Wednesday, January 24, 2018

How does Virginia Woolf uses the narrative technique “stream of consciousness" in her novel Mrs. Dalloway?

This pathbreaking novel is told entirely through stream of consciousness. In other words, there is no outside narrator setting up and describing the scene or telling us, as readers, what to think. As Woolf outlines in her essay "Mr. Bennet and Mrs. Brown" she rejects the Edwardian—and Victorian—narrator who provides a "normative" frame for a work and lots of descriptive embellishment that is supposed to stand in for "objectivity." Woolf, instead, wanted to capture the pure subjectivity of real, lived experience. As we go through our days, we don't have a "narrator" telling us what to think: we simply react to the raw experience of what we encounter as we process it inside our heads.
In Mrs. Dalloway, Woolf moves in and out of the heads of various characters. We see everything through the subjective eyes of whatever character whose thoughts and perceptions Woolf happens to be "downloading" at that moment. The experiences that molded these characters—and their memories as well—determine how they react to what is going on around them in the single day of Mrs. Dalloway's party. So as a character walks down a London street, what he or she encounters experientially will trigger a line of thoughts and memories that Woolf will record.
Woolf goes in and out of so many heads without any contextualizing structure that it can become confusing, and one has to work hard to keep track of what is going on. This is a hallmark of modernism: writers like Woolf, Joyce, and Stein wanted readers to be alert and actively engaged in the reading process was slightly disoriented and didn't become mechanical and predictable.


Virginia Woolf is often recognized as a pioneer in the use of stream of consciousness, but to simply make that observation is not quite enough. Indeed, Woolf's writing style differs quite remarkably from other writers who use the technique, especially James Joyce, whose landmark novel Ulysses uses the stream of consciousness masterfully and is often presented as the quintessential modernist novel. Joyce's technique, however, is quite different from Woolf's. Joyce, for instance, directly reports what his characters think in the way that they would think it, especially in the final chapter, in which he realistically represents the messy pattern of human thought by giving us Molly Bloom's interior monologue with very little punctuation. Woolf's style throughout Mrs. Dalloway is still stream of consciousness, but it is also very different from Joyce's standard. For example, though Woolf spends most of the novel occupying her protagonists' thoughts, and though she mimics the flux of the interior monologue, she does not try to mimic the messy progress of human thought like Joyce. Instead, she uses a style that is very similar to free indirect discourse, in which a narrator's style adopts the persona of certain character's (Jane Austen was a master of this narrative technique as well), giving the reader a narrative colored by the personality of the protagonist. Take, for example, the second paragraph of the book:

For Lucy had her work cut out for her. The doors would be taken off their hinges; Rumplemayer's men were coming. And then, thought Clarissa Dalloway, what a morning--fresh as if issued to children on a beach. (3)

In this paragraph, we actually indirectly occupy Clarissa's consciousness, seeing the world through her eyes and experiencing a narrative firmly under the control of her interior processes. The morning is not fresh because it is objectively fresh, but rather because Clarissa thinks it's fresh, and so our experience of the world is also an experience of Clarissa's interior life. Thus, Woolf's style is unique in that, though it doesn't attempt to depict the exact way that thoughts happen as Joyce does, she still presents a continuous stream of personalized thoughts. Later, this technique becomes even more unique as Woolf jumps from consciousness to consciousness, exploring the interior lives of characters like Peter Walsh and Septimus Smith. In this way, though Woolf is certainly not the only writer to use stream of consciousness, she certainly made the technique her own by blending it with free indirect discourse.  

Calculus and Its Applications, Chapter 1, 1.8, Section 1.8, Problem 28

Determine the $y'$ of the function $\displaystyle y = (x^4 + x)^{\frac{2}{3}}$
By using Chain Rule,

$
\begin{equation}
\begin{aligned}
y' &= \frac{d}{dx} \left[ (x^4 + x)^{\frac{2}{3}} \right]\\
\\
&= \frac{2}{3} (x^4 + x)^{\frac{2}{3} - 1} \cdot \frac{d}{dx} (x^4 + x)\\
\\
&= \frac{2}{3} (x^4 + x)^{-\frac{1}{3}} (4x^3 + 1)\\
\\
&= \frac{2(4x^3 + 1)}{3(x^4 + x)^{\frac{1}{3}}}
\end{aligned}
\end{equation}
$


Then, by using Quotient Rule and Chain Rule

$
\begin{equation}
\begin{aligned}
y'' &= \frac{2}{3} \cdot \frac{d}{dx} \left[ \frac{4x^3 + 1}{(x^4 + x)^{\frac{1}{3}}} \right]\\
\\
&= \frac{2}{3} \left[ \frac{(x^4 + x)^{\frac{1}{3}} \cdot \frac{d}{dx} (4x^3 + 1) - (4x^3 + 1) \cdot \frac{d}{dx}
\left[ (x^4 + x)^{\frac{1}{3}} \right] }{\left[ (x^4 +x)^{\frac{1}{3}} \right]^2} \right]\\
\\
&= \frac{2}{3} \left[ \frac{(x^4 + x)^{\frac{1}{3}} (12x^2) - (4x^3 + 1) \left[ \frac{1}{2} (x^4 + x)^{-\frac{2}{3}} (4x^3 + 1) \right] }{\left[ (x^4 +x)^{\frac{1}{3}} \right]^2} \right]\\
\\
&= \frac{2}{3} \left[ \frac{(x^4 + x) (12x^2) - \frac{(4x^3 + 1)^2}{2(x^4 + x)^{\frac{2}{3}}} }{(x^4 + x)^{\frac{2}{3}}} \right]\\
\\
&= \frac{2}{3} \left[ \frac{2(12x^2) (x^4 + x)^{\frac{5}{3}} - (4x^3 + 1)^2 }{2(x^4 + x)^{\frac{2}{3}} (x^4 + x)^{\frac{2}{3}} }\right]\\
\\
&= \frac{1}{3} \left[ \frac{24x^2 (x^4 + x)^{\frac{5}{3}} - (4x^3 + 1)^2 }{(x^4 + x)^{\frac{4}{3}}} \right]
\end{aligned}
\end{equation}
$

Tuesday, January 23, 2018

sum_(n=2)^oo 1/(sqrt(n) -1) Use the Direct Comparison Test to determine the convergence or divergence of the series.

Direct comparison test is applicable when suma_n and sumb_n are both positive series for all n such that a_n<=b_n
If sumb_n converges ,then suma_n converges,
If suma_n diverges, then sumb_n diverges.
Given series is sum_(n=2)^oo1/(sqrt(n)-1)
Let b_n=1/(sqrt(n)-1) and a_n=1/sqrt(n)=1/n^(1/2)
1/(sqrt(n)-1)>1/sqrt(n)>0 for n>=2
sum_(n=2)^oo1/n^(1/2) is a p-series
The p-series sum_(n=1)^oo1/n^p , is convergent if p>1 and divergent if 0For the series sum_(n=2)^oo1/n^(1/2) p=1/2<1 so it diverges as per the p-series test.
Since the series sum_(n=2)^oo1/sqrt(n) diverges, so the series sum_(n=2)^oo1/(sqrt(n)-1) diverges as well by the direct comparison test.

Calculus and Its Applications, Chapter 1, Review Exercises, Section Review Exercises, Problem 44

Differentiate $\displaystyle g(x) = (5 - x)^2 (2x - 1)^5$.

By using Product Rule and Chain Rule,

$
\begin{equation}
\begin{aligned}
g'(x) &= (5 - x)^2 \cdot \frac{d}{dx} (2x - 1)^5 + (2x - 1)^5 \cdot \frac{d}{dx}(5 - x)^2\\
\\
g'(x) &= (5 - x)^2 \cdot 5(2x - 1)^{5 - 1} \cdot \frac{d}{dx} (2x - 1) + (2x - 1)^5 \cdot 2(5 - x)^{2 - 1} \cdot \frac{d}{dx} (5 - x)\\
\\
g'(x) &= (5 - x)^2 \cdot 5(2x - 1)^4 (2) + (2x - 1)^5 \cdot 2 (5 - x)(-1)\\
\\
g'(x) &= 10(5 - x)^2 (2x - 1)^4 - 2(5 - x)(2x - 1)^5\\
\\
g'(x) &= 2(5 - x)(2x - 1)^4 [5 (5 - x) - (2x - 1)]\\
\\
g'(x) &= 2(5 - x)(2x - 1)^4 [ 25 - 5x - 2x + 1]\\
\\
g'(x) &= 2(5 - x)(2x - 1)^4 (26 - 7x)\\
\\
g'(x) &= 2(5 - x)(26 - 7x)(2x - 1)^4
\end{aligned}
\end{equation}
$

College Algebra, Chapter 1, 1.5, Section 1.5, Problem 68

Find all solutions, real and complex of the equation $\displaystyle x^6 + 9x^4 - 4x^2 - 36 = 0$


$
\begin{equation}
\begin{aligned}

x^6 + 9x^4 - 4x^2 - 36 =& 0
&& \text{Given}
\\
\\
(x^6 + 9x^4) - (4x^2 + 36) =& 0
&& \text{Group terms}
\\
\\
x^4(x^2 + 9) - 4 (x^2 + 9) =& 0
&& \text{Factor out } x^4 \text{ and } 4
\\
\\
(x^4 - 4)(x^2 + 9) =& 0
&& \text{Factor out } x^4 - 4
\\
\\
x^4 4 =& 0 \text{ and } x^2 + 9 = 0
&& \text{Zero Product Property}
\\
\\
x^4 =& 4 \text{ and } x^2 = -9
&& \text{Solve for } x
\\
\\
x =& \pm \sqrt[4]{4} \text{ and } x = \pm \sqrt{-9}
&& \text{Recall that } i^2 = -1
\\
\\
x =& \pm \sqrt[4]{4} \text{ and } x = \pm \sqrt{9i^2}
&& \text{Simplify}
\\
\\
x =& \pm \sqrt[4]{4} \text{ and } x = \pm 3i
&&

\end{aligned}
\end{equation}
$

What are some key similarities and differences between The House of Mirth and A Doll's House?

Edith Wharton's The House of Mirth and Henrik Ibsen's A Doll's House share a number of thematic similarities.
1. Women using their charms (for lack of anything else): In The House of Mirth, Lily Bart is a society woman with no money. She is related to old New York powerhouses, but she herself is nearly destitute. Because of this, she can only rely on her good looks and charming personality to entertain the rich. This is the only way she can "smoke their cigarettes" and share their bread. With no money, Lily Bart finds herself in a role no different than Nora Helmer's.
Nora, whose finances depend on her husband's, also uses her charms to keep him happy, as there is nothing else she can use on her behalf. The result is that, like Lily, she has become little more than entertaining company to those who mingle with her, especially her husband. She and Lily are basically taken for the charm they offer and nothing else.
2. Dependent women: Lily and Nora are at the mercy of their environments. Lily's New York set decide when she comes on board their yachts and when she gets to leave them. They decide her vacations, entertainment, and expenditures simply because she depends on them for those things. On her own, Lily Bart is a nobody.
Nora is also a nobody—so much so, in fact, that leaving her family is seen as a social faux pas. She has been disenfranchised as a woman forever. Now that she wants to move away from a life that has been dependent on men, she realizes that it will be a terribly hard thing to do.
3. Money is everything: In both worlds, Lily's and Nora's, the want for money is ever present. In Lily's set, everyone is rich (except her), but they also want to become richer. In Nora's world, the middle-classes are thriving and moving up the social ladder, making them want to acquire money, reputation, and the benefits that were once unique to those who were born rich. As such, we see that money fixation is a theme in both literary works. Money is not only power but also "freedom from care" and a prospect for happiness.
The key difference between the two works is setting. Lily's story takes place in ruthless New York: a hierarchical society where family name, family fortune, and financial achievements serve as the only measures to determine the worth of people. All characters are shallow and static, even Lily Bart, to a point. In the end, Lily dies trying to make amends for a shallow life, but we cannot quite tell if her essence and character were truly changed for the better or just forged by dire circumstances.
Contrastingly, Nora is quite a deep, dynamic character; she only appears to be static and flat. In reality, she seeks depth and warmth from her husband, who only looks at his own financial and social advances. As a result, she has to leave her shallow home altogether, knowing that she no longer belongs in that world.

How does Sherlock Holmes make a good literary detective in relation to other detectives? What qualities does he have?

Sherlock Holmes is a good literary detective because he is entertaining.  He has a complete understanding of human nature, but at the same time a complete disregard for other people’s feelings.  He is as self-centered as he is brilliant.  His deductions and interesting cases make him fun to read. 
Your topic is a little vague, so I am not sure what you mean by other detectives.  By comparison to Watson, who is not really a detective, Holmes is much more intelligent.  He is the one who solves the cases, and Watson follows along and assists.  Watson is always enamored of Holmes and believes him to be so brilliant that he doesn’t mind his personality quirks, including the insults Holmes seems to throw his way. 

“I am afraid, my dear Watson, that most of your conclusions were erroneous. When I said that you stimulated me I meant, to be frank, that in noting your fallacies I was occasionally guided towards the truth...." (The Hound of the Baskervilles, Ch. 1) 

Sherlock Holmes was a model for many other literary detectives, including Nero Wolfe, Rex Stout’s American version of Holmes. Wolfe was similar to Holmes in that he was brilliant and quirky.  He, too, was antisocial.  Both of them could be languid, staying home for days at a time either pouting or thinking.  While Holmes dabbled in drugs, it was food that pleased Nero Wolfe.  Neither liked women.  Both had a trusty assistant, but Nero Wolfe’s assistant Archie Goodwin did most of the legwork.  Wolfe rarely left the house.  He was as fat as Holmes was thin.
Besides Nero Wolfe, Sherlock Holmes inspired scores of other literary detectives in books, radio, television, and movies. Some of these are adaptions, such as the BBC's Sherlock, which modernizes Holmes and Watson by bringing them to present-day London, and others are just detective procedurals.  One thing is for sure:  People seem to love a good mystery with a quirky detective.

Why is the fact that the Americans are helping the Russians important?

In the late author Tom Clancy’s first novel, The Hunt for Red October, the assistance rendered to the Russians by the United States is impor...