Creation Phase

 

Creation Phase. Solve the following problems, clearly outlining and explaining your thought
process, in such a way that you and your peers can easily understand your solutions. You can
either write very neatly on paper, and scan your solutions with your phone (use the Dropbox app
rather than just a photo,) or (even better) type your solutions (using for exemple Overleaf, which
is described in Pip’s Tutorial 0,) and upload to your Kritik account. This step is due by 11:00pm
on Wednesday Oct 6th.
Consider the initial value problem (at time t0 = 1):
(
x˙ = f(x) = (x − a)
1/n, a ∈ R, n > 1 odd,
x(1) = x0
(A) Find the largest set A ⊂ R where f is continuous, and the largest set B ⊂ R where f is
continuously differentiable.
(B) Using the Existence and Uniqueness Theorem from class, find all possible initial values x0 at
t0 = 1 for which the above initial value problem has a unique solution in some time interval around
t0 = 1.
(C) For the remaining initial values x0 at t0 = 1, find at least 4 different solutions.
(D) Finally, consider the special case a = 1, n = 3 and x0 = 0, namely the following initial value
problem:
(
x˙ = (x − 1)1/3
,
x(1) = 0
Using (C), explain why there is a unique solution to this problem in some time interval around
t0 = 1. Find that solution explicitly and find the largest time interval I ∈ R in which this solution
makes sense. This solution can be extended to all of R: find an extension and explain why this
extension is not unique. (Hint: recall (A).)
Evaluation Phase. After the due date you will receive 4 submissions of solutions to the above
problems, which you are to evaluate using the criteria in the rubric: Results, Explanation, Interpretation and Presentation. The written form of the solution and a clear explanation of the approach
used is as important as the mathematical content. The idea is to see how your classmates solve
and present the results, and to give feedback to your peers. You will be required to make a written
criticism of each submission, indicating places where the student has done well and where improvement is needed. (You will be evaluated on how useful your remarks are!) The ideal is what you
would expect in a textbook: a complete and perfectly written solution which explains everything in
a concise and clear way. You will receive a solution which you may use to help you in the evaluation
phase. Remember that there may be more than one correct and clear method for proving any
statement in mathematics

 

Sample Solution

Curley’s Wife and her significance in the novel is how she revolves around the novels main themes and events. Curley’s Wife is left out for being a female, she often searches for companionship with the ranch worker. She is married but she in not happy, we know this as, she states to Lennie “I don’t like Curley he aint a nice fella.” This is why she tries to talk to other men on the ranch however she usually ignored because the workers think that a “ranch aint no place for a girl.” Or as Carlson states “women should be at home where she belongs.” The fact that she is deprived from a place of physical work is objective of how women were portrayed in the 1930’s. They suppose to be at home and raise a family. Curley’ wife feels insecure because of the loneliness she feel. Curley’s wife says “none of them care how I gotta live.” This shows her frustration and realisation of her issues of being a female during 1930s and Steinbeck draws a readers attention to this. Similar to Crooks, Curley’s Wife is not named. This carries on throughout the novel, highlighting her lack of identity on the ranch and how she is viewed as the belonging of her husband, the use of the possessive apostrophe reminds us of this. In addition to her self doubt, she tries to fight her loneliness and isolation by being violent. Her vicious attacks on Crooks to getting him “strung up on a tree” and the attacks on Lennie due to his mental disability, show how loneliness can not only change a person, but destroy them. Despite the representation of threat that she is appointed (an aspect in which we see in the scene that takes place in Crooks’ room), Curley’s wife belongs to the less powerful and deprived group that are in Crooks’ room, such as Candy, Crooks and Lennie, Curley’s wife has very little authority in her world. She is controlled by her more patriarchal husband, feared by the hands of the ranch and isolated as the only woman on the ranch. All of the emotions Curley’s Wife encounters come as a result of the loneliness she feels, and these clearly represent of what a terrifying character she is. Also, through out the novel she still remains ‘Curley’s wife’ This fact helps to provide her character to be seen as an object – George constantly warms Lennie to keep away, she is a person to be feared from a distance. The others, the men, also talk about her in ways that are compatible with the fact that the “tart” presents a danger to the men living on the ranch. Another way in which Steinbeck presents Curley’s Wife is through the use of irony. Curley’s Wife only gets negative attention, but it is the only attention she can get because she can’t get the attention which she desires to get from being in the limelight, this links to her American dream to be a film star. The ranch hands don’t give her this

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