...MATH 364A: Ordinary Differential Equations (Midterm 1) Name: Student ID: Signature: Question 1 (40 points) Solve the following initial value problems. (a) y + t3 y = t3 y(0) = 0. (b) y = − (1+x) y y(−1) = 1. Question 2 (40 points) Solve the second-order initial value problem 2y − 3y − 5y = 0 y(0) = 0 2 y (0) = 1. Question 3 (40 points) For each equation below, first determine whether the equation is exact or not exact. If the equation is exact, find the solution. (a) cos(y) + (2y − x sin(y)) dy = 0. dx (b) 3xy 2 + (y 3 + 3x2 ) 3 dy = 0. dx Question 4 (40 points) Consider the following first-order differential equation y = (y 2 − 1)(4 − y 2 ). Find all critical (equilibrium) solutions and classify their stability. 4 Question 5 (40 points) (True/False) In each of the following, determine whether the given function solves the given differential equation or initial value problem. (a) If k > 0 denotes any real constant, then the function y(t) = e−kt solves the initial value problem y = −ky y(0) = 1. (b) The function y(t) = (1 − t)−1 = 1/(1 − t) solves the initial value problem y = y2 y(0) = 1. (c) The function y(t) = e2t solves the second-order initial value problem y = 2y y(0) = 1 y (0) = 2. (d) Any function y(x) defined by the implicit equation x4 + 2x2 y 2 + y 4 = C solves the differential equation x3 + xy 2 + (x2 y + y 3 )y = 0. 5 Question 6 (Extra Credit, 10 points) An object with mass...
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...heal. In the novel, Ordinary People by Judith Guest, the main character, Conrad Jarrett, is recovering from his suicide attempt. After his brother's death, his life starting falling apart, which led him his attempt. After spending a month in the hospital, he finally comes home and that's when he starts his journey to recovery. Throughout the novel, the reader can clearly tell what events...
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...The Ordinary Men in “Ordinary Men: Reserve Police Battalion 101 and the Final Solution in Poland” Name of Student Name of Instructor Name of Institution Date Submitted The Ordinary Men in “Ordinary Men: Reserve Police Battalion 101 and the Final Solution in Poland” Introduction The book “Ordinary Men: Reserve Police Battalion 101 and the Final Solution in Poland” was published in 1992. The book is written by Christopher Browning. It talks about the Holocaust, which involved the killing of the Jewish people by the Nazis. The event took place between 1942 and 1943. The book is mainly based on the findings of a study conducted on the causative factors made evident in the testimonies of people serving in German Reserve Unit 101. The study was carried out in the 1960s. The Police Battalion 101 was ordered to massacre and deport Jews living in Poland. At the time, the country was occupied by the Germans. The German legal investigations involved 210 of the men 20 years later. The investigations looked into war crimes in order to press charges against certain members of the government. The men who carried out these atrocities were middle-aged. Their average age was 39 years (Browning 48). Surprisingly, they seemed to have voluntarily taken part in the exercise. The reason is that none of them was coerced to participate in the killings. The men would end up following the orders given in spite of the fact that they were contrary to what they deemed right. In this paper, the author...
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...Professor Brown The Holocaust: History and Memory April 23, 2012 Ordinary Men In Christopher R. Browning’s Ordinary Men: Reserve Police Battalion 101 and The Final Solution in Poland, Browning describes the story of how “ordinary men” were placed in an extraordinary situation that forever changed these men’s lives. Browning’s novel focuses on the role of the German Order Police, more specifically Reserve Battalion 101, and how they played a small, yet significant role in carrying out Hitler’s “Final Solution.” By focusing on the unit of Reserve Battalion 101, Browning aims to shed some light on how a battalion of less than 500 men could cause the deaths of nearly 83,000 Jews in the span of less than a year. Through his research, Browning illustrates how these men were not cold-blooded killers recruited for such a job, but rather a group of “ordinary” middle-aged men shaped by the situation at hand to carry out unspeakable acts all in search of a judenfrei world. When analyzing Browning’s work, the question of who were the men of Reserve Battalion 101 must first be answered. Originality, the main task of Reserve Battalion 101 was to aid in the “Germanizing” of Germany’s newly acquired regions, such as Poland, through deportations of the “undesirables” to the “east.” Places like the Łódź ghetto became the new homes for hundreds of thousands of Polish Jews, forced to live in sealed-off communities. Between November 1940 and May 1941, Reserve battalion 101 was assigned...
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...Daquan Jackson 3/11/14 Prof. Powell Mus 101 The song I chose for this assignment is Ordinary people by John legend which to me is a great song. Ordinary people came in out in 2004 in Legends album Get Lifted. The song doesn’t have any personal meaning for me; I just really enjoy listening to song for some reason. There’s only one instrument throughout this song and it’s the piano which Legend plays himself. The man has a great voice which makes me keep listening to his music because if it wasn’t for that I don’t think I would listen to him. This songs is completely different to all the other music I listening I listen to more Spanish and house music then I do to soul, in fact this is probably the only soul song I actually have listened to more than once. This is different to the music I listen to because most of what I listen to makes no sense and has no meaning to it, unlike ordinary people which actually talks about real life situations that people in relationships go through even today. According to Legend the point of this song was to say that relationships are tough and no one will really know the outcome and that even if it does work it will require compromise but even with that the relationship won’t end the way you would want it to. Ordinary people is a soul/ R&B song that talks about guilt, contradiction, fear and doubt. In this line ("I know I misbehaved/and you've made your mistakes/and we both still got room left to grow") he talks about how people in...
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...The poem An Ordinary Person by Rabindranath Tagore is about how humans do not appreciate the things around them and how they want the things that they do not have. The poem also shows how humans are constantly attracted to things that are foreign to them. The literary device allegory is very important to this poem. The poem could be seen as a poem a poem about a man simply going to the future and becoming the center of attention because he has been resurrected. However, the poem could also be interpreted as how humans do not see the extraordinary things in the world around them and how they don’t seem to care about their ordinary world. In the poem, the peasant man seems to be sent into the future, where everyone adores him. All the people, “besiege him on all sides,” and take every word from his mouth. They are eager to know everything about him because, to them, he is extraordinary. This relates to real life where humans do not see or care for the average people around them. The peasant, like everyone else, is extraordinary even though they are not usually seen as anything but normal. The poem shows the flaw in humans, where it takes a work for people to see someone in a different light. The rhythm of the poem is also important. When reading the poem, the poem first seems to starts off steady and slow. Then, near line eight, the rhythm of the poem picks up and seems more demanding. The words feel sharp and the come out very fast and emotionally. It feels as if though the...
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...#1 What was the purpose of the Order Police? What was their function within the larger Nazi hierarchy? Generally speaking, who were the members of Police Battalion 101 (their background, age, affiliations, occupations, etc.) The purpose of the Order Police, a group of about 500 policemen, most of them being from Hamburg, was made up of ordinary men. Most of them were in their 30's and 40's because they were too old to join the army or they were from the middle or lower class. It included men who were professional policemen, businessmen, truck drivers, machine operators, teachers and construction workers before the war. Battalion 101 of the Order Police and alongside other Order Police battalions had enough power needed to carry out the devastating mass killings of the Jews in Poland. The Order police were involved in mass atrocities against the Jews as Browning states in the third chapter. In this chapter he gives insight of how Jews were murdered in the Soviet Union. Orders to kill innocent Jews or anyone who was suspected to be anti-Germany, came from the German government. Alongside the Jews being killed they were also humiliated. Some of the police commanders were extremely rude like urinating on a Jew while they are begging for mercy. Many Jew were forced into the woods and shot and also moved to concentration camps. In the fourth chapter of the book the order police were trusted with moving the Jews as they were commanded to do. #2 What happened at the massacre...
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...Sujaan Lal Greek Classics Paper Brian Doherty 11/4/12 Beneath the Surface: The Significance of Somax, the Ordinary Carter There has always a bond between a father and his son that is somewhat unexplainable. The strong generational connection between the two paves the way for both deep intimacy and love but also an overwhelming sense of grief their loss. David Malouf’s Ransom appropriates a section of Homer’s tale for closer examination in which he gives voice to Somax, a character of his own invention. Although he is introduced as an ordinary carter, Somax and his journey become intrinsic to Priam’s own self-discovery. The story of the carter helps his King experience a range of emotions he has never explored and introduces Priam to what it is like to “simply be a man.” Malouf draws an interesting comparison between Somax and Idaeus to differentiate between royalty and the common man. In the book, Somax is renamed Idaeus, the name of the royal wagoner. Priam’s selection of a peasant carter is in an effort to follow his vision and speak for himself. If a royal carter or herald had spoken for him, it would seem as if the gods had played a major role in their fate. Malouf throughout the book argues that Gods do not control fate, humans hold their destiny in their own hands. Additionally, Priam chooses to forgo his royal garb and its decadence for something more plain in an effort to appear more as a father than a king. Here we see Malouf taking a more modern approach in...
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...Where do you live? what do you do? what is your major? etc. A lot of people asks that sample question. I like to answer this question. Because I'm satisfied for my life and my environment. I live in Chicago, I'm start to learning English... I live in apartment, i like to study English in my little room. I love my little common room, I love to study here... One of my favorite place is definitely my " Ordinary home ". I think we all have a favorite place in our mind. This place is meaningful place and all the time keep our unforgettable memory. When i was child i was watch News and read Newspaper a lot. Some of news is happy, some of them horrible. There are many many homeless children ' information on the news. When i read or watch this homeless children ' news, after that i feel weird, uncomfortable and keep think about them. They are just like me. Why are they sleeping in the street? Where is their parents? What are they eating? Are they have warm clothes? many questions come to my mind. Almost every night before i go to bed i think homeless children, begging to some help them and pray for them. Sometimes I can't sleep well. But still i can't help them. I was too young. Then i thought i always need to compare my life to other children ' life. I'm one of lucky person in the whole world. First of all, I have a large family, dad, mam and sister. We have a apartment to live, we have a warm clothes to wear, we have a enough food for to eat. We don't have expensive house...
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...Out of the Ordinary, the Wife of Bath. Novelist and philosopher C. Joy Bell, author of “Saint Paul Trois Chateaux” and “Sun is snowing” once said, “I don’t fit into any stereotype and I like myself that way” (Bell). This is the exact description of the Wife of Bath as she is the kind of person that stands out from the rest. Although she comes from the medieval period, she has characteristics of a modern woman such as power and affluence. During the medieval period, women were viewed as subordinate creatures to men. A typical medieval woman married and began raising children soon after reaching puberty. Husbands had full control over their wives and a wife had to be loyal to her husband and obey him at all times. Blewitt described this saying; “A wife . . . must please her husband and be totally obedient to him, even when he is unjust and violent” (Blewitt 662). A woman’s sole purpose was to bear children, ". . . a wife's first duty was to provide her husband with an heir, and she could be divorced if she were barren"(Rhinesmith 601). They remained largely indoors, having no true chance to receive a formal education or hold economic or social power. The Wife of Bath is a complete opposite of the typical medieval woman. Although she married early, she is not under the control of any man. In fact, she uses sexual power to control her husbands by depriving them of sex in order to get what she wants. Another thing that distinguishes her from the typical medieval woman is that she...
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...Ordinary Men Christopher Browning’s book, Ordinary Men: Reserve Police Battalion 101 and the Final Solution in Poland, examines how ordinary men in Reserve Police Battalion became such cruel, cold-blooded killers. During World War II, the Police Battalion 101 helped cleanse out Poland as part of the Final Solution. The Final Solution was Nazi Germany’s plan to execute all European Jews during the World War II. Most of the Battalion 101 were made up of working class or lower middle class from Hamburg area, with majority of them falling in the age between 37 to 42, which “would not seem to have been a very promising group from which to recruit mass murderers on behalf of the Nazi vision of a racial utopia free of Jews” (Browning, pg.48). As ordinary as the men of the Battalion 101 were, the question remains how most men in the Battalion became killers and what caused this behavior. Browning cities several theories to how such ordinary men could commit such atrocities, such as “wartime brutalization, racism, segmentation, and routinization of the task, special selection of the perpetrators, careerism, obedience to orders, deference to authority, ideological indoctrination, and conformity” (Browning, pg.159). Out of these theories, conformity is the most important reason how the ordinary men in the Police Battalion 101 became killers. The Reserve Police Battalion 101 was a group of ordinary men from Hamburg, with most men not having any experience in any kind of military...
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...Within the Jarret family, Beth, Conrad and Calvin all have different problems, which all still exist among present day people. Each individual's problem involves another member of the family, resulting in a new problem. Beth is a perfectionist who is inexperienced with tragedy, Conrad searches for himself while trying to please people around him, and Calvin is overcautious about his son. Although all three have different problems this film depicts how one person's problems can affect the entire family. Beth's inability to forgive forces her son, Conrad, into living for others, and her husband, Calvin into obsession with his son's feelings. Conrad's mother refuses to forgive him for his suicide attempt, because she believes he did it in order to destroy her perfectly ordered life. To begin with, Beth likes to believe that life is faultless so her family is forced to tolerate it. Beth is used to a perfect life therefore she is unable to adjust when something goes wrong. By learning her irritations, Beth's family allows her to maintain the perfect image. However, by encouraging her to keep up the perfection, Beth will assume flawlessness is the norm. Secondly, Beth is accustomed to perfection; as a result she takes Conrad's suicide attempt as his revolt, and refuses to forgive him saying "Blame me for the whole thing... That whole vicious thing! He made it as vicious, as sickening as he could! The blood-all that blood! Oh, I will never forgive him for it! He wanted to kill me,...
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...Reina Cyrelle Montevirgen BSA-1A 1:15-2:45 PM Persuasive Speech (About Texting) Teens, I’d like to offer you some advice that may be the most important lesson you’ll ever learn about driving—although it may have only been covered briefly in a single lesson of your driver’s education course. Texting while driving is a serious distraction and one that could cost you your life or the lives of others. I know how hard it is to put the phone down and concentrate on the road. Even as an adult, I sometimes struggle with avoiding distractions while I’m driving. But there are plenty of other options and a lot of good reasons to keep your eyes on the road. I know you may think that it only takes a second to type that text and hit send. However, in actuality, the average text takes your eyes away from the road for five seconds. If you’re going 55 mph, then five seconds is the amount of time it takes you to drive the length of a football field. A better alternative is to wait until you reach your destination. Or, if you absolutely must respond to a text sooner, find a safe place to pull over. You may also think that you’re a good enough driver that you can safely send a text message without interfering with your ability to operate your vehicle. Statistics show that teen drivers who text spend approximately 10% of their driving time driving outside of their lane. But it’s hard to know that if you aren’t looking. If having the phone within reach is too much...
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...In the movie, Ordinary People, directed by Robert Redford, talked about a man named Conrad who suffered from depression. His brother died, not too long ago. Him and his parents tried their best to stay strong as possible. Conrad’s lowest point in life was when he would get flashbacks of what has happened in the past. Mostly, it is about his brother letting go from his hand and drown. Also, the flashbacks was not even a dream from his sleep. He was once with his friends where he had a flashback of a cemetery. We all readily agree that it is a horrifying accident and nobody should ever go through. Poor Conrad would always wake up sweaty from nightmares. He also avoid interacting with people, especially his own parents. His parents are Cal and...
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...3. Materials This section will describe the materials that were used in the laboratory experiments that will be presented in this thesis. 3.1 Portland CEMENT Portland cement is composed of a combination of limestone and either shale, clay, sand, or iron. These materials are ground and blended together and heated in a kiln from 2600o F to3000o F. This causes the materials to fuse together to create clinker. Cooled clinker is then ground with gypsum (CaSO4*2H20). The addition of gypsum controls the aluminate chemistry and the setting time of cement concrete. Portland cement reacts with water to form a paste that binds the aggregate particles together to form concrete. Ordinary Portland Cement (OPC) of grade 53 is used in the project. The cement...
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