Comparing Eulers Method with Numerical Methods Thesis

Comparing Eulers Method with Numerical Methods - Thesis Example Nonetheless, differentiation of equation expressing these systems and shapes was noted to be quite complex. Moreover, these equations are only capable of describing extremely large systems and shapes, so pure mathematical analysis on them is quite impossible. The complex nature of these systems led to the usefulness of numerical approximation and computer simulations. Therefore, this paper will analyze Euler’s method in differentiating these complex mathematical equations. Notably, the numerical approximation techniques that are applied in solving the differential equation were thought of and developed long before the existence of the programmable computers. During the Second World War, people (particularly women) used mechanical calculators (in their rooms) to solve differential equations for war purposes. However, the introduction and increase in programmable computers and computer applications have decreased the cost and increased the speed, thereby increasingly easing solv ing the difference equations of complex systems (Kuang and Cong, 2007). For example, laptops can easily compute a long term interjectory of over one million interacting molecules. For about five to ten years ago, this problem seemed inaccessible to even the then fastest analog supercomputers. This essay will introduce the fundamental principle of numerical approximation and relate to geometry and curved surfaces. Thereafter, it will analyze how simple geometric problems can be handled using Euler’s method. Generally, numerical differential equations are always represented in the equation or functions, f. These functions can handle a wider range of ordinary differential equation (ODEs) and partial differential equations (PDEs). A system of ordinary differential equations can contain any number of unknown functions. However, all these functions must be a derivative of a single independent variable, t that is the same for other functions (Kuang and Cong, 2007). On the other hand , partial differential equations often have two or more independent variables. Differential Equations There are numerous ways of solving differential equations. However, there are fundamental equations upon which all other equations are built. The first order system of differential equation takes the simplest order dy/dt = f(y, t) or y? = f(x, y). Where dy/dy represents the change in y with time and f(y, t) is a function of variables y and t. notably, there are numerous notations for the change d/dt. The most common ones include ? and y’. This equation satisfies numerical integration that means computation from initial point y0 (the initial condition) to the other successive conditions y1, y2, y3 †¦ since differential equations cannot be solved analytically, they take an algorithm that computes the function or equation as precise as possible, that is, yn+1 from yn. In some cases, y may be a vector while the evolution equation may be non-linear differential equations. Pro blem Formulation The main theme of this essay is to use first order differential to solve differential equation under certain set conditions. Consider that the fundamental differential equation of the first order of ordinary differential equation is dy/dx = f(x, y) with the initial boundary condition being y(x0) = y0. Approximate the function y(x) over the sample values of xn

Platos Form of Good and Justice Essay Example | Topics and Well Written Essays - 250 words

Platos Form of Good and Justice - Essay Example He was dissatisfied with the conditions that were prominent in Athens.The democracy here was failing and it was heading to ruins. He characterized his own concept of justice by bashing the notions that were held by the likes of Glaucon's and Adeimantus. This paper will look into the concept of the good of justice in and of itself as challenged. It will also focus on the Good of the Soul, its three form nature and immortality.Glaucon on justice presupposes that human good is made of a combination of power, wealth and pleasure and because these are limited, there have to be a competition among men for them. He says that it is natural for one to pursue what he sees as good.Socrates refutes the social contract and the bases of Glaucon’s argument by saying that the ultimate source of value is not found in nature and not in the human notion of social contract but it is a notion grasped by the intellect that is enlightened, which is the Form of Good. From his arguments he comes with the prospect of the good of the soul where he says that the soul is tripartite in nature and also that it is immortal and when one dies, their soul lives on. He used the three elements of the soul to explain how the society should be and the concept of Justice and Good is elaborated.This reasoning according to me it is very valid. It gives a reasoned version of what Good is and the concept of Justice coupled with Good. It gives the basis of what Plato was later to conceive as the Form of Good/Justice.

ENG 315 Presentation Critique Assignment Example | Topics and Well Written Essays - 500 words - 1

ENG 315 Presentation Critique - Assignment Example While it can be concluded from the title that the program is a meal-delivery system for the seniors, the presentation could have started with a visual description of how it will be like to have food easily and readily available to people who need it. However, this did not ruin the overall understanding of the audience on the topic. The opening statement is very catchy and able to get the audience interest. The speaker said: â€Å"Meals on wheels is taking action to end senior hunger.† Not only is the opening line catchy, it immediately gives a hint of the problem that the presentation is trying to resolve. The main points, such as what the program is, what the problem is, statistical data proving there is indeed a continuing problem, why the problem needs to be alleviated, and what the program can do were properly emphasized. However, the important detail of how a senior can enroll in the program was left out. The speaker utilized the â€Å"problem solution pattern† of speech, where the presentation informs the audience of the risks of the problem, the importance, the causes, and the solution. This pattern is alerts the audience to the fact that the issue is something to be concerned of. No, there were no transitions carried out, which makes some area of the presentation abruptly stopped. Good transitional phrases would be: â€Å"Why do we need to know this?† Such would also recapture the attention of the audience. The presentation was summarized, but somewhat too briefly. The summary was only about what the program does. It did not reiterate the reality of the problem, and did not restate how the program is a big relief for this problem. Taken on the emotional level, the closing statement is strong. However, it lacked information. The closing statement seems to call for people to take action: â€Å"Every one of us can play a very important role in the life of a senior. I encourage you to make a difference!† How? Can ordinary people call and enroll a

A letter to the editor in the Wall Street Journal Essay - 6

A letter to the editor in the Wall Street Journal - Essay Example ts ahead of credit cards, I would like to bring to your attention my support and satisfaction towards the article and the author because I felt that it highlighted the reasons for that payment trend and was straight to the point. The payment of Mortgages before the credit card has been the normal way and has been in effect for a very long period of time, this is exactly what lenders expect from consumers. New information from TransUnion, which is a firm that deals with reporting credit related information, supports this stand that normal payment methods were back to effect at the end of the year 2013 due to a rise experienced in home values. The main findings from the research carried out shows strong links between the value of homes and payment behaviors. Further supporting this case is the findings that were published from all the fifty states in the United States which clearly point out that a decline in home values together with high unemployment rates saw borrowers skip mortgage payments but still make payments on their credit cards. There is an example of Nevada, between the years 2006-2009, where the value of houses went down by 57%. Borrowers were seen to skip making mortgage payments while staying true to credit card payments. It’s clear that people would be more willing to default on mortgage payments because foreclosure is not really an immediate problem. it involves a long process which takes months if not years. Credit card payments on the other hand would be hard to miss, by doing so the reaction would be immediate. Banks should therefore continue to ease standards on mortgages to the payments of mortgages ahead of credit

Analysis paper - social media Essay Example | Topics and Well Written Essays - 750 words

Analysis paper - social media - Essay Example networking sites such as Facebook, Twitter, LinkedIn, Google+, Instagram and other social platforms have been found to be the major causes of loneliness among many people all over the world. This paper is a critical analysis of Stephen Marche’s argument that the use of Facebook tends to promote people’s preference for loneliness through solitude and isolation. In achieving this, I have discussed the contributions of Facebook on personal loneliness among various groups of people across the world. Among the key social networking sites commonly used today, Facebook, takes the largest share of online users compared to other social networking sites aforementioned. It is common to find people of different ages, academic levels, and social status deeply glued on Facebook, chatting, posting, writing comments on other friends’ posts or doing the mere liking of posts and comments made by their acquaintances. Lecturers have complained of deteriorating performances in their subjects even by their favorite students due to the influence of technology (specifically social networks). Besides, affecting their performances in various courses, fondness with social networking sites has increasingly isolated friendship ties between various students and their close allies. Solitude is not a recent phenomenon in the society. The feeling has long been in existence since the advent of humanity. The perception and causes of solitude are, however, its most common determinant. Different from the traditional forms and causes of solitude, the current causes are self-inflicted other than natural. The natural conditions of solitude are seamlessly endurable since they were somehow beyond the reach of the victims. The need to express oneself as a move to defend ego and register high sensation among peers and friends keeps most Facebook users glued to their social sites trying to compose and post suitable posts and comments that would resonate appropriately with their acquaintances. The

The economic analysis of the U.S. Endangered Species Act Term Paper

The economic analysis of the U.S. Endangered Species Act - Term Paper Example An overview of the objectives and structure of the Endangered Species Act provides a very detailed and broad protection for many of the colorful species that inhabit this Earth. Wildlife and plants when listed as endangered fall under the net of this protection outlining procedures that federal agencies should follow and adhere to if there is the slightest chance the species are jeopardized. Not only does the Endangered Species Act of 1973, written by a team of lawyers and scientist and written into law by President Nixon, protects endangered species it also provides security for their "ecosystems upon which they depend" as well. The Endangered Species Act enables legislation for the Convention on International Trade in Endangered Species of Wild Fauna and Flora, commonly known as CITES. Criminal and civil penalties provide for the violations of the Act and the Convention.

The American Civil War Essay Example for Free

The American Civil War Essay The impact that religion had on reforms from the 1820s to the 1850s can clearly be seen in the effect that it had in contributing to the American Civil War. Religion played a key role in the different positions that the North and the South were going to take with regard to the issue of slavery. The Presbyterian, Baptist and Methodist teachings espoused themes of both unity and separation. This was echoed well during the activities in 1837, 1844 and 1845, respectively, when the bond of national unity was broken. Instead of unifying a country, most of the religious influences during this time caused the alienation of most sectors by projecting distorted images. In turn, this led to the establishment of independent sects in a once united country. This rift and sectional independence was sustained by the growing moral outrage that each side felt for each other. The overemphasis of the church, during this period, on individualism failed to provide the leadership necessary to steer the nation through many issues, none more pivotal than that of slavery. An example of this would be the reforms instituted by the Republican Party. These reforms were rooted on a form of Calvinism that was deeply moderated. The southern evangelicals on the other hand, attempted to resist the influence of religion into politics by supporting the confederacy. The opposite reforms that each side was about to take from the 1820s to the 1850s was caused by the inability of religion to collectively and squarely address the issue of slavery. For the north, it was reforms that were rooted on social action while the South focused their reforms on personal piety. While both sides championed the Bible in their quest to resolve the issue on slavery, they each took opposing opinions which eventually took them down the path of one of the most radical reforms in American history.