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1. cover page 2. prefaces In the Name Of Allah , the Most Gracious and the Most Merciful First of all, I would like to say thank you, for giving me the strength to do this project work. Not forgotten my family for providing everything, such as money, to buy stuffs that are related to this project work and their advise, support which are the most needed for this project such that internet, books, laptop and all that. They also supported mean encouraged me to complete this task so that I will not procrastinate in doing it. Then I would like to thank my teacher, Madam Kee Hon Lek for guiding me and my friends throughout this project. We had some difficulties in doing this task, but she taught us patiently until we knew what to do. She tried to teach us until we understand what we supposed to do with the project work. Last but not least, my friends who were doing this project with me and sharing our ideas. They were very helpful. 3. itroductio The purpose of this project work is to provide an opportunity for students to apply mathematical concepts and skills in problem-solving that they have learnt in classroom. This project work can help students to understand Additional Mathematics more easily and aid students in visualize certain mathematical concepts which are difficult to show clearly through pen and paper. In addition, this project work is essential to help students to learn how to cope with future challenges using their mathematical abilities. It also aims to foster moral values in line with a student's academic development. Besides this, the students are encouraged to do their own research. As a result students become more independent. It also makes the learning process more fun and effective. This project work also makes add math an enjoyable and exciting subject encouraging the students to learn math more skills in more heuristic manner. Therefore it is beneficial to all students who take Additional Mathematics. 4. history of differetio The concept of a derivative in the sense of a tangent line is a very old one, familiar to Greek geometers such as Euclid (c. 300 BC), Archimedes (c. 287 – 212 BC) and Apollonius of Perga (c. 262 – 190 BC). [1] Archimedes also introduced the use of infinitesimals, although these were primarily used to study areas and volumes rather than derivatives and tangents; see Archimedes' use of infinitesimals. The use of infinitesimals to study rates of change can be found in Indian mathematics, perhaps as early as 500 AD, when the astronomer and mathematician Aryabhata (476 – 550) used infinitesimals to study the motion of the moon. [2] The use of infinitesimals to compute rates of change was developed significantly by Bhāskara II (1114 – 1185); indeed, it has been argued [3] that many of the key notions of differential calculus can be found in his work, such as Rolle's theorem . [4] The Persian mathematician, Sharaf al- Dīn al - Tūsī (1135 – 1213), was the first to discover the derivative of cubic polynomials, an important result in differential calculus; [5] his Treatise on Equations developed concepts related to differential calculus, such as the derivative function and the maxima and minima of curves, in order to solve cubic equations which may not have positive solutions. [6] The modern development of calculus is usually credited to Isaac Newton (1643 – 1727) and Gottfried Leibniz (1646 – 1716), who provided independent [7] and unified approaches to differentiation and derivatives. The key insight, however, that earned them this credit, was the fundamental theorem of calculus relating differentiation and integration: this rendered obsolete most previous methods for computing areas and volumes, [8] which had not been significantly extended since the time of Ibn al-Haytham (Alhazen). [9] For their ideas on derivatives, both Newton and Leibniz built on significant earlier work by mathematicians such as Isaac Barrow (1630 – 1677), René Descartes (1596 – 1650), Christiaan Huygens(1629 – 1695), Blaise Pascal (1623 – 1662) and John Wallis (1616 – 1703). Isaac Barrow is generally given credit for the early development of the derivative. [10] Nevertheless, Newton and Leibniz remain key figures in the history of differentiation, not least because Newton was the first to apply differentiation to theoretical physics, while Leibniz systematically developed much of the notation still used today. Since the 17th century many mathematicians have contributed to the theory of differentiation. In the 19th century, calculus was put on a much more rigorous footing by mathematicians such as Augustin Louis Cauchy (1789 – 1857), Bernhard Riemann (1826 – 1866), and Karl Weierstrass (1815 – 1897). It was also during this period that the differentiation was generalized to Euclidean space and the complex plane. derivative The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function or dependent variable) which is determined by another quantity (the independent variable). It is a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time is advanced. The derivative measures the instantaneous rate of change of the function, as distinct from its average rate of change, and is defined as the limit of the average rate of change in the function as the length of the interval on which the average is computed tends to zero. The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. In fact, the derivative at a point of a function of a single variable is the slope of the tangent line to the graph of the function at that point. The notion of derivative may be generalized to functions of several real variables. The generalized derivative is a linear map called thedifferential. Its matrix representation is the Jacobian matrix, which reduces to the gradient vector in the case of real-valued function of several variables. The process of finding a derivative is called differentiation . The reverse process is called antidifferentiation . The fundamental theorem of calculus states that antidifferentiation is the same as integration. Differentiation and integration constitute the two fundamental operations in single-variable calculus. [1] 5. general guidlies 6. questios & diagram’s give 7. aswers 8. coclusio After doing research, answering questions, drawinggraph, some problem solving, I saw that the usage of differentiation and arithmatic progression is important indaily life. It is not just widely used in markets but also ininterpreting the condition of the surrounding like the airor the water. Especially in conducting an air-pollutionsurvey. In conclusion, statistics is a daily life essecities. Without it, surveys can’ t be conducted, the stock market can’ t be interpret and many more. So, we should bethankful of the people who contribute in the idea of statistics . 9. reflection While I conducting this project, a lot of information that Ifound. I have learnt how tank is made in our daily life.Apart from that, this project encourages the student towork together and share their knowledge. It is also encouragestudent to gather information from the internet, improvethinking skills and promote effective mathematicalcommunication.Not only that, I had learned some moral values that Ipractice.T his project had taught me to responsible on theworks that aregiven to me to be completed. This project alsohad made me felt more confidence to do works and not to giveeasily when we could not find the solution for the question. Ialso learned to be more discipline on time, which I was givenabout a month to complete this project and pass up to myteacher just in time. I also enjoy doing this project I spend mytime with friends to completemthis project and it had tightenour friendship.Last but not least, I proposed this project should becontinue because it brings a lot of moral value to the studentand also test the students understanding in AdditionalMathematics
