Quarter 4. Round your answer to at least three decimal places.

Newton's method approximation

Help with 3 incircled problems on attachment. thanks For each initial approximation, determine graphically what happens if Newton's method is used... Use Newton's method to approximate the indicated root of the equation... Use Newton's method to find all roots of the equation...

Elements in an Abelian Group

Let G be the direct sum of a countably infinite number of copies of Z. Find an element of End_Z(G) which has a left inverse, but is not a unit. Please explain in detail. Think of elements of End_Z(G) as infinite matrices with integer entries. Definition: Let G be an abelian group and let End_Z(G) be the set of all grou

Mathematical Method for Economics

1. The per period sales of a new product, x(t), evolves over time according to x(t):= A / (1 + b * e - c t ) where A, b and c are positive constants. a) By taking the limit of x(t) as t tends to infinity, show that per period sales tends to A as t increases. b) Show that the rate of growth of sales is proportional to

Finite Element Method Problem

Let F be a finite field. Show that every element of F is the sum of two squares. (hint: given , show that and each have more than elements. (See attached file for full problem description with proper symbols) ---

Basis and Finite and Infinite Field Extensions

Find a basis for the extension of and also calculate We know already that is infinite. Give an example of fields and (with neither nor equal to ) such that: a) and are both infinite b) is infinite and is finite. (See attached file for full problem description with proper symbols) All gaps are Q,

Newton's method approximation

Use Newton's method to approximate the x value of the point near x=3 of 2 functions 1. f(x) = 3 - x 2. g(x) = 1/(x^2) + 1 Do this problem for complete iterations to get an answer of about .001 of the real value hint let H(x) = f(x) - g(x)

Conjugacy Classes Non-Identity Elements

G is a finite group with elements a and b. Let the conjugacy classes of these elements be A and B respectively and suppose |A|^2, |B|^2 < |G|. Prove that there is a non-identity element x in G s.t. x commutes with both a and b.

Test Binary Relations

Test the binary relations on S for reflexivity, symmetry ,antisymmetry, and transitivity A) S = Q X p Y <-> ABS(X) <= ABS(Y) B) S = Z X p Y <-> x -y is an integral multiple of 3 C) S = N X P Y <-> X is odd D) S = Set of all squares in the place S1 p S2 <-> length of side of S1 = length of side S2 E)

Finite-Element Method Description

Please see the attached files for full problem description. Using Finite-Element Methods, assuming that stiffness of each element is equal to f.

It is dealing with finite automatons

(a)For each of the following languages over the unary alphabet {a}, construct a finite automaton accepting it. i. {a^2} ii. {a^2, a^3, a^4} (b) Let A be any finite nonempty subset of {a, a^2, a^3, a^4,...}. Is there always a finite automaton that accepts A?