Rethinking Calculus

Mathematics can sometimes seem scary for me, and I am sure that a lot of other high school students feel the same way. Maybe, it’s because we often see math as merely a series of problems to be solved and rules to master and apply. Calculus is one of the branches of math that some students like me find intimidating to learn.This paper aims to establish an appreciation and better understanding of calculus by reviewing its historical groundings and giving the practical application of the subject.The foundation of calculus did not just appear in history, in fact, mathematicians had encountered numerous difficulties and problems that had led to their desire to find ways in which to offer solutions. It is the case that although Isaac Newton and Gottfried Leibniz were the ones to formulate the theorems of Calculus we know today, a fair share of mathematicians began utilizing concepts of calculus as early as the greek period. Calculus was developed from ancient Greek geometry.It was mainly use to Democritus calculated the volumes of pyramids and cones, probably by regarding them as consisting of infinitely many cross-sections of infinitesimal (infinitely small) thickness, and Eudoxus and Archimedes used the â€Å"method of exhaustion†, finding the area of a circle by approximating it arbitrarily closely with inscribed polygons. In fact it was Archimedes who was the first person to find an approximation of the area of the circle using the â€Å"method of exhaustion†; it was the first samples of integration and led to the approximated values of ?(pi). In line with the developments in the field of theoretical mathematics, it can be said that mathematicians encountered their own difficulties with math problems before they were able to actually find the answers through calculus. It was not until the 16th century when mathematicians found the need to further develop the methods that could be used to calculate areas bounded by curves and spheres.Johannes Kepler for example had to find the area of the sectors of the ellipse in order for him to proceed with his work in planetary motion. He was lucky enough to find the answer in two tries despite the then crude methods of calculus. Imagine if he was unable to compute the area of ellipses during that time, chances are there would have been a delay in the development of astronomical science. It was through Kepler’s exploration of integration that laid groundwork for the further study of Cavalieri, Roberval, and Fermat.The latter especially contributed a great deal to calculus by generalizing the parabola and hyperbola as y/a = (x/b)2 to (y/a)n = (x/b)m and y/a = b/x to (y/a)n = (b/x)m respectively. It is the case that some mathematicians (like Joseph Louis Langrange) consider Fermat to be the father of calculus, especially with his formulation of the method used in acquiring the maxima and minima by calculating when the derivative of the function was 0; this method is not far fro m that which we use today in solving such equations.The formulas we use today to determine motion at variable speeds use calculus. Toricelli and Barrow were the first mathematicians to explore the problem of motion by implicitly applying the inverse of differentiation, integral and derivative as inverses of each other in asserting that the derivative of distance is velocity and vice versa. Newton and Leibniz are considered to be the inventors of calculus because of their discovery of the fundamental theorems of calculus.However though both shares credit for the latter, Newton was able to apply it further showing its use both in his works in physics and planetary motion which are considered the most significant of all his contributions. The three laws of motion echoed if not are born out of the notion that since the world changes and derivatives are the rates of changes, and then the latter becomes pivotal to any scientific endeavor that attempts to understand the world. Newton was a ble to use calculus in determine a lot of things during his time.We must remember though, that in voicing Newton it is good to reminisce his advice that abstractions and concepts don’t stand alone, they’re pieced together with other ideas to find a solution, an answer. This goes with his Newtonian laws, which if we are to really understand we must see how it relates with his law of gravitational force. Calculus bridges the gaps between theoretical math and the applied sciences/mathematics; if we are to look at it exclusively then we would miss the entire point of why we use it as such fail to realize its true value.Calculus plays a role in the natural, physical as well as the social sciences; it is being employed in solving numerous problems that wishes to determine the maximum and minimum rates of change. It is capable of describing the physical processes that occur around us. It has even been used to solve paradoxes created during the time of Zeno in ancient Greece. It is impossible to imagine how we can be able to understand the world today without the calculus as one of our tools in acquiring knowledge. We may perhaps still be slaves to mystical forces that were claimed to be the cause of change in this world.Mathematics would remain to us mere abstractions if calculus was not introduced to become the mediator of thought and practice. The development of other disciplines would have not followed without first establishing the existence of the fundamental concepts of calculus. Things which in history were thought to be inconceivable were able to have a figure that man can understand and therefore have the capacity to manipulate though not complete control. Students like me get frustrated when trying to solve a mathematical problem and failing once or twice.Reading on the history of calculus made me realize that mathematicians would not have come up with the theorems and methods we use today if they too decided to simply get frustrated. In as mu ch as Calculus teaches you at what rate things change and how the infinite can be understood, one could also learn the value of knowing something even if exclusively it seems unimportant. In order for us to appreciate the subject we must look at it as part of the greater system of knowledge, without it all things would not be coherent.

There are many reasons why you could argue the ‘Class Structure’ is changing in the Contemporary UK

Firstly, up until the 1980's wealth was becoming more fairly distributed across the population, however since the 1980's this trend has reversed and the gap between rich and poor has rocketed. Now a days, most wealth remains in the hands of a tiny minority whilst the majority float above the fine line of poverty. New Right sociologists claim that the old ruling class has disintegrated and a share owning expanded middle class has emerged. Peter Saunders now claims minority rule by a minority class has been replaced with a nation of stakeholders. However the continued existence of a ‘power elite' controlling the majority of wealth and power has been well documented by John Scott. Manual work patterns have changed also, i.e. in the primary and secondary industry manual jobs have declined significantly, whilst service sector jobs have increased. The expansion of the Welfare state has caused professional and non manual jobs to increase, results in a bloated middle class. The traditional working class has also changed, with women becoming a more influential and important member of the work force. Part time work has increase too. As a result of a rising global economy a geographical shift in the traditional working class has emerged. In the West there has been a growth in non manual employment with an extension of state services, in particular teachers, nurses, clerks etc There has also been an increase the employment of women and part time low insecure employment. Roberts claims the middle class has expanded but also ‘fragmented' into a number of distinct groups, i.e. professionals, managers, self employed. Roberts call these strata within the middles class ‘class fractions' each with its own culture, norms and values. Professionals tend to employ internally, therefore if your father is a professional you are much more likely to be employed. Savage suggest that professionals have a strong sense of class solidarity as evidence of their willingness to take collective action to protect their values, i.e. Occupational Associations-BMA, law society and lower down the NUT There has been a significant increase in self employed people, especially in the areas of consultancy in the finance, ICT areas. Large numbers of employed managers have their own consultancy business too. It is understood that Henry Ford shaped the traditional working class with his first moving assembly line in the 1914. Work was divided up into much more manageable loads and presented to a much lower skilled work force in return for lower labour costs. Fordism shape both working class and its sense of solidarity. However with manufacturing in decline this class has also begun to decline. Henry Braveman argues that Fordism still impacts working class as workers are constantly de-skilled with the introduction of technology. This introduction of technology has also dented the middle class occupations as white collar clerical/ technical are subject to proletarianisation by the impending application of technology. Marxists suggest that revolutionary class consciousness will be the result of such trends. Daniel Bell suggests that we are now living in a post fordist or post industrial age where work is based intellectual creativity rather than physical effort. Businesses also take more care of their workforce through better conditions, pay and concern for professional development. To support these claims by Bell the primary and secondary industries have declined whilst tertiary have expanded, as a result fewer people in Western Europe now work more with their brains than with their hands. Service sector workers lack the old structures of union and solidarity, thus seemingly becoming more privatised. There has been a growth of highly skilled new technology workers (wired workers) whom work from home, enjoying increased flexibility, challenge and autonomy. However there is strong evidence against Bell's theory, i.e. some sociologists argue that manual work has simply followed market conditions to low labour costing parts of the world. Also some argue the point that most computer workers sit in fact sit front of computers to input simple repetitive data, in poor conditions and for low pay.

To which extent have the reforms of the judicial system in Russia been Essay

To which extent have the reforms of the judicial system in Russia been successful - Essay Example The sovereignty and self-government of the Russian Federation and the initiation of judicial reforms was announced. On the orders of President Boris Yeltsin, in 1991, the highest ranking body in the Russian nation, the Supreme Soviet of the Russian Federation, accepted the idea of reform for the Russia’s judicial system. The Supreme Soviet of the Russian Federation in 1993 ratified the Law on Jury Trial despite the resistance that was staged by the Prosecutor General. All major court cases that the local courts came under the jurisdiction of the jury trials. This system of jury trial was realised in 9 areas of the Soviet Russia. Since then, the practice of jury trials has become normality. In the year 2000 alone, judges in Russia had tried about 900,000 legal cases, with 1,300,000 defendants, and 450,000 appeals. This number pales in comparison with the numbers of court cases that the judges before the introduction of jury trials were forced to cope with. Though even after the reforms of the nineties many Soviet residents were forced to deal with lengthy procedures in order to get justice, it was a considerable improvement from the days when residents could not possibly hope for their cases to be tried due to the backlog of cases in the court. In 1996, further reforms were summarily stopped. This was because the Russian authorities realised that the reforms were not affecting the most critical of institutions. For example, law enforcement establishments, and institutions such as the public prosecutors and the militia were not inspired to implement change. Russian society had long accepted the reality that the only way through which people could be coerced to tell the truth in some circumstances was through the use of torture. This was an accepted practice that even had supporters among the members of the Russian public. Another reason why the reforms of the early nineties period were not far reaching is because there were not enough finances to implement the reforms in all areas. For example, Russian judges were given measly salaries that left them open to being bribed. In Russia, the highest courts have their requirements provided by the President's Administration. For this reason, there are many verdicts of the Russian Federation’s Supreme Court which are divergent (Hoffman 2011). Though often democratic in theory, the decisions of the Constitutional Court can actually end up intensifying the real situation. Following the verdict of the Constitutional Court, the legal right of defendants to come before the jury began to be viewed as a provision that was specially authorised by the president’s administration. However, this remained something that could only be practiced in the highest court. Other lower level courts continued the practice of accepting money as well as gifts from the regional governors. This is outlawed by the Russian Constitution; nevertheless the courts had no choice but to take bribes. If they refu sed to accept such gifts, they would be forced to stop all operations because of outstanding bills, and the lack of amenities such as chairs, and paper. Even the buildings in which court cases were tried were decrepit and in serious need of repairs. The regional courts situated in Saint-Petersburg and Moscow were some of those involved in the most cases of bribery. Therefore, the mayor of Moscow tended to win in all

Fitness program for Snooki from jersey shore Essay

Fitness program for Snooki from jersey shore - Essay Example cise, exercise gives individual the benefits that cannot be achieved from dieting as it allows the individual to boost their metabolism while making sure the body burns the fats that are not needed. Exercise can be used to build muscles, enhance the shape of the body and result in a firm and toned body while dieting alone cannot promise a body that is firm and toned. When combined with dieting, exercise increases the rate of losing weight (Caballero, Allen and Prentice, 411). Nicole â€Å"Snooki† Polizzi is a reality TV personality and dancer who is famous for being a member of the cast of the MTV reality show Jersey Shore among other shores including talk shows. She has struggled with anorexia while growing up as a consequence of cheerleading but her parents helped her deal with the disease. As an adult, she gained weight especially when she was starring in Jersey Shore. This fitness program is aimed at assisting her reduce her weight to healthy levels through working out and a healthy diet. This fitness program takes between four to twelve weeks depending on the weight that is to be lost. It should be followed together with healthy eating and a control of portions, which means eating the appropriate food in the required quantities at the correct times so that it can be easier to burn pounds of fat each week. The program will include a resistance program that will assist in gaining muscles meaning that progress will have to be monitored through body measurements as well as body fat percentages. In order to maximize the reduction of body fat, the type of food and its portions should be changed to fit the new way of life. Losing weight can be achieved with the kind of diet a person takes but in order to increase the muscle strength and cardiovascular fitness, gym workouts will be required. Therefore, a weight loss fitness program should stimulate as much fat as possible through three full body workouts every week with two day of cardiovascular exercises and two

Chapter review Essay Example | Topics and Well Written Essays - 1000 words

Chapter review - Essay Example While the peacebuilding operations have gained pace, the studies with respect to the challenges and operations of peace building have also come into focus. They try to bring about therefore, a globalization of not merely the goods and services but the way a state should function. They promote democracy and free market mechanism. These standards are thus getting transmitted from the western regions (serving as the core) to the periphery (the nations undergoing reconstruction). This is the main point of argument in this research paper. The idea is not to proclaim that such globalization is not appropriate, but to focus on the perspectives of peacebuilding operations leading to promotion of a single kind of framework in terms of economy and administration. In this context, the activities of the peacebuilders might be related to the idea behind ‘mission civilisatrice’, which is the policy of civilizing the dependent countries followed by Europe during the colonial period. Th e analysis followed for the paper is qualitative in nature and secondary research method is followed to empirically show how the peace promoting organizations have promoted the liberal market democracies in the war-shattered nations. In the first section the author presents this empirical analysis and explains the mechanisms through which this process is put into action by the peacebuilders. In the second section the author first connects the idea of peacebuilding and that of ‘military civilisatrice’. Next, he associates peacebuilding operations with globalisation. The paper describes in the empirical analysis, how organizations like US Agency for International Development (USAID), The Organisation of American States (OAS) etc have promoted the western ideologies of liberal market democracy in peripheral countries like Namibia, Angola, Rwanda, Nicaragua, Guatemala, Cambodia,

Importance of Providing Additional Support to the Prisoners, Prison Research Paper

Importance of Providing Additional Support to the Prisoners, Prison Management - Research Paper Example The rate of crime has increased drastically over the years and in the absence of a comprehensive professional and continuous learning and development program, that seeks to enhance the lives of the citizens as a whole, curbing crime and ensuring a safe neighborhood is inconceivable. Statistics reveal that approximately two-thirds of the prisons in England and Wales are stuffed with inmates well beyond their actual capacity. According to the Howard League for Penal Reform, approximately 52, 500 prisoners are stuffed in jails which are overcrowded, similarly, in HMP Preston, 661 prisoners are forced to live in a jail which has a capacity of holding 356 inmates, the worst case by far. (BBC News, 2009). Such staggering statistics call for immediate reformative measures which involve proactive policies to keep people out of jails. This, however, can be achieved only through the adoption and implementation of a wide-ranging program that focuses on providing adequate training to those in ch arge, i.e., the prison officers who are entrusted with the responsibility of providing security, supervising, offering training as well as rehabilitating the offenders through motivation and encouragement. Preventing prisoners from reoffending is one of the key objectives of any criminal justice system. Although punishing the offenders for their crimes, is the most widely accepted tools of justice, punishment alone cannot and does not guarantee a safe and healthy society. In order to create a harmonious environment and safeguard the interests of the general public, it must be ensured that the offenders abstain from indulging in any criminal activities.

Relationship Marketing and Customer Service Article

Relationship Marketing and Customer Service - Article Example Repeat orders will go to those sellers who have done the best job or nurturing these relationships." The changes in the global business environment necessitates relationship marketing in order for business organizations to compete more efficiently, attract potential, and retain current customers. According to the words of the marketing guru Philip Kotler (2005), the current business arena is turning "hypercompetitive" characterised by the presence of more intense competition among industry rivals and more bargaining power from customers. Thus, in order to survive and succeed in their markets, companies are required to rethink and revamp their current strategies and put their customers into center (Kotler 2005). These trends and developments in the market put strong pressure on companies and put into spotlight relationship marketing. Relationship marketing is an idea which dates back as far as 1960s evolving from direct response marketing during the period. Its reemergence in the 1980s is prompted by the initial research done by Leonard Berry and Jag Sheth at Emory which states that, "What is surprising is that researchers and businessmen have concentrated far more on how to attract customers to products and services than to retain them" (Pressey and Matthews 2000, pg. 272) Relationship marketing has been elaborated and broadened by the marketing theorists Theodeore Levitt in 1983. Relationship marketing is defined as "a philos... Relationship marketing thereby marks a transition from the traditional marketing approach of finding more customers for a product. In essence, relationship marketing is in recognition that a customer contributes to an organization his lifetime purchases of the company's product if it is able to design marketing strategies which can cultivate loyalty and develop good relationships (Kotler 2005). From its origin, relationship marketing has introduced a radical change on how business organizations think and conduct their operations. Traditionally companies have focused on attracting customers thereby facilitating only one-time transactions. However, the loyalty of a customer for a product and brand will facilitate repeat sales transactions thereby enhancing the firm's total profit and revenue. Thus, it becomes imperative for companies to long-term relationship with customers rather than on individual transactions by understanding the needs of the current customer as they go through their life cycles (Relationship Marketing 2007). Developing strong relationship with customer is strongly dependent on ensuring the delivery of satisfaction and delight. Levitt likens company's relationship with its customers into marriage: "The sale, then, merely consummates the courtship at which point the marriages begins The quality of marriage determines whether there will be continued or expan ded business, or trouble, or divorce" (Berger 2006). The expansion and facilitation of this new strategic approach to marketing can be directly credited to the advancement in technology specifically the establishment of customer relationship

Online Alternative Dispute Resolution Essay Example | Topics and Well Written Essays - 6250 words

Online Alternative Dispute Resolution - Essay Example Dispute resolution is the process of resolving disputes between parties, and there are various methods of dispute resolution, which includes such things as: lawsuits (litigation), arbitration, mediation, conciliation, as well as many types of negotiation. Dispute resolution processes fall into two major types: adjudicative processes, such as litigation or arbitration, in which a judge, jury or arbitrator determines the outcome; and consensual processes, such as mediation, conciliation, or negotiation, in which the parties attempt to reach agreement. Some use the term dispute resolution to refer only to alternative dispute resolution (ADR); of which generally depends on agreement by the parties to use ADR processes, either before or after a dispute has arisen. However, dispute resolution can also take place online by using technology in certain cases. Online Dispute Resolution, a growing field of dispute resolution, uses new technologies to solve disputes. It also involves the applica tion of traditional dispute resolution methods to disputes which arise online.1 There are a vast array of factors, elements, and subordinated issues in this subject matter, and in order to come to a clearer and more knowledgeable understanding on this issue, the following questions must be addressed: 1. What is the definition and scope of application in regards to Online Dispute Resolution 2. What is the importance of the rise of Online Dispute Resolution 3. What are the similarities and differences between Online Dispute Resolution and Alternative Dispute Resolution 4. What are some problems affecting efficiency in regards to Online Dispute Resolution in the shadow of the law 5. What are some problems affecting efficiency in regards to the trust mechanism in the online environment By thoroughly discussing these five questions, we can come to a more intellectual and critical point of view on the subject matter at hand. The aim of this paper is to discuss all of this, as well as any and all key elements and factors in relation to this. This is what will be dissertated in the following. What is the Definition and Scope of Application in Regards to Online Dispute Resolution Online Dispute Resolution is a branch of dispute resolution which uses specific technology in order to facilitate the resolution of disputes between parties. It primarily involves negotiation, mediation or arbitration, or a combination of all three. In this respect it is often seen as being the online equivalent of Alternative dispute resolution (ADR). However, ODR can also augment these traditional means of resolving disputes by applying innovative techniques and online technologies to the process.2 Online Dispute Resolution can take place either entirely or simply partly online and primarily concerns two types of disputes: those that arise in cyberspace and those that arise offline. As Internet usage continues to expand, it has become increasingly necessary to design efficient mechanisms for resolving Internet disputes because traditional mechanisms, such as

Discuss the most common challenges faced by management in an Essay

Discuss the most common challenges faced by management in an international context - Essay Example Besides the common challenges the management faces, globalization and the rise of multinational organizations have created challenges from communicational dimensions. In this essay, four main communication barriers will be discussed; they are cultural barriers, distance barriers, trust barrier (inner barrier), and the language barrier. In the process of international management, cultural understanding is a crucial factor to create opportunities for economic growth and development. To create cultural understanding, the manager is challenged with the task of learning and comprehending other cultures and contexts. This serves to reduce as much cultural difference as possible, and avoid communication breakdowns wherever the company or organization may encounter it. For example, while Arabs treat their leaders as heroes and worship them as long as they remain in power, Iranians expect their leaders to exhibit power and strength. (Phatak, 2005, p.5) Most common cultural differences are broadly categorized based on the following factors- power distance, uncertainty avoidance, human orientation, collectivism, assertiveness, gender egalitarianism, future orientation, and performance orientation. (Phatak, 2005, p.5) It is the management’s responsibility to analyze other cultures and minimize any cultural problems to maximize efficiency. This results in better business expansion, improved production and better image for the company. A manager who has a better understanding of the various cultural factors will be able to adopt appropriate management techniques and procedures that adapt to differing cultural values and beliefs. For this to occur, it is important that the manager accurately analyses the situation and acts accordingly or it may lead to a sharp decline in efficiencies. In leadership at every level possible, the most important factor is ‘trust’. Without trust in