Factors to Consider in Teaching Young Language Learners

Introduction. Teaching English: More than Teaching Language Teaching, in general, and teaching the English language, in particular, is a challenging and complex task. It involves numerous stages of the crucial factors’ analysis, identification of the existing methods for managing specific problems and providing learners with the necessary resources.Advertising We will write a custom research paper sample on Factors to Consider in Teaching Young Language Learners specifically for you for only $16.05 $11/page Learn More These resources are needed to acquire the necessary information and train the corresponding reading, writing, and speaking skills. However, apart from the specified challenged, an English language teacher faces the necessity to play the role of an inspirer and a leader, supporting students and encouraging them to develop the ability to learn independently and understand what they need in order to accomplish a particular goal. The pro cess of teaching languages to young children owes most of its complexity to the fact that, despite a common idea of young learners acquiring information fast, students need extensive help and consistent support. To meet the needs of the target audience, a teacher must design the strategy that will promote active learning among the students and motivate them to learn more, therefore, increasing the rates of enthusiasm and involvement among them. Literature Review: What Young Language Learners Need A detailed analysis of the existing studies on teaching English to young learners will reveal that the process in question demands that the teacher should be able to address the specific needs of young learners. Particularly, it is important to keep in mind that crucial cognitive skills are developed at the specified age. Thus, a teacher must be able to identify the unique characteristics of learners and provide them with the opportunities for becoming proficient in English. Local Studies: Recent Tendencies in Education An overview of the existing resources on the subject matter shows that the Saudi Arabian education process is focused on integrating the traditional Islamic values into the learning process (Gawi, 2012). As a result, the process of the required information acquisition occurs by interpreting the data in question through the lens of the Islamic philosophy and worldview (Gawi, 2012). One must also bear in mind that there has been a sharp increase in the number of students and teachers recently; particularly, the introduction of numerous ESL learners into the environment of public schools needs to be brought up as the key factor shaping the teaching strategies (Malihi, 2015). Foreign Studies: Addressing the Needs of ESL Students Foreign studies also point to the necessity to consider the use of games as the key to promoting early childhood learning. However, researches also show that the consistent focus on entertainment rather than education may occur as a symptom of teachers’ lack of enthusiasm in promoting change in the classroom.Advertising Looking for research paper on education? Let's see if we can help you! Get your first paper with 15% OFF Learn More The teaching strategy based solely or mostly on games may also be interpreted as the symptom of the teacher’s lack of involvement in the learner’s progress (Gaynor, 2014, p. 123). Therefore, when evaluating the teaching approach adopted, one must also consider the factors that defined the choice of a particular strategy. While studies have shown that young learners acquire information and train skills more efficiently when playing educational games, the use of the latter will not make for the lack of teachers’ concern. Foreign studies also point to the possibility of developing bilingualism in young children (Nunan, 2010). It should be noted, though, that the specified prospect may become a possibility in cases of high parental involvemen t rates. In other words, it is necessary that parents should help students develop the necessary skills by creating the environment, in which learners will train the skills of using both languages. The need to schedule the learning process is, perhaps, the trickiest requirement. The existing studies, therefore, point to the fact that the issue regarding early education is not as simple as it might seem. There are indications that young children learn the information related to languages very fast and develop an intrinsic understanding of the languages true. However, young learners will not necessarily display the readiness to learn the English language at the same pace and with the same enthusiasm. Herein the need to design the approach that will encourage young students to develop English speaking, reading, and writing skills lies (Rahman Alhaisoni, 2013). Problem Analysis: Factors Affecting the Learning process Among Young Students Needless to say, age plays a significant role in the identification of learners’ needs. In the specified scenario, it is important to take into account that young learners who are at the stage of acquiring essential knowledge do not necessarily display the tendency for rapid skills acquisition. Specifically, previous studies conducted on the subject matter delivered mixed results concerning the students’ ability to acquire information faster at the early stages of their development (Copland Garton, 2014, p. 224). In other words, a teacher must realize that student will need substantive help to attain the required level of proficiency. In addition, studies point out that young learners tend to acquire information in a manner that presupposes a stronger emphasis on acquisition rather than learning. Indeed, as recent studies show, the significance of formal language learning should clearly be downplayed compared to the process of training communicative skills in the target language despite the common misconception (Su karno, 2008, p. 59). Therefore, it is important to make sure that the process of learning should be focused on developing specific habits.Advertising We will write a custom research paper sample on Factors to Consider in Teaching Young Language Learners specifically for you for only $16.05 $11/page Learn More Learners’ Aptitude, Motivation, and Learning Styles The importance of the social environment, in which the students have been growing up and which define the way that the students view specific phenomena from are an essential factor shaping the teaching strategy to be adopted by the educator. Specifically, the social environment, in which the learners live, dictate the ideas and concepts that the instructor will use to help the learners train a particular language skill. In order to teach students to speak English, the teacher will have to create the environment, in which the will be required to use their language skills, and the specified e nvironment must be inviting. The creation of the atmosphere that students view as familiar and, therefore, inviting to engage in a communication process, will help motivate them to train the corresponding skills. Apart from changes in the social environment, it is strongly suggested that the emphasis should be placed on games as the key tool for achieving high engagement rates in the classroom. Particularly, it is suggested that the teachers should encourage students to engage in the activities such as memory games (e.g., the â€Å"snowball† game), word matching games, etc. Attaining high engagement rates requires meeting the needs of all students. In other words, it is essential to remember that even young students have very diverse skill levels character traits; thus, it is imperative to make sure that the tasks assigned to them correspond to their command of English and their background knowledge. Specifically, it will be crucial to provide the students with disabilities w ith the support that will help them acquire the English speaking skills fast. Apart from the factors attributed to learners, there are teacher factors that affect the choice of the corresponding strategy in a tangible way. Specifically, the tools that teachers use to educate deserve to be considered closer. Specifically, the significance of the teacher’s ability to provide comprehensive information regarding the English language, communicate with students, create tasks, supervise the learners and evaluate the students’ performance is obvious. To teach students English efficiently, an educator must revolve professionally so that they could inspire their learners and be efficient leaders. Moreover, the adoption of the strategies aimed at controlling students’ behavior, such as creating the so-called stop signs (Garton, Copland, Burns, 2011, p. 14) is as an essential tool for promoting the acquisition of the English speaking, reading, and writing skills by the Sau di Arabian students. Apart from the development of a coherent teaching strategy, an instructor must design the approach that will help To evaluate the learners’ performance teachers should consider both traditional and modern tools. Specifically, tests (both traditional and online ones) should be viewed as the basic tool of an English language instructor.Advertising Looking for research paper on education? Let's see if we can help you! Get your first paper with 15% OFF Learn More Speaking of which, it is essential to realize that a language teacher performs the roles of an instructor, a lecturer, a motivator, a coach, and a guide. To be more exact, a teacher not only provides students with instructions and information but also inspires them to learn more and, more importantly, learn independently. . One of the most efficient tools in evaluating the performance of young students, assessment by observation can be deemed essential to their success as it helps identify the slightest hiccups in the education. Thus, the emerging issues can be addressed correspondingly, and the learning process will remain uninterrupted. Self-assessment is another important method of evaluating progress. As it has been stressed above, a teacher must inspire students for self-directed learning and meta-cognition as the means of identifying the needed mode of teaching and acquiring the necessary information in an efficient manner. Therefore, the learners must be provided with an oppo rtunity to evaluate their progress on their own. The given goal can be accomplished by assigning students with the tasks related to peer assessment and self-evaluation. Learning Materials: Resources to Consider The significance of learning materials is especially high for young learners, as these materials define their further understanding of the subject matter and, therefore, their ability to acquire knowledge. Therefore, it is crucial to incorporate different types of resources including visuals, textbooks, online tools, etc. First, the significance of a curriculum must be addressed. It is essential to make sure that the continuity of the learning process should be maintained. Thus, the provision of a consistent learning process can be facilitated. The continuity in the learning activity can be facilitated by revising the information learned previously during the first ten to fifteen minutes of the lesson. The importance of textbooks and the scheduling of the curriculum are not t o be overrated in the early education setting, either. As a recent study explains, the problem of improving the quality of education as the means of promoting higher performance rates among learners through educating teachers has not been on the state’s agenda for quite a while (Maltihi, 2015, p. 98). However, the importance of the teachers’ competency is obvious, as it contributes to the provision of a perfect learning environment for young students. Therefore, an adequate arrangement of the existing learning resources and the students’ time is essential to the outcomes of the learning process. In addition to textbooks, learners need graphic examples of the information acquired in the process of studying. Herein the necessity to use various tools for exemplifying data lies. Although the use of visual aids and textbooks is the most common practice, the adoption of the information technology tools has recently gained popularity due to numerous positive effects. V isual aids can be interpreted as a crucial part of the young students’ learning process. Posters, pictures, charts, maps and other visual tools for arranging information can be deemed as very efficient. They are popular for a reason; helping learners identify essential data and summarize it, they allow for memorizing it fast by visualizing it. In addition, to reach a particular demographics, a teacher must appeal to their vision of the world. Consequently, it is essential to take the students’ cultural background into account. In the setting in question, the teacher must adopt the approaches that will help them appeal to the students from middle-, low-, and high-income families, the students from the American, African American, Asian, and other ethnic backgrounds, etc. To enhance the communication process, it will be reasonable to incorporate the use of modern tools such as online assessments, the use of iPods in the classroom, etc., to promote active learning. To addr ess the needs of young learners, a teacher should consider the use of both traditional resources, e.g., printed books, exercises, etc., and the adoption of interactive online tools. Thus, the learners will be able to receive the necessary information in a manner that involves exciting and engaging activities. As a result, the students will be capable of memorizing the necessary information fast and recall it easily when necessary. More importantly, the use of the latter set of tools will help create the environment that is close to natural English-speaking one. Hence, the learners will practice their newly acquired skills more efficiently. Learning Environment and Exposure to English There is no need to stress that the role of parents in the process of children’s early development is crucial. It is important to make sure that parents take an active part in their children’s education and that they encourage the further use of the skills acquired during lessons by the le arners. However, to facilitate a flawless learning process, the teacher must also make sure that the classroom environment creates the premises for successful knowledge acquisition. Particularly, a teacher must arrange the classroom environment in the ay that allows for the interaction between the students and the teacher as well as among the students. Conclusion: Fostering Development to Complete a Student as a Person An educator must bear in mind that teaching young students means inspiring them for further learning and providing them with the set of skills that will help them educate themselves efficiently in the future. More importantly, a teacher must make sure that the students will be able to engage in the process of self-directed learning as they grow older. In other words, a teacher of young learners must facilitate the students’ personal development along with the academic one. To provide learners with this opportunity, a teacher must consider their unique character istics and create the environment, in which they feel comfortable learning. Reference List Copland, F., Garton, S. (2014). Key themes and future directions in teaching English to young learners: Introduction to the Special Issue. ELT Journal, 68(3), 223– 230. Garton, S., Copland, F., Burns, A. (2011). Investigating global practices in teaching English to young learners. Birmingham, AL: Aston University. Gawi, E. M. K. (2012). The effects of age factor on learning English: A case study of learning English in Saudi schools, Saudi Arabia. English Language Teaching, 5(1), 127–139. Gaynor, B. (2014). Teaching English to young learners in Japan: Communicative competence and classroom reality. In Proceedings of CLaSIC 2014 (pp. 118–127). Japan: Muroran Institute of Technology. Maltihi, J. F. A. (2015). Saudi EFL teachers’ readiness and perceptions of young learners teaching at elementary schools. English Language Teaching, 8(2), 86–100. Nunan, D. (2010) .Teaching English to young learners.. Anaheim, CA: Anaheim University. Rahman, M. M. u., Alhaisoni, E. (2013). Teaching English in Saudi Arabia: Prospects and challenges. Academic Research International, 4(1), 112–118. Sukarno, O. (2008). Teaching English to young learners and factors to consider in designing the materials. Jurnal Ekonomi Pendidikan, 5(1), 57–73. This research paper on Factors to Consider in Teaching Young Language Learners was written and submitted by user Marco Avila to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.

Football

Football Free Online Research Papers Football is an all-American sport. It is America’s favorite pass time game. Football is also, from some people’s point of view, the single-handedly most violent sport around. Football has two variations to tackle. These are touch football; for people who cant play tackle football, and flag football for the little kids that don’t fit the pads. No matter how bad football seams to be for some it still has rules such as: 1. No taunting opposing players 2. No purposely hurting other players 3. Do not cross the line of scrimmage before the ball has moved more than a fraction of an inch 4. Show good sportsmanship to the opposing team 5. No foul language These are just a couple of the games rules At all times there are two teams on the field. There are four different teams. They are the two different special teams (kick off, and kick return) there also is the offence and defense. All teams have 11 players. The offence has, 1 quarterback, 1 halfback, 1 fullback, 1 running back, 2 tight ends, 2 guards, 1 center, and 2 tackles. On the defense team there is 2-6 linebackers, 2 defensive tackles, 1 safety, and 2 defensive ends. On the kickoff team there are ten runners and a kicker. On the kick return team you have the 4 front blockers, the 4 middle blockers, and the 3 returnees. Points are made by making a touchdown. To make a touchdown you must run the ball into the in-zone. Sound easy? That is where the defense comes in. The defense is stationed in front of the offence to try to keep them from getting the ball into the in-zone. The offence has four tries to get the ball into the in-zone. If they don’t get the ball in by the third try they can try it one more time, or, if the are to far to make a run play, they will try to make it through the goal post with a punt. If they run and make it they get the points and get the point after. If they don’t make it it is turned over to the other team. If they make the punt they get one point, if not it is turned over. Football is one of America’s best games ever invented. It is a free form game. This makes it easier to come up with new plays, you don’t know what will happen next. This is why so many people like it. Research Papers on FootballThe Hockey GameHip-Hop is ArtThe Effects of Illegal ImmigrationMarketing of Lifeboy Soap A Unilever ProductUnreasonable Searches and SeizuresEffects of Television Violence on ChildrenTwilight of the UAWThe Spring and AutumnResearch Process Part OneThe Fifth Horseman

Critical Thinking Master Case Study Example | Topics and Well Written Essays - 4000 words

Critical Thinking Master - Case Study Example The commitments by his team members or his Boss regarding iScanner are not valid because they do not know the bigger picture. Pat is trying to put her weight on him because she holds a senior designation in the company. Marketing personnel have the habit to jump to conclusions in the spurt of their aggression without trying to understand the product capabilities and positioning in a market segment. Pat hasn't done her homework in estimating the sales performance of the proposed product. Chris hasn't done his homework in concluding the budgetary figures The Organization hasn't developed any new product for more than a decade and hence lacks expertise in the same. Chris said yes to the plan under pressure from Pat and Cliff. He has not given due diligence from his side as well. Assumptions by Pat Lambert: Pat has a sound retail background and hence feels that her thoughts about the market are more powerful than survey reports and data analysis. She is more than convinced about the success of her idea. Getting into an innovation will ensure ample time to Pat thus taking her away from immediate revenue target pressures After reading the high level specifications of the iScanner software, Pat assumed that slight modifications in the product will make it suitable to be used in the application of her thought. Pat got a positive response from Kelly in a discussion that, in the perspective of Pat was a serious discussion while Kelly assumed that it is a casual discussion out of curiosity. Pat took his positive reply as "Technical Approval". An approval from Chris is good enough for her to build a proposal to Cliff. Kelly is too junior to be involved in the bigger picture at this... Kelly is proud to be the key architect of the iScanner Software and hence assumes that no plans in the company pertaining to this product can be successful without his approvals. He got mad when he came across a number of features defined by Pat that were discussed with his Boss and the CEO but not with him. He is not worried about the safety of his job in the company. Whatever might happen to others in the organization, he is convinced that his job cannot be taken because he is indispensable for the organization. Pat got a positive response from Kelly in a discussion that, in the perspective of Pat was a serious discussion while Kelly assumed that it is a casual discussion out of curiosity. Pat took his positive reply as "Technical Approval". An approval from Chris is good enough for her to build a proposal to Cliff. Kelly is too junior to be involved in the bigger picture at this stage and specifically when he has already given his so called "Technical Approval". Pat thought that after seeing the approvals from Cliff and Chris, Kelly will immediately get to work (given his level in the company, he is not supposed to question her decision and their approvals).

Are All Animals Created Equal Essay Example | Topics and Well Written Essays - 1250 words

Are All Animals Created Equal - Essay Example The setting in which the animals work from must be considered standpoint before these animals are subjected to acts that are proven detrimental and harsh that will give rise to pain and pleasure (Singer 1989, p. 149). This provides that there must be a certain understanding of the act being done towards them like slaughtering for consumption purposes and experimentation in the medical. These acts invariably highlight that humans are superior from other species and they have the freedom to do such act since these animals are means to an end (Steinbock 1978, p. 253). The aforementioned condition shows that in order for equality to be achieved, there must be an elimination of suffering. However, Singer failed to consider that the conditions of suffering, pain and pleasure for animals is not really the same to that of humans since humans have an intrinsic capacity that animals do not have: rational thinking (Steinbock 1978, p. 254). This rational thinking gives way for humans to have a v ery utilitarian approach on animals (Singer 1989, p. 150). Utilitarianism tries to ensure that humans maximize the things present around them to achieve their needs and desires (Armstrong 2007, p. 2). Given this scenario, there is nothing that appears to be problematic since this only ensures that humans achieve and gain what they need like food for them survive. However, humans, in most cases, failed to understand and appreciate the findings of modern science like the consumption of alternatives to animal meat like soy beans (Singer 1989, p. 152). Since they have failed to recognize the presence of the innovations in the food industry that can mitigate the necessity to slaughter animals, they constantly resort to a very hedonistic nature of things in which the problems rise. There will be constant lavishing of animal meat and it is considered moral for some individuals under a utilitarian perspective. This is indeed true because this has been the convention of human beings for year s. The maximization of the utilitarian approach allows them to use it for abuse and do not consider the effects of it.  

Research Paper Example | Topics and Well Written Essays - 1250 words - 3

Research Paper Example The way in which this peril was met builds the basis of current admiration for the struggle of Black vote—a struggle fuelled by the sacrifice of those who were murdered, beaten, or injured by a white supremacist attitude. This research paper discusses the history of the Black vote in the United States. The Black Struggle for Voting Rights Recognition that Blacks already voted prior to the Voting Rights Act of 1965 was presented in the famed Dred Scott resolution in 1856 wherein a Supreme Court dominated by Democrats stated that Blacks â€Å"had no rights which a white man was bound to respect; and that the Negro might justly and lawfully be reduced to slavery for his benefit† (Jaffa 286). Justice Benjamin Curtis, the only non-democrat, opposed that statement and showed a long documentary history to prove that numerous Blacks in the U.S. had frequently practiced citizens’ rights—that numerous Blacks during the American Revolution â€Å"possessed the franch ise of [voters] on equal terms with other citizens† (Muhammad 17). States that guaranteed and safeguarded the rights of Blacks to vote in the 18th century were New York, New Hampshire, Maryland, and Delaware. Pennsylvania and Massachusetts also guaranteed the Blacks’ right to vote in their constitution. Indeed, a Black Republican, Robert Brown Elliott, asked in 1874 (Middleton 109): â€Å"When did Massachusetts sully her proud record by placing on her statute-book any law which admitted to the ballot the white man and shut out the black man? She has never done it; she will not do it.† Because of such legislations, early American cities had a larger number of Black voters than Whites; and when the suggested American Constitution was presented to the people in the latter part of the 18th century, it was approved by both White and Black voters in several states (Barton para 4). However, this is not to suggest that every Black was granted voting rights; free Blacks, excluding those in South Carolina, were allowed to vote but slaves were prohibited to exercise voting rights. But in several states this was insignificant, because many individuals and groups persevered to abolish slavery during the American Revolution (Fauntroy 62). Even though Britain had disallowed the eradication of slavery in the colonies prior to the Revolution, as autonomous states they had the power to abolish slavery, just like what happened in New York, New Hampshire, Vermont, Rhode Island, Connecticut, Massachusetts, and Pennsylvania. In addition, Blacks in numerous states were not only granted voting rights but also rights to participate in public affairs (Barton para 5). In Alabama, 99 Blacks were voted for the State Legislature, 127 Blacks for Louisiana’s Legislature, 50 Blacks for South Carolina’s, and 42 for Texas Legislature (Barton para 15). These Republican governing bodies acted immediately to guarantee and safeguard the right to vote for Blacks, ba n segregation, and grant Blacks access to juries, law enforcement, public transportation, and so on. At a time when majority of southern Democrats had not yet approved the vow of fidelity to the U.S. and thus were not allowed to vote, they still tried to threaten and get in the way of the endorsement of Blacks’

Application And Use Of Complex Numbers

Application And Use Of Complex Numbers HISTORY OF COMPLEX NUMBERS:- Complex numbers were first conceived and defined by the Italian mathematician Gerolamo Cardano, who called them fictitious, during his attempts to find solutions to cubic equations. This ultimately led to the fundamental theorem of algebra, which shows that with complex numbers, a solution exists to every polynomial equation of degree one or higher. Complex numbers thus form an algebraically closed field, where any polynomial equation has a root. The rules for addition, subtraction and multiplication of complex numbers were developed by the Italian mathematician Rafael Bombelli. A more abstract formalism for the complex numbers was further developed by the Irish mathematician William Rowan Hamilton. COMPLEX NUMBER INTERPRETATION:- A number in the form of x+iy where x and y are real numbers and i = is called a complex number. Let z= x+iy X is called real part of z and is denoted by R (z) Y is called imaginary part of z and is denoted by I (z) CONJUGATE OF A COMPLEX NUMBER: A pair of complex numbers x+iy and x-iy are said to be conjugate of each other. PROPERTIES OF COMPLEX NUMBERS ARE:- 1) If + = + then = 2) Two complex numbers + and + are said to be equal If R (+) = R ( +) I (+) = I ( +) 3) Sum of the two complex numbers is ( +) +( + = (+ ) + (+) 4) Difference of two complex numbers is ( +) ( + = () + () 5) Product of two complex numbers is ( +) ( + = +( ) 6) Division of two complex numbers is = + 7) Every complex number can be expressed in terms of r (cosÃŽÂ ¸ + sinÃŽÂ ¸) R (x+) = r cosÃŽÂ ¸ I (x+) = r sinÃŽÂ ¸ r = and ÃŽÂ ¸ = REPRESENTATION OF COMPLEX NUMBERS IN PLANE The set of complex numbers is two-dimensional, and a coordinate plane is required to illustrate them graphically. This is in contrast to the real numbers, which are one-dimensional, and can be illustrated by a simple number line. The rectangular complex number plane is constructed by arranging the real numbers along the horizontal axis, and the imaginary numbers along the vertical axis. Each point in this plane can be assigned to a unique complex number, and each complex number can be assigned to a unique point in the plane. Modulus and Argument of a complex number: The number r = is called modulus of x+ and is written by mod (x+) or ÃŽÂ ¸ = is called amplitude or argument of x+ and is written by amp (x+) or arg (x+) Application of imaginary numbers: For most human tasks, real numbers (or even rational numbers) offer an adequate description of data. Fractions such as à ¢Ã¢â‚¬ ¦Ã¢â‚¬  and à ¢Ã¢â‚¬ ¦Ã¢â‚¬ º are meaningless to a person counting stones, but essential to a person comparing the sizes of different collections of stones. Negative numbers such as à ¢Ã‹â€ Ã¢â‚¬â„¢3 and à ¢Ã‹â€ Ã¢â‚¬â„¢5 are meaningless when measuring the mass of an object, but essential when keeping track of monetary debits and credits. Similarly, imaginary numbers have essential concrete applications in a variety of sciences and related areas such as signal processing, control theory, electromagnetism, quantum mechanics, cartography, vibration analysis, and many others. APPLICATION OF COMPLEX NO IN ENGINEERING:- Control Theory In control theory, systems are often transformed from the time domain to the frequency domain using the Laplace transform. The systems poles and zeros are then analyzed in the complex plane. The root locus, Nyquist plot, and Nichols plot techniques all make use of the complex plane. In the root locus method, it is especially important whether the poles and zeros are in the left or right half planes, i.e. have real part greater than or less than zero. If a system has poles that are in the right half plane, it will be unstable, all in the left half plane, it will be stable, on the imaginary axis, it will have marginal stability. If a system has zeros in the right half plane, it is a nonminimum phase system. Signal analysis Complex numbers are used in signal analysis and other fields for a convenient description for periodically varying signals. For given real functions representing actual physical quantities, often in terms of sines and cosines, corresponding complex functions are considered of which the real parts are the original quantities. For a sine wave of a given frequency, the absolute value |z| of the corresponding z is the amplitude and the argument arg(z) the phase. If Fourier analysis is employed to write a given real-valued signal as a sum of periodic functions, these periodic functions are often written as complex valued functions of the form where à Ã¢â‚¬ ° represents the angular frequency and the complex number z encodes the phase and amplitude as explained above. Improper integrals In applied fields, complex numbers are often used to compute certain real-valued improper integrals, by means of complex-valued functions. Several methods exist to do this; see methods of contour integration. Residue theorem The residue theorem in complex analysis is a powerful tool to evaluate path integrals of meromorphic functions over closed curves and can often be used to compute real integrals as well. It generalizes the Cauchy and Cauchys integral formula. The statement is as follows. Suppose U is a simply connected open subset of the complex plane C, a1,,an are finitely many points of U and f is a function which is defined and holomorphic on U \ {a1,,an}. If ÃŽÂ ³ is a rectifiable curve in U which doesnt meet any of the points ak and whose start point equals its endpoint, then Here, Res(f,ak) denotes the residue of f at ak, and n(ÃŽÂ ³,ak) is the winding number of the curve ÃŽÂ ³ about the point ak. This winding number is an integer which intuitively measures how often the curve ÃŽÂ ³ winds around the point ak; it is positive if ÃŽÂ ³ moves in a counter clockwise (mathematically positive) manner around ak and 0 if ÃŽÂ ³ doesnt move around ak at all. In order to evaluate real integrals, the residue theorem is used in the following manner: the integrand is extended to the complex plane and its residues are computed (which is usually easy), and a part of the real axis is extended to a closed curve by attaching a half-circle in the upper or lower half-plane. The integral over this curve can then be computed using the residue theorem. Often, the half-circle part of the integral will tend towards zero if it is large enough, leaving only the real-axis part of the integral, the one we were originally interested Quantum mechanics The complex number field is relevant in the mathematical formulation of quantum mechanics, where complex Hilbert spaces provide the context for one such formulation that is convenient and perhaps most standard. The original foundation formulas of quantum mechanics the Schrà ¶dinger equation and Heisenbergs matrix mechanics make use of complex numbers. The quantum theory provides a quantitative explanation for two types of phenomena that classical mechanics and classical electrodynamics cannot account for: Some observable physical quantities, such as the total energy of a blackbody, take on discrete rather than continuous values. This phenomenon is called quantization, and the smallest possible intervals between the discrete values are called quanta (singular: quantum, from the Latin word for quantity, hence the name quantum mechanics.) The size of the quanta typically varies from system to system. Under certain experimental conditions, microscopic objects like atoms or electrons exhibit wave-like behavior, such as interference. Under other conditions, the same species of objects exhibit particle-like behavior (particle meaning an object that can be localized to a particular region of space), such as scattering. This phenomenon is known as wave-particle duality. Application of complex number in Computer Science. 1) Arithmetic and logic in computer system Arithmetic and Logic in Computer Systems provides a useful guide to a fundamental subject of computer science and engineering. Algorithms for performing operations like addition, subtraction, multiplication, and division in digital computer systems are presented, with the goal of explaining the concepts behind the algorithms, rather than addressing any direct applications. Alternative methods are examined, and explanations are supplied of the fundamental materials and reasoning behind theories and examples. 2) Recticing Software engineering in 21st century This technological manual explores how software engineering principles can be used in tandem with software development tools to produce economical and reliable software that is faster and more accurate. Tools and techniques provided include the Unified Process for GIS application development, service-based approaches to business and information technology alignment, and an integrated model of application and software security. Current methods and future possibilities for software design are covered. In Electrical Engineering: The voltage produced by a battery is characterized by one real number (called potential), such as +12 volts or à ¢Ã‹â€ Ã¢â‚¬â„¢12 volts. But the AC voltage in a home requires two parameters. One is a potential, such as 120 volts, and the other is an angle (called phase). The voltage is said to have two dimensions. A 2-dimensional quantity can be represented mathematically as either a vector or as a complex number (known in the engineering context as phasor). In the vector representation, the rectangular coordinates are typically referred to simply as X and Y. But in the complex number representation, the same components are referred to as real and imaginary. When the complex number is purely imaginary, such as a real part of 0 and an imaginary part of 120, it means the voltage has a potential of 120 volts and a phase of 90 °, which is physically very real. Application in electronics engineering Information that expresses a single dimension, such as linear distance, is called a scalar quantity in mathematics. Scalar numbers are the kind of numbers students use most often. In relation to science, the voltage produced by a battery, the resistance of a piece of wire (ohms), and current through a wire (amps) are scalar quantities. When electrical engineers analyzed alternating current circuits, they found that quantities of voltage, current and resistance (called impedance in AC) were not the familiar one-dimensional scalar quantities that are used when measuring DC circuits. These quantities which now alternate in direction and amplitude possess other dimensions (frequency and phase shift) that must be taken into account. In order to analyze AC circuits, it became necessary to represent multi-dimensional quantities. In order to accomplish this task, scalar numbers were abandoned and complex numbers were used to express the two dimensions of frequency and phase shift at one time. In mathematics, i is used to represent imaginary numbers. In the study of electricity and electronics, j is used to represent imaginary numbers so that there is no confusion with i, which in electronics represents current. It is also customary for scientists to write the complex number in the form a + jb. In electrical engineering, the Fourier transform is used to analyze varying voltages and currents. The treatment of resistors, capacitors, and inductors can then be unified by introducing imaginary, frequency-dependent resistances for the latter two and combining all three in a single complex number called the impedance. (Electrical engineers and some physicists use the letter j for the imaginary unit since i is typically reserved for varying currents and may come into conflict with i.) This approach is called phasor calculus. This use is also extended into digital signal processing and digital image processing, which utilize digital versions of Fourier analysis (and wavelet analysis) to transmit, compress, restore, and otherwise process digital audio signals, still images, and video signals. Introduce the formula E = I à ¢Ã¢â€š ¬Ã‚ ¢ Z where E is voltage, I is current, and Z is impedance. Complex numbers are used a great deal in electronics. The main reason for this is they make the whole topic of analyzing and understanding alternating signals much easier. This seems odd at first, as the concept of using a mix of real and imaginary numbers to explain things in the real world seem crazy!. . To help you get a clear picture of how theyre used and what they mean we can look at a mechanical example We can now reverse the above argument when considering a.c. (sine wave) oscillations in electronic circuits. Here we can regard the oscillating voltages and currents as side views of something which is actually rotating at a steady rate. We can only see the real part of this, of course, so we have to imagine the changes in the other direction. This leads us to the idea that what the oscillation voltage or current that we see is just the real portion of a complex quantity that also has an imaginary part. At any instant what we see is determined by a phase angle which varies smoothly with time. We can now consider oscillating currents and voltages as being complex values that have a real part we can measure and an imaginary part which we cant. At first it seems pointless to create something we cant see or measure, but it turns out to be useful in a number of ways. 1) It helps us understand the behaviour of circuits which contain reactance (produced by capacitors or inductors) when we apply a.c. signals. 2) It gives us a new way to think about oscillations. This is useful when we want to apply concepts like the conservation of energy to understanding the behaviour of systems which range from simple a mechanical pendulums to a quartz-crystal oscillator. Applications in Fluid Dynamics In fluid dynamics, complex functions are used to describe potential flow in two dimensions. Fractals. Certain fractals are plotted in the complex plane, e.g. the Mandelbrot set Fluid Dynamics and its sub disciplines aerodynamics, hydrodynamics, and hydraulics have a wide range of applications. For example, they are used in calculating forces and moments on aircraft, the mass flow of petroleum through pipelines, and prediction of weather patterns. The concept of a fluid is surprisingly general. For example, some of the basic mathematical concepts in traffic engineering are derived from considering traffic as a continuous fluids. Relativity In special and general relativity, some formulas for the metric on spacetime become simpler if one takes the time variable to be imaginary. (This is no longer standard in classical relativity, but is used in an essential way in quantum field theory.) Complex numbers are essential to spinors, which are a generalization of the tensors used in relativity. Applied mathematics In differential equations, it is common to first find all complex roots r of the characteristic equation of a linear differential equation and then attempt to solve the system in terms of base functions of the form f(t) = ert. In Electromagnetism: Instead of taking electrical and magnetic part as a two different real numbers, we can represent it as in one complex number IN Civil and Mechanical Engineering: The concept of complex geometry and Argand plane is very much useful in constructing buildings and cars. This concept is used in 2-D designing of buildings and cars. It is also very useful in cutting of tools. Another possibility to use complex numbers in simple mechanics might be to use them to represent rotations.

The Wife of Bath :: Essays Papers

The Wife of Bath In the "Wife of Bath's Prologue," she tells the other pilgrims that she has much experience since she has been married five times. She believes in experience rather than in writing. We can see this in the quotation: "Who painted the leon, tel me who? By God, if wommen hadden writen stories, As clerks han within hir oratories, They wolde had writen of men more wikkednesse Than al th merk of Adam may redresse." [Norton, 132] She is very upset about the painting of a man killing a lion. Her fifth husband always reads his book about wicked wives, and he amuses himself by telling her the stories; however, she doesn't like this. She is beautiful, powerful, energetic and relies on her experience, not on any writings or paintings. To highlight her strong and powerful appearance, she wears characteristic clothes. She puts strikingly big kerchiefs on her head, which seem to weigh about ten pounds, and she wears scarlet red stockings. She also wears a hat, and it is as broad as a buckler. Garters hold her red stockings, and her shoes are soft and new. There is a pair of sharpened spurs on her feet. This probably tells us that she has had many experiences with all husbands in her life. She wears a long wide skirt. Her face is as bold as her character is, fair complexioned, and red. On the journey, she walks slowly and sits down easily. Overall, she has been respectable throughout her life. Chaucer also describes her as being deaf in one ear with a gap tooth. It was very rare for a woman in the fourteenth century to travel as a pilgrim, talk about her experiences and thoughts in public and to be married five times. The Wife of Bath is an independent and powerful woman. She strongly believes in herself and in experience rather than in written authority, which are the texts written by men. She feels this way more after she marries her fifth husband. Her fifth husband always reads a book about wicked wives. He wants to control her; however, she doesn't like it. Therefore she takes a page out of his book that he always reads since the book affects him badly; then he hits her when he finds out about her disrespectful behavior. This is the reason for her deafness. She strongly believes she or women can write much better than men do.