Write ideas for a one-page summary on each of the following three topics from your text:

1. Euler circuits, including their definition, recognition, how to create them, and how to prove they exist.
Describe Nearest Neighbor, Sorted Edges, and Kruskal's algorithms. Illustrate their use.
Describe the characteristics of Simplex Method and Alternative to the Simplex Method. Illustrate their use in solving a practical problem.

2. Find three Web sites that demonstrate a practical application of the use of Euler circuits. Write a five to six sentence description of each Web site. For more information on a Links Assignment and samples, please go here: Links Assignment

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Provided is a response, including websites and sources referenced.

Euler Circuit is a special circuit that passes along each edge exactly once. There is a theorem, the Euler theorem that allows one to know exactly when it is possible to find an Euler circuit on a graph. Nearest neighbor is when you pick a starting vertex and form a circuit which starts and ends at that vertex by always travelling along the edge coming out of your vertex that has the lowest weight, being careful to never visit a vertex twice until all have been visited once. This is a quick and easy method, even though it may not give the best possible answer. Sorted edges occur when you "grab" edges until you have a complete circuit. The edge grabbed will always be the one with the lowest weight that has not been grabbed yet, as long as grabbing it does not cause a circuit to form ...

Solution Summary

The solution assists with writing ideas for a summary on each of the given topics regarding Euler circuits.

I have attached six problems (the odd ones from my textbook) that I need assistance with solving. I have no idea how to approach these problems. My professor has assigned the even for homework. I thought if I could see how the odd were worked, I would be able to follow the examples to do the even. Thank you for your assi

Determine the Euler-Lagrange equation for the variational problem arising from the integral of F(x, u, u_x) = x u_x and discuss what conclusions can be drawn from the result. Here, u_x denotes the partial derivative of the dependant variable u with respect to x.

Q12: (i) Calculate phi(15) in THREE ways.
(ii) Express in modular arithmetic
[hint:the number of integers from 1 to m that are relatively prime to m is denoted by phi(m). it is the number of elements in the set a:1=a=m and gcd(a,m)=1 ]

Please show all working. You may tabulate your solutions.
a. Use the explicit Euler to simulate two steps of the system...
See attached for full problem description.

A factory worker places 93 newly created circuits on a shelf to be checked for quality. Of these, 8 will not work correctly. Suppose that she is asked to randomly select two circuits, without replacement, from the shelf. What is the chance that both circuits she selects will be defective? Show step by step work! Approximate the

Please see attached file on Transients in RLC circuits and Laplace transform.
Please complete the following examples and show detailed workings and narratives including transposition of formula and graphical display where required.

Truth tables are related to Euler circles. Arguments in the form of Euler circles can be translated into statements using the basic connectives and the negation as follows:
Let p be "The object belongs to set A." Let q be "the object belongs to set B."
All A is B is equivalent to p -> q
No A is B is equivalent to p -> ~q

I need help using Euler an the improved Euler methods: (look at attachment for better formula display)
1. Consider the initial value problem y' = 2xy, y(1) = 1. Use the Euler's method and improved Euler's method with h = 0.1and h = 0.05 to obtain approximate values of the solution at x = 1.5. At each step compare the approxim

See the attached file.
Consider the Lotka-Volterra system. Consider the following system of differential equations
dx/dt=-x(2-y),t_0=0,x(t_0=1), (2)
dy/dt=y(1-2x),t_0=0,y(t_0 )=2, (3)
Let [0; 40] be th