ASSIGNMENT OF CALCULUS AND ANALYTICAL GEOMETRY NAME . TAHIR KAHAN STUDENT ID . 15FBSCSM72 BATCH . FALL 2015 COURSE . CALCULUS AND ANALYTICAL GEOMETRY DEPARTMENT . COMPUTER SCIENCE SEMESTER . 1st ASSIGNMENT NO . 1 Question # 1 : Describe in detail the importance of calculus and analytical geometry in our life with reference to its uses in computer science as well as in real life? Answer : Calculus and analytical geometry have a very important roll in our daily life but only few people know that . I think the great example of using of calculus and analytical geometry in our life is radar and setellite . Radar : Radar is basically …show more content…
Satellite is basically working by the principle of calculus and analytical geometry it take the signals from sourse from one part of the world and send it to the defferent part of the world with in second etc. In computer science we can use the calculus and analytical geometry because of programming point of view and there are so many usage in computer science . By using calculus and analytical geometry we can meassure the path of 3D shape objects in any programme etc. Question # 2 : Is there any difference between imaginary numbers and complex numbers ? If yes , then identify the reason , if no , then give example to support your argument ? Answer : Yes there is a difference between imaginary number and complex numbers . Complex numbers is a system and imaginary number are the part of that system …show more content…
What benefit does it give to us in order to write a complex numbers in term of polar form ? when will you prefer to use complex number in polar form ? Answer : We use to write the polar form of complex number in order to understand the graphical shape of complex numbers . Through the polar form fo complex number we can easily understand that where it can be drawn it on a plane and what is angle between them , where its angle can be move , what is the imaginary axis what is the real axis how much displacement it coward . Its all the important things that we can eualvate throug polar form of the complex numbers . I prefer to use the polar form of complex where I want know about the possition of the particullar complex number and so on . Question # 4 : How will you distinguish between argument and principle argument of complex number ? write it in your own words ? Answrer : Argument : An argument of the complex number z = x + iy, denoted arg z, is defined in two equivalent ways: 1. Geometrically, in the complex plane, as the angle φ from the positive real axis to the vector representing z. The numeric value is given by the angle in radians and is positive if measured
Geometry is used in Auto Mechanics in many ways; for example, cam and crankshaft, oil pump, fuel delivery, rings, valves, piston, and speed.
as the “r-value” and “r” can be any value between -1 and +1. It can be
My first opportunity to use math outside the academic world was in my part time job with United parcel Service. It was an eye-opener for me in that mathematical techniques, in combination with computers, could be used for solving very complicated real-life problems, such as predicting and controlling the continuos flow of 300 million packages per day. I was deeply impressed by the numerical masterpieces of Jim Gilkinson and Dick Marga, the project managers. They led the way in showing how one could overcome some serious limitations of computers for solving linear systems of equations.
The argument in this paper that even though the onus of the discovery of calculus lies with Isaac Newton, the credit goes to Leibniz for the simple fact that he was the one who published his works first. Appending to this is the fact that the calculus wars that ensue was merely and egotistic battle between humans succumbing to their bare primal instincts. To commence, a brief historical explanation must be given about both individuals prior to stating their cases.
After my twelfth grade, the inherent ardor I held for Computer Sciencemotivated me to do a bachelors degree in Information Technology. Programming and Math, a paragon of logic and reasoning have always been my favorite subjects since childhood. I still vividly remember the time during my graduation,when I was successful in creating a simple calculator application as a class assignment.The joy I derived from creating something that is used by a lot of people to help them perform complex calculations,made me realize the power of computing in its true sense.It was also in my graduation that I developed an immense interest in programming languages such as Java, C++ an...
Mathematics is everywhere we look, so many things we encounter in our everyday lives have some form of mathematics involved. Mathematics the language of understanding the natural world (Tony Chan, 2009) and is useful to understand the world around us. The Oxford Dictionary defines mathematics as ‘the science of space, number, quantity, and arrangement, whose methods, involve logical reasoning and use of symbolic notation, and which includes geometry, arithmetic, algebra, and analysis of mathematical operations or calculations (Soanes et al, Concise Oxford Dictionary,
According to (Khan): A complexometric titration as defined by IUPAC as a volumetric titration where a soluble complex can be formed by titrating a metal ion with a ligand in an aqueous solution and a titrant is one of the reacts used in the titration. [4]
Many years ago humans discovered that with the use of mathematical calculations many things can be calculated in the world and even the universe. Mathematics consists of many different operations. The most important that is used by mathematicians, scientists and engineers is the derivative. Derivatives can help make calculations of anything with respect to another event or thing. Derivatives are mostly common when used with respect to time. This is a very important tool in this revolutionary world. With derivatives we can calculate the rate of change of anything with respect to time. This way we can have a sort of knowledge of upcoming events, and the different behaviors events can present. For example the population growth can be estimated applying derivatives. Not only population growth, but for example when dealing with plagues there can be certain control. An other example can be with diseases, taking all this events together a conclusion can be made.
...bsp;Using Analytic Geometry, geometry has been able to be taught in school-books in all grades. Some of the problems that are solved using Rene’s work are vector space, definition of the plane, distance problems, dot products, cross products, and intersection problems. The foundation for Rene’s Analytic Geometry came from his book entitled Discourse on the Method of Rightly Conducting the Reason in the Search for Truth in the Sciences (“Analytic Geomoetry”).
Ever wonder how scientists figure out how long it takes for the radiation from a nuclear weapon to decay? This dilemma can be solved by calculus, which helps determine the rate of decay of the radioactive material. Calculus can aid people in many everyday situations, such as deciding how much fencing is needed to encompass a designated area. Finding how gravity affects certain objects is how calculus aids people who study Physics. Mechanics find calculus useful to determine rates of flow of fluids in a car. Numerous developments in mathematics by Ancient Greeks to Europeans led to the discovery of integral calculus, which is still expanding. The first mathematicians came from Egypt, where they discovered the rule for the volume of a pyramid and approximation of the area of a circle. Later, Greeks made tremendous discoveries. Archimedes extended the method of inscribed and circumscribed figures by means of heuristic, which are rules that are specific to a given problem and can therefore help guide the search. These arguments involved parallel slices of figures and the laws of the lever, the idea of a surface as made up of lines. Finding areas and volumes of figures by using conic section (a circle, point, hyperbola, etc.) and weighing infinitely thin slices of figures, an idea used in integral calculus today was also a discovery of Archimedes. One of Archimedes's major crucial discoveries for integral calculus was a limit that allows the "slices" of a figure to be infinitely thin. Another Greek, Euclid, developed ideas supporting the theory of calculus, but the logic basis was not sustained since infinity and continuity weren't established yet (Boyer 47). His one mistake in finding a definite integral was that it is not found by the sums of an infinite number of points, lines, or surfaces but by the limit of an infinite sequence (Boyer 47). These early discoveries aided Newton and Leibniz in the development of calculus. In the 17th century, people from all over Europe made numerous mathematics discoveries in the integral calculus field. Johannes Kepler "anticipat(ed) results found… in the integral calculus" (Boyer 109) with his summations. For instance, in his Astronomia nova, he formed a summation similar to integral calculus dealing with sine and cosine. F. B. Cavalieri expanded on Johannes Kepler's work on measuring volumes. Also, he "investigate[d] areas under the curve" ("Calculus (mathematics)") with what he called "indivisible magnitudes.
Calculus, the mathematical study of change, can be separated into two departments: differential calculus, and integral calculus. Both are concerned with infinite sequences and series to define a limit. In order to produce this study, inventors and innovators throughout history have been present and necessary. The ancient Greeks, Indians, and Enlightenment thinkers developed the basic elements of calculus by forming ideas and theories, but it was not until the late 17th century that the theories and concepts were being specified. Originally called infinitesimal calculus, meaning to create a solution for calculating objects smaller than any feasible measurement previously known through the use of symbolic manipulation of expressions. Generally accepted, Isaac Newton and Gottfried Leibniz were recognized as the two major inventors and innovators of calculus, but the controversy appeared when both wanted sole credit of the invention of calculus. This paper will display the typical reason of why Newton was the inventor of calculus and Leibniz was the innovator, while both contributed an immense amount of knowledge to the system.
Malcolm, Shirley, and Treisman, Uri. “Calculus Success for All Students.” Calculus for a New Century: A Pump not a Filter, Steen, Lynn (ed.). Mathematical Association of America: Washington, DC, 1987.
Many seem to think of mathematics as being nothing more than a series of numbers and formulas that they must learn, in order to pass a particular requirement for their college degree. They rarely, if ever, stop to think about the importance of mathematics and how it actually affects them and the people around them. It is ...
This evaluation has not only allowed me explore calculus more in depth, but also physics, and the way the world works. This has personally allowed me to explore the connections between math and real-world situations, which is hard to find in textbooks.
The abstractions can be anything from strings of numbers to geometric figures to sets of equations. In deriving, for instance, an expression for the change in the surface area of any regular solid as its volume approaches zero, mathematicians have no interest in any correspondence between geometric solids and physical objects in the real world. A central line of investigation in theoretical mathematics is identifying in each field of study a small set of basic ideas and rules from which all other interesting ideas and rules in that field can be logically deduced. Mathematicians are particularly pleased when previously unrelated parts of mathematics are found to be derivable from one another, or from some more general theory. Part of the sense of beauty that many people have perceived in mathematics lies not in finding the greatest richness or complexity but on the contrary, in finding the greatest economy and simplicity of representation and proof.