...MONEERAH INTEGRATED SCHOOL Merila, Ubaldo Laya, Iligan City S.Y. 2013- 2014 A Requirement in Mathematics IV: Calculus Controversy: Leibniz vs. Newton by Noronsalih Ali, Jra Submitted to Ms. Moneerah A. Bint- Usman Dedication I would like to dedicate this research to my adviser, teacher Monie. And to all of the people who inspired me, especially my parents for their support and to God for giving me enough knowledge to make this study successful. Acknowledgement Abstract This research explores more about the history of the two Mathematicians and how did they invent calculus with the same idea. This is a study about a controversy in Mathematics where Sir Isaac and Gottfried von Leibniz were involved. It tackles about who was the real father of calculus and who gets the credit of inventing it. Inside this paper, the researcher will also discuss a brief summary about Calculus, and short biography of the Mathematicians that were involved in this matter. Many people debates about this matter and we will also tackle some of it in this study. Introduction: So who really invented calculus first? Was it Sir Isaac Newton or Gottfried von Leibniz? Well let's do some investigation. There is no doubt about it that Newton and Leibniz made great mathematical breakthroughs but even before they began studying Calculus there were other people such as Archimedes and Euclid who discovered the infinite and infinitesimal. Much of Newton and Leibniz's work...
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...AP Calculus was the most difficult of all the classes. This class was a struggle to get through, but I was able to pull through. When most people first think of the term mathematics or the word “Calculus,” they don’t get too excited. Most people tend to say “I hate math!” or the big one, “When are we ever going to use it in our lives.” Calculus meant one needed to be prepared to keep up. There was no time to lose in this class. Struggling in class definitely made it harder to learn. I knew right then I had to do something in order to and get help so as not to be left behind. My analysis as to why it was such a difficult subject would be the fact that I was not intellectually prepared to go into such convoluted math problems, though it was...
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...falling apples. Wether this is true or not, we may never know. The point is that Isaac Newton was a brilliant minded physicist before he even began to thing about calculus....
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...requirements these professional must obtain, and then explain how they work with physicians. What limitations do these professionals have versus a physician? Why do you think some physicians might oppose using these professionals to provide care? Do you think these professionals play a critical role in healthcare? Why or why not? I am going to talk about an OD Doctor of Optometry. The reason I am going to talk about this profession is because what would happen if we lost one of our senses like Vision. I know that that is one of the senses that I would hate to lose. I don’t mind losing my smell or taste or even touch. When should I decide that I want to go to Optometry School? Honestly I would get a head start when you are beginning your freshman year of college. There are 21 schools of Optometry in the United States including Puerto Rico. So you should have an idea on what school you would want to attend. Most doctors would say that they have a list of 3 or 4 schools that they would attend. They would contact the schools and see what is required for undergrad work. So I decided to check out NECO (New England College of Optometry) I chose NECO because it is one of the top schools in the country and it is based out of Boston too. Applicants to the Doctor of Optometry program need to demonstrate at least three years of undergraduate preparation. Within this period of study the student must have credits for the following specific course work: (NECO 2015) Biology with Lab 2 Semesters ...
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...BATANGAS FACTORS AFFECTING THE ACADEMIC PERFORMANCE OF ENGINEERING STUDENTS In partial Fulfillment for the Requirements for Methods of Reasearch by Carandang, Castillo, Gonda, Santos, I. Introduction Engineers nowadays are in demand to lots of companies here and abroad. In fact, thousands of engineering graduates and board passers work mostly in other countries. This is the reason why lots of students took engineering courses. Engineering has always been considered as a very difficult course by most of the students. It’s almost always the last thing that will come to the minds of the students when it comes to choosing their course or program. Engineering, as a program has a lot of difficulties within its name. There are lots of math and science subjects and instructional activities that students will really find it difficult to pass. It requires a great responsibility in achieving the title “Engineer”. Some students who are already taking up engineering doesn’t know the hardships that they are still about to face, that’s why a large number of students tend to have a low academic performances. The field of engineering has become so diverse in recent years that a definition is not easy to come by. Engineers still build skyscrapers, design machinery, and oversee public works. They also address society's needs and problems on a number of other scales with a unique blend of technology and science. At the macro level, environmental engineers are quantifying...
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...people you surround yourself with and the groups you are part of. You cannot and will not pass college by yourself. You need to have a good group of friends that will help you. There friends need to be some you can rely on to be loyal and helpful. You need to have some people in every class that you talk to this way if you ever miss a class you can get a copy of the notes and go over what went on and what was assigned that day. Organize study groups in your classes and...
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...next lesson in the hope that they will be able to understand that one. This is a recipe for disaster. Math is very much like learning to read. If you don't know your letter sounds then you have no hope of being able to sound out words of course there is no way possible that you could read a book. All math courses are taught in a specific sequence because the every topic builds on the previous topic. If you are having a problem with a topic, continue working with that one until you understand it and can work problems successfully. Watch the DVD section over again, attend tutoring, read the book and examples a second time, or even get a totally different book to have it explained a different way...but whatever you do not turn the page and tackle the next topic. If you do, you will get even more frustrated and you in all likelihood will begin to give up hope. 2) Work example problems and check your answers to gain practice with every lesson. The entire premise of the DVD series is to "learn by example" and it is quite simply the easiest way to learn Math. After watching the section on the DVD and reading the section in your textbook, begin working examples...
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...CALCULUS II Three Dimensional Space Paul Dawkins Calculus II Table of Contents Preface............................................................................................................................................. ii Three Dimensional Space .............................................................................................................. 3 Introduction ................................................................................................................................................ 3 The 3-D Coordinate System ....................................................................................................................... 5 Equations of Lines.................................................................................................................................... 11 Equations of Planes .................................................................................................................................. 17 Quadric Surfaces ...................................................................................................................................... 20 Functions of Several Variables................................................................................................................. 26 Vector Functions ...................................................................................................................................... 33 Calculus with Vector Functions ....................
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...Congratulations on earning an A in Chem 111. I knew you could do it. It wasn’t easy but attending every lecture and recitation helped a lot. Not just from getting the hands on learning but also because by attending every class I got to participate in all the in class activities like earning all the iclicker points so I never fell behind. Even though videos of the class were provided online, I didn’t think that not going to class was an option. I knew I was a visual learner and by attending class I was physically and mentally engaged in what we were learning and was able to understand the example that was provided in class more than I would if I just watched it on a video. Also by contributing to my group in recitation, I was able to learn more from the other students in class and was able to teach them what I...
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...the situation and it is natural to think of the effects of our actions, however we cannot always accurately predict the effects of our actions. Deontological – the idea that acts are inherently right or wrong; they are right or wrong by their very nature. Absolutism – the idea that things are right or wrong, and remain so in all situations. This approach is clear-cut as it leads a list of what is right and wrong, however it is inflexible; it doesn’t consider the situation, and who decides what is right and wrong? Subjective morality – when moral judgements are based on individual opinions. Respects individual opinions and people can take responsibility for their own actions, however do all individuals opinions deserve respect? This may lead to disagreements. Objective morality – when moral judgements are based on external values/systems/rules. This approach gives authorities the ability to give guidance and advice, however there is disagreement about which authorities to trust. Utilitarianism (Teleological/Relativist): Is an ethical theory, which aims to help us work out what is right, and what is wrong. It focuses on bringing the greatest amount of happiness to the greatest number of people. Bentham: Hedonic Calculus – his method that measures the amount of happiness/pleasure an action will bring. He says if this is applies, it’ll lead to the right action. 7 PARTS TO THE CALCULUS: Intensity of pleasure, certainty of pleasure, duration of pleasure, continuity...
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...Chapter 3 The Relational Model Review Questions 3.1 Discuss each of the following concepts in the context of the relational data model: (a) Relation (b) Attribute (c) Domain (d) Tuple (e) Intension and Extension (f) Degree and Cardinality. Each term defined in Section 3.2.1. 3.2 Describe the relationship between mathematical relations and relations in the relational data model? Let D1, D2, . . . , Dn be n sets. Their Cartesian product is defined as: D1 D2 . . . Dn {(d1, d2, . . . , dn) | d1 D1, d2 D2, . . . , dn Dn} Any set of n-tuples from this Cartesian product is a relation on the n sets. Now let A1, A2, . . ., An be attributes with domains D1, D2, . . . , Dn. Then the set {A1:D1, A2:D2, . . . , An:Dn} is a relation schema. A relation R defined by a relation schema S is a set of mappings from the attribute names to their corresponding domains. Thus, relation R is a set of n-tuples: (A1:d1, A2:d2, . . . , An:dn) such that d1 D1, d2 D2, . . . , dn Dn Each element in the n-tuple consists of an attribute and a value for that attribute. Discussed fully in Sections 3.2.2 and 3.2.3. 3.3 Describe the differences between a relation and a relation schema. What is a relational database schema? A relation schema is a named relation defined by a set of attribute and domain name pairs. A relational database schema is a set of relation schemas, each with a distinct name. Discussed in Section 3.2.3. 3.4 Discuss the properties...
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...than that. He shaped the way we view things today, and has accomplished everything despite having an exceedingly depressing backstory. Newton was born January 4th, 1643, and nobody expected him to amount to much (or live, for that matter)....
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...Chapter 3 The Relational Model Review Questions 3.1 Discuss each of the following concepts in the context of the relational data model: (a) Relation (b) Attribute (c) Domain (d) Tuple (e) Intension and Extension (f) Degree and Cardinality. Each term defined in Section 3.2.1. 3.2 Describe the relationship between mathematical relations and relations in the relational data model? Let D1, D2, . . . , Dn be n sets. Their Cartesian product is defined as: D1 × D2 × . . . × Dn ’ {(d1, d2, . . . , dn) | d1 ∈ D1, d2 ∈ D2, . . . , dn ∈ Dn} Any set of n-tuples from this Cartesian product is a relation on the n sets. Now let A1, A2, . . ., An be attributes with domains D1, D2, . . . , Dn. Then the set {A1:D1, A2:D2, . . . , An:Dn} is a relation schema. A relation R defined by a relation schema S is a set of mappings from the attribute names to their corresponding domains. Thus, relation R is a set of n-tuples: (A1:d1, A2:d2, . . . , An:dn) such that d1 ∈ D1, d2 ∈ D2, . . . , dn ∈ Dn Each element in the n-tuple consists of an attribute and a value for that attribute. Discussed fully in Sections 3.2.2 and 3.2.3. 3.3 Describe the differences between a relation and a relation schema. What is a relational database schema? A relation schema is a named relation defined by a set of attribute and domain name pairs. A relational...
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...Study Guide: Lesson 4 A Little Logic Lesson Overview Logic is the primary tool or methodology in studying philosophy. Philosophy is about analyzing and constructing arguments and a good understanding of the basics of logical reasoning is essential in performing that task. The next 3 lessons will focus on logic and analyzing arguments. In this lesson, you will first be introduced to the laws of logic. These are the first principles for all reasoning. We will then discuss the specialized terminology we use in logic. Finally, we will examine 2 major kinds of logical reasoning: deductive and inductive. We will consider different forms of arguments under each and discuss how to evaluate these arguments. Take note that a large part of this lesson is about learning the terminology for logic. Tasks Read and take notes from chapter 5 of Philosophy: Critically Thinking about Foundational Beliefs, “A Little Logic.” As you read, make sure you understand the following points and questions: * Why are the laws of logic foundational? * The Law of Logic makes discourse possible. If they are not recognized as true, than nothing we claim makes any sense. Therefore, it is important to have a firm grasp of these laws. * List and explain the 3 laws of logic. 1. Noncontradiction – “Something cannot both be and not be at the same time and in the same respect. Expressed symbolically: ~ (P•~P).² It reads, “It is not the case that there can be both P and non-P”. 2....
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...the user into learning by principles of problem solving such as: sandbox, pleasantly frustrating, and well-ordered problems. Video games, to the general public, aren’t generally accepted as tools to engage the player in learning. The image of a gamer to most is no better than an obese man with unkempt hair and a bag of potato chips sitting on his couch/computer chair all day. Though this really isn’t the case, gamers comes in all kinds of appearances, it can be easy to see why people think this. The amount of time some people spend on their gaming devices is pretty haunting. Some people near 20 hours per day gaming, which is slightly superhuman. Though this is at a far extreme, what we see from this is engagement. What other activities do people want to do for that long every single day? As is the case with Limbo, many video games do an excellent job in engaging the user into constant problem solving. They player isn’t just watching in a zombie-like state, they are using their brain to figure out what to do next, where they should go, how they can get there. In Limbo if you aren’t thinking constantly, you won’t progress through the game. One could...
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