Friday, October 18, 2019

Coninental Airlines Case Study Research Paper Example | Topics and Well Written Essays - 1000 words

Coninental Airlines Case Study - Research Paper Example n the last decade of the 20th Century, where Continental got out of the bankruptcy channel and started its way out to growth, the company as comparatively to EDS was just one of the company seeking solutions. As certain programming and IT management is not the core part of an Airline company, these operations were inevitably going to be outsourced to professional skills providing consultants and implementers. Now laying within the company, Continental after being stable towards its economic inflow through the Go Forward Plan was looking towards innovation. This also caused for major managerial change with much more skilled and innovative people. The difference is then directly seen when the core group of Continental was downsized and better people were hired who required newer, better and quicker solutions to the problems. When compared to EDS, at the end of first five years, Continental started to grow somewhat of a critical thinking system through the leadership of Bethune and Bren neman. That happened as they returned the company to profitability. Wejman being in charge and comparing the history through the scope of Continental in the relationship to EDS is of much regard towards the future five years. The most important of that being is stability towards Continentals constant change of managerial staff, executive office staff and creating constant long run solutions with systematic modifications throughout the year(s). Continental being a growing company, now was looking forward for IT solutions in all aspect to provide maximum concentration towards customer relations. Clearing making the prime priority to gain trust of the customers to have them fly often with Continental ensuring quality and time-saving incentives. Having made a World Wide Web domain, the IT outsourcing then was necessary to have a smoother in house work load. (Consulting, 2009) This major change was not necessary a easy solution to play with on EDS part and required sudden changes from the

Thursday, October 17, 2019

Male Bird Song Evolves in order to Attract a Female for Mating Research Paper

Male Bird Song Evolves in order to Attract a Female for Mating - Research Paper Example Further these qualities are also indicators of the physiological characteristics and genotype of the male partner and thus have high likelihood of influencing female choice. However the study of birdsong and its evolutionary significance in influencing female choice is yet at its infancy. Many new aspects are beginning to emerge. Deriving conclusions and making generalization at this stage would be inappropriate and inaccurate. MALE BIRD SONG EVOLVES IN ORDER TO ATTRACT A FEMALE FOR MATING INTRODUCTION Birdsong can be defined as long complex vocalizations produced mainly in breeding season (Catchpole & Slater, 1995). The best known birds in terms of their singing abilities are oscine birds, also referred to as passerines or perching birds. They belong to the order Passeriformes and are classified on the basis of their unique musculature of the syrinx or the vocal organ (Warner, 1972). In most of the temperate species of passerines, the males are exclusively the singers. The male bird sings either as a means of expression during male-male aggression or for attracting the female (Catchpole & Slater, 1995). ... BACKGROUND Communication is a primary requisite for functional ability. Humans must communicate to form relationships, fulfil their needs, organize and function. Animals communication is essential for food gathering, reproduction and survival; the three basic needs of all animals. However, unlike humans animals do not speak. In fact all animals possess their unique methods of communication (Hauser, 2000). Flowers send signals in form of fragrances and colour at the time of bloom to insects for pollination; meerkats communicate through scent, sounds and body language; lions communicate through body contact and sound, while birds communicate verbally through songs and coos (Rowe & Skelhorn, 2004). Communication systems, irrespective of nature and origin, comprise of two essential components: signal and tactical design. The signal is an important carrier of information from the sender to the receiver. In researches involving communication, study of nature of signal as an important deter minant of its goal is pursued (Rowe & Skelhorn, 2004). The signal evolution is in accordance with the function it is expected to perform. This is termed as strategic component of the signal (Guilford & Dawkins, 1991). Tactical design encompasses the properties of the communication determined by the transmission characteristics of the environment and the sensory and perceptual abilities of the receiver. To define the latter the term â€Å"receiver Psychology† was introduced by Guilford and Dawkins (1991) and was considered a significant determinant of the evolution of signals. Studies on bio-acoustics or animal sounds can be traced back to a research paper published by

Example of Advertisement Assignment Example | Topics and Well Written Essays - 250 words

Example of Advertisement - Assignment Example For instance, Nike Company has to advertise different football uniforms as well as well the soccer ball. In doing so, it will be intending to attract more clients to buy its products. First, the company starts by introducing itself to its clients (Burges, 2007). For instance, the Nike advert states that; Nike is a multinational company that specializes in the production of quality sports material at an affordable cost, meeting our customer demand is our primary responsibility. The sports products we offer include football uniforms, boots as well as socks among other things in the sports industry. The advert will be targeting various football clubs across the world. The company will have to use social media as a marketing strategy to reach many people in short time. In addition, it will be targeting fans of particular sport or sportsman or woman because many individuals like associating themselves with their respective heroes. The primary purpose of an advertisement is to attract customers into the company thus boosting company image before the public. In addition, the promotion is supposed to change the perception of individuals or consumers towards that particular product (Burges, 2007). Moreover, the development strategy is also meant to increase sales volume of the company thus increasing its profitability. The advert message will be to convince the client about the quality of the product. In addition, the letter will also affirm the client on the ability of the company to deliver timely products as per

Wednesday, October 16, 2019

Male Bird Song Evolves in order to Attract a Female for Mating Research Paper

Male Bird Song Evolves in order to Attract a Female for Mating - Research Paper Example Further these qualities are also indicators of the physiological characteristics and genotype of the male partner and thus have high likelihood of influencing female choice. However the study of birdsong and its evolutionary significance in influencing female choice is yet at its infancy. Many new aspects are beginning to emerge. Deriving conclusions and making generalization at this stage would be inappropriate and inaccurate. MALE BIRD SONG EVOLVES IN ORDER TO ATTRACT A FEMALE FOR MATING INTRODUCTION Birdsong can be defined as long complex vocalizations produced mainly in breeding season (Catchpole & Slater, 1995). The best known birds in terms of their singing abilities are oscine birds, also referred to as passerines or perching birds. They belong to the order Passeriformes and are classified on the basis of their unique musculature of the syrinx or the vocal organ (Warner, 1972). In most of the temperate species of passerines, the males are exclusively the singers. The male bird sings either as a means of expression during male-male aggression or for attracting the female (Catchpole & Slater, 1995). ... BACKGROUND Communication is a primary requisite for functional ability. Humans must communicate to form relationships, fulfil their needs, organize and function. Animals communication is essential for food gathering, reproduction and survival; the three basic needs of all animals. However, unlike humans animals do not speak. In fact all animals possess their unique methods of communication (Hauser, 2000). Flowers send signals in form of fragrances and colour at the time of bloom to insects for pollination; meerkats communicate through scent, sounds and body language; lions communicate through body contact and sound, while birds communicate verbally through songs and coos (Rowe & Skelhorn, 2004). Communication systems, irrespective of nature and origin, comprise of two essential components: signal and tactical design. The signal is an important carrier of information from the sender to the receiver. In researches involving communication, study of nature of signal as an important deter minant of its goal is pursued (Rowe & Skelhorn, 2004). The signal evolution is in accordance with the function it is expected to perform. This is termed as strategic component of the signal (Guilford & Dawkins, 1991). Tactical design encompasses the properties of the communication determined by the transmission characteristics of the environment and the sensory and perceptual abilities of the receiver. To define the latter the term â€Å"receiver Psychology† was introduced by Guilford and Dawkins (1991) and was considered a significant determinant of the evolution of signals. Studies on bio-acoustics or animal sounds can be traced back to a research paper published by

Tuesday, October 15, 2019

Managerial communication; Proposal Report Assignment

Managerial communication; Proposal Report - Assignment Example However when employees are promoted to managerial ranks they are obliged to quickly learn and create a rapport more efficiently to maintain their position. Business leaders can improve their communication skills through practice and commitment applying crucial approaches that will determine how effective they communicate with their juniors. Communication defines most businesses resulting into efficient marketing campaigns, great customer service and improved employee employer relationship, Wardrope (2005) . Because recipients need different communication at different situations and locations, business leaders need to master the art of effective communication suitable for each audience. Poor communication is regarded to have a negative effect into the way businesses operate. For example, poor communication can cause employee conflict thereby harming the influence on organizational culture. The aim of this paper is to look at three business communication models, outline and offer usefu l advice relevant to business communication for a managerial position. Intercultural communication has been a topic of several research and studies over the last decade. The significance of understanding the interactions and associations between individuals from several places has grown due to globalization. Businesses, Information Technology and the Internet have made the world a global village. Intercultural communication occurs when people persuaded by several cultures discuss common ideas in association. Globalization has connected the world closer than before. Business operations across cultures occur daily. To enable business run smoothly inter cultural communication is very vital. Interactions are in most times intercultural when distinct groups are most prominent in establishing the language, non verbal behaviors, values, relational styles and prejudice with which those people relate Kim (2001). When people from different cultures share experiences, their

Developmentally Appropriate Practices Essay Example for Free

Developmentally Appropriate Practices Essay Feedback is a very important aspect in teaching any subject but it is most important in an algebra class. This is because there are many instances when particular students tend to repeat implicit errors hidden in their solutions. In a large class, it is unmanageable to study each of the student’s solutions in order to find just what the student is doing wrong. Therefore, it is more practical to provide feedback in collaboration with members of the class. This is done by letting students present their solutions to homework or quizzes on the board. Afterwards, the solutions are not only checked but critiqued by their classmates for errors which the teacher providing guided questions. This way, students will be able to see how errors are committed and avoid them in the future. They would also be able to interact which addresses a social need at their stage of development. In any classroom, it is important that students are free to think about all the possibilities of the knowledge presented to them. One way of addressing this is through giving very practical problems which groups of students can solve independently through methodologies that they themselves would think of based on the current lesson. This strategy allows the students to interact and think autonomously about how best to address the problem. Of course, not all students are the same and the teacher should have a way of figuring out their individual needs and learning styles. This can be solved by administering questionnaires at the beginning of the course that can determine the learning styles of the different members of the class. Based on the results, the teacher can now better plan how instruction would be delivered to obtain maximum effectiveness. Lastly, the teacher should inspire the class to love the subject and see its value in the real world. This can be done through ample input of real world applications. In presenting word problems, their applications to real life should not be superficial. I explore the use of models, multimedia, and hands-on experiments in order to be able to let students completely visualize the real-life value of the problem. TPE 7 Teaching English Learners (1 Page) Students who are learning English as a second language are often at a disadvantage in a typical math class because they end up having a hard time understanding the discussions due to the language barrier. In occasions when there are members of the class that are not native English speakers, the first intervention that I employ is to always remember to use more basic English when delivering subject content. For example, when discussing about solutions of quadratic equations, I have to make it clear that the terms solutions, zeroes, and roots all just mean the answers as to what is â€Å"x† or whatever variable I am using. Another way to facilitate more effective instruction in a class of English as a Second Language (ESL) learners is to incorporate culturally relevant examples in lessons. Using objects, places, and people that are familiar to ESL learners in word problems help them associate the content of the problem with its solution better and motivate them to try and answer the problem because it has develops a better meaning for them. Of course, there must be appropriate balance of culturally relevant examples used and there should be ample input of popular culture examples as well. Finally, when there are students who are really having a hard time understanding English in class, I make it a point to use as few words as I can and describe lessons in terms of symbols and numbers instead of words. When explaining how to get the solution of an equation such as 2x – 4 = 7, I will not go on explaining about transposing one number from the rest and changing the sign. Instead, I will show the students that by adding a +4 on both sides, I would not really be violating the equality and the same is true when I divide both sides of the equation by 2 afterwards. By showing the solution in this manner, I give less verbal explanations and more visual ones which would be better appreciated and absorbed by learners who do not understand the common language of instruction so well.

Sunday, October 13, 2019

Application of complex number in engineering

Application of complex number in engineering INTRODUCTION A complex number is a number comprising area land imaginary part. It can be written in the form a+ib, where a and b are real numbers, and i is the standard imaginary unit with the property i2=-1. The complex numbers contain the ordinary real numbers, but extend them by adding in extra numbers and correspondingly expanding the understanding of addition and multiplication. 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 = -1 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: If x1+ iy1 = x2 + iy2 then x1- iy1 = x2 iy2 Two complex numbers x1+ iy1 and x2 + iy2 are said to be equal   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  If R (x1 + iy1) = R (x2 + iy2)   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  I (x1 + iy1) = I (x2 + iy2) Sum of the two complex numbers is   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  (x1 + iy1) + (x2 + iy2) = (x1+ x2) + i(y1+ y2) Difference of two complex numbers is   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  (x1 + iy1) (x2 + iy2) = (x1-x2) + i(y1 y2) Product of two complex numbers is   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  (x1+ iy1) ( x2 + iy2) = x1x2 y1y2 + i(y1x2 + y2 x1) Division of two complex numbers is   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  (x1 + iy1) (x2 + iy2) = x1x2 + y1 y2)x22+y22 + iy1x2  ­ y2 x1x22+y22 Every complex number can be expressed in terms of r (cosÃŽ ¸ + i sinÃŽ ¸)   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  R (x+ iy) = r cosÃŽ ¸   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  I (x+ iy) = r sinÃŽ ¸   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  r = x2+y2 and ÃŽ ¸ = tan-1yx 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 = x2+y2 is called modulus of x+ iy and is written by mod (x+ iy) or x+iy ÃŽ ¸ = tan-1yx is called amplitude or argument of x + iy and is written by amp (x + iy) or arg (x + iy) Application of imaginary numbers: For most human tasks, real numbers (or even rational numbers) offer an adequate description of data. Fractions such as 2/3 and 1/8 are meaningless to a person counting stones, but essential to a person comparing the sizes of different collections of stones. Negative numbers such as -3 and -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 Incontrol theory, systems are often transformed from thetime domainto thefrequency domainusing theLaplace transform. The systemspolesandzerosare then analyzed in the complex plane. Theroot locus,Nyquist plot, andNichols plottechniques all make use of the complex plane. In the root locus method, it is especially important whether thepolesandzerosare 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 beunstable, all in the left half plane, it will bestable, on the imaginary axis, it will havemarginal stability. If a system has zeros in the right half plane, it is anonminimum phasesystem. Signal analysis Complex numbers are used insignal 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 analysisis 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 ω f (t) = z where ω 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 analysisis 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 ÃŽ ³ is a rectifiable curve in which doesnt meet any of the points ak and whose start point equals its endpoint, then Here, Res(f,ak) denotes the residue off at ak, and n(ÃŽ ³,ak) is the winding number of the curve ÃŽ ³ about the point ak. This winding number is an integer which intuitively measures how often the curve ÃŽ ³ winds around the point ak; it is positive if ÃŽ ³ moves in a counter clockwise (mathematically positive) manner around ak and 0 if ÃŽ 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.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  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 black body, 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 ofspace), such as scattering. This phenomenon is known as wave-particle duality. Application of complex number in Computer Science. 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. 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 -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 andcomplex numberswere 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, andvideosignals. 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 aphase anglewhich 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. It helps us understand the behaviour of circuits which contain reactance (produced by capacitors or inductors) when we apply a.c. signals. 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 Influid 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 onaircraft, 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 Inspecialandgeneral relativity, some formulas for the metric onspacetimebecome simpler if one takes the time variable to be imaginary. (This is no longer standard in classical relativity, but isused in an essential wayinquantum field theory.) Complex numbers are essential tospinors, which are a generalization of thetensorsused 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. BIBLIOGRAPHY Websites: http://www.math.toronto.edu/mathnet/questionCorner/complexinlife.html http://www.physicsforums.com/showthread.php?t=159099 http://www.ebookpdf.net/_engineering-application-of-complex-number-(pdf)_ebook_.html. http:www.wikipedia.org. http://mathworld.wolfram.com http://euclideanspace.com Books: Engineering Mathematics, 40th edition-B S Grewal. Engineering Mathematics-Jain Iyenger. Engineering Matematics-NP Bali