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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

### The solution gives explanations on 10 true or false questions.

A set is any collection of objects?

### 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

### Quantitative Method for Time Estimates

A simple project listing of five and their respective time estimates are presented below: Acitvity Immediate predecessor Time in days A None 1 B A 2 C

### 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.

### FOIL Method for Multiplying

See attached file. Multiply w+1/2 by w+1/4.

### 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

### Initial Value Problem and Method of Characteristics

Solve the following initial data problem: u_x + u_y = u^2 u(x,0) = h(x) I have that x_t = 1, y_t = 1 and z_t = z^2 also, x(0) = s, y(0) = 0 and z(0)=h(s) from this I have x=s + t and y=t Please provide a detailed solution of how to find z.

### Inverse Power Method and Shifted Inverse Power Method

I posting few questions from Exercise 9.2. 3/d,c 4/c,d In question 3 and 4 i need to find inverse power method and as well as Shifted Inverse Power Method. Please send solved answers, please mention each and every step. Please send the answer with the prescribed time.

### Determine the probability from the given situation with Venn Diagram

Conditional Probabilities The records of Midwestern University show that in one semester, 38% of the students failed mathematics, 27% of the students failed Physics and 9% of the students failed mathematics and Physics. A student is selected at random. (a)If a student failed Physics, what is the probability that he or she

### Finite abelian groups with elements of certain orders

Give examples of finite abelian groups in which all elements (except the identity element) are of the same order.

### 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

### Prove that every element of a subset is of finite order.

Let G= , x*y be the fractional part of x+y .(i.e:x*y=x+y-[x+y] where [a] is the greatest integer less than or equal than a). Show that all the elements of the subset of all rational elements of this group are of finite order. Please see the attached file for the fully formatted problems.

### BAR AND BEAM ELEMENTS, finite elements method

Please solve problem in jpg file. See notes in pdf file.

### Newton's Method and Four Rectangles and the Right Endpoint Method

Question #1. Find the positive root of the equation cos(x) = sin(x) + x^4 using Newton's method (Do only 3 iterations). Question #2. The acceleration of object is given by the following equation: a(t) = cost(t) - 3t^2 + e^t. We also know that v(0) = 8cm/sec and s(0) = 32cm. Find the position of the object after 3 seconds.

### Statics - Finite Elements Methods : Beams and Springs

Problem 1: (Please see the attached file for the fully formatted problems.) The figure shows a beam element with the following properties: E=200 GNm2,I = 5-l0m4, L = 4m, A=250 mm2 and a bar element with: A = 500 mm2, E 200 GNm2. Find: 1. The stiffness matrix of each clement in the local (element) coordinate system. 2. The

### finite extension of fields K/k which have prime degree

Show that a finite extension of fields K/k which have prime degree have only trivial subextensions.

### Covering Maps Investigated

Let q: X->Y and r:Y->Z be covering maps; let p=(r(q(x))). Show if r^(-1)(z) is finite for each z in Z, p is a covering map.

### Finite Difference Methods for PDEs

See the attached file. B. A beam is resting horizontally on the sharp edges of a room with width L, and has a ceiling attached in the shape .... At time t = 0 the glue releases and the beam vibrates. Describe the vibration for t > 0 if the situation is described by ... Boundary and initial values are given by ..... Hint:

### Showing a quotient space is a complete metric space; Finite measurable space; Symmetric difference; Equivalence relations

Let (X,B,mu) be a complete, finite measuable space. For each C,D in B, set d(C,D) = mu (C / D) where C / D is the symmetric difference of C and D. We say that two measurable sets C,D are equivalent if d(C,D)=0 (this is an equivalence relation). Let E be the set of equivalence classes, and show that d introduces a metri