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The Official Newsletter of St. Joseph-03, submitted as a requirement for Basic Calculus 080
CORRELATION: Linking Limits and Physics
CALCULATING LIMITATIONS. College Students from The University of Wisconsin race to solve differing equations during their Calculus class. From FreePik.com
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FEATURE
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CALCULUS: Bridging Limitless Innovation
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EDITORIAL V
Millennial’s
PROBLEM SOLVING: Who is the real problem? Math? or You?
APPLIED IN EVERYDAY LIFE
Here are some jobs that will satisfy your urge in applying Limits and Continuity. Astronaut. Aerospace engineer. Mathematician.
Scan to read Software developer.
Digi-Newsletter
Economist.
CALCULUS: APPLIED IN EVERYDAY LIFE
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CALCULUS: an entailed story behind the discovery
Chemical engineer. Physicist.
by Danica Althea N. Villarosa
Newton and Leibniz, the founders of Calculus, never addressed the most fundamental principle of modern calculus, the limits, it was evident in the creations of Eudoxus and Archimedes. Limit is the value that a function (or sequence) “approaches” as the input (or index) “approaches” some value, it is “the mathematics branch of knowledge that deals with limits and one or more variables’ distinctions and integration of functions.” The theory of limits for calculating curved figures and the volume of a sphere was first created by Archimedes of Syracuse in the third century B.C. By sculpting these figures into tiny pieces that can be estimated, and then raising the size of pieces, the limit of the sum of the pieces can be set to the required quantities. The study of Archimedes, The Method, was unknown until 1906 when mathematicians obtained that Archimedes was close to solving infinitesimal calculus.
Even as the study of Archimedes was obscure till the twentieth century, many established a modern mathematical definition of limits. In the seventeenth century, the Englishman Sir Issac Newton and the German Gottfried Wilhelm von Leibniz founded the fundamental principles of calculus simultaneously (about which the principle of limits is a crucial component). Ancient Greeks realized that by splitting it into even more parts that accommodate the area more tightly, one might enhance the precision of finding the area of randomly oriented regions. Through using limits, it is possible to make the “pieces” that make up the area of a region only a point wide, at which point the area approximation becomes precise. In addition to engineering, mathematics, and science, integrals have many other applications. Limit concept is an essential element for the development of mathematical analysis, and a lack of understanding clearly could lead to problems in dealing with ideas such as convergence, continuity, and derivatives. Limit is linked
to many other ideas, e.g. infinity, functions, and infinitesimals. If an individual grasps the idea of limits, the ideas connected with them are becoming easier to work with, but it is challenging for students to make a perception of the idea. In fact, many great mathematics researchers have found it difficult to handle time-limits precisely. Calculus corresponds to themes in an exquisite, brain-bending manner. Limits allow us to understand a number from a range. We can study the points around it so that we can higher understand the value we would like to understand. This is a systematic analysis of the limitations and their implications. There are few direct functional applications to the general principle of the limit theorem. Rather, for its generality, parts of the theorem are being used to establish the algebra of groups, rings, and areas, and to establish a rational basis for calculation, geometry, and topology. These fields of mathematics are all commonly used in the areas of physics, chemistry, biology, and electrical and computer technology.
Mathematicians have worked with limits at different periods and with various approaches for hundreds of years with challenges that have taken years to resolve. Nearness is vital to unlocking limits: it is only after proximity is defined that the limit has an exact meaning. Learning mathematics is an effort that requires a number of skills that are different for different mathematical topics. How a person learns mathematics may also vary. Some have been through hard work followed by periods of enlightenment, while others merely go through hard work. Mathematics has several characteristics, such as the use of models describing the world today, the compact and unmistakable formulations for clear exposure, and the deductive rationale for proving and problem-solving. Each property provides its own range of difficulties for mathematics learners, often including a transitional phase, for example, from a model to the actual life, from everyday language to a mathematical expression, or from one phase to another in a math equation.
CALCULUS: THERE’S INFINITY IN CONTINUITY
Postsecondary teacher.
Mechanical engineer.
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Nothing takes place in the world whose meaning is not that of some maximum or minimum -Euhler This is from Leonard Euhler’s sayings from about 200 years ago regarding Limits and Continuity in Calculus, Leonhard Euler said that it’s an interesting and perspective granting thought that he thought would be appropriate for his discussions. Euler is absolutely direct to the point here. He implied that in everything, no matter where it falls on a continuum, it is always defined in relation to a maximum or minimum.
The efficacy of both the
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collaborative efforts and preCONTINUITY: A simultaneous search for Mathematical sense student cisely designed worksheets are also
by DAN ESCLAMADO
A research study was conducted by Nalini Maharajh, Deonarain Brijlall & Nadaraj Govender. The research plan is to succeed in making a second year pre service using a sophisticated notion of the concept definition of continuity of single-valued functions in differential calculus. This research was published online on 20 Aug 2013. This research was conducted at the University of KwaZulu-Natal, South Africa. The research was conducted to develop a new mathematical sense or create a internal process to the concept of continuity. The student researchers are very well disciplined and have multiple experiences in teaching courses of
mathematics. The student researcher specializes in teaching mathematics to high school students at the University of KwaZulu-Natal, South Africa. A simultaneous approach was ventured; one through student researcher-collaborations and the other through instructional design worksheets, to create sophisticated numerical understandings of the concept definition of continuity. The worksheets were properly sequentially structured, using visual presentations of examples and non-examples of continuous functions, to instigate an extensive numerical comprehension of the concept of continuity.
Continuity, in basic calculus means, conscientious formulation of the intuitive concept of a function that varies with no sudden jumps or breaks. The research study was thoroughly conducted to achieve the best outcome. The conducted study was qualitative; it discloses that on the cognitive processes during the creation of this hypothesis of continuity of single-valued functions acquired from analysis of the well-structured worksheets, the worksheets were systematic. The students who were participating in this study were carefully handpicked and specialized in this special course.
discussed in depth. The result of collaborative effort was unexpected. In this concern, the concept image and the concept definition with regard to a deeper understanding of continuity in differential calculus were scrutinized within a Vygotskian paradigm. Vygotsky’s dual-stimulation method placed learners in problem-solving situations that were above their innate capacities, nearby aids, such as visual aids. The results of this research is showed that preservice mathematics students illustrated the ability to make use of oral and written mathematical language, this shows a great improvement in their ability to comprehend mathematical symbols, visual or pictorial models and mental images
to create internal processes to develop an advanced-mathematical sense of the concept of continuity of single-valued functions. On discerning functions as numerical entities, they could control these entities, which were comprehended as a system of operations. The conclusion of this study was that the students showed great improvement in their comprehension on visual mathematical sense. Vygotsky’s dual stimulation method illustrated a significant outcome to the conducted study. The student researcher’s surpassed their limits by being placed in a situation were above their innate capacities, of the concept of continuity of single-valued functions. On discerning functions as mathematical institutes and visual aids were available.
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The Official Newsletter of St. Joseph-03, submitted as a requirement for Basic Calculus 080
EDITORiAL
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CALCULUSBridging Limitless innovation
Millennial’s
by Ariane Diane I. Tagulalap
Digest
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ath is truly a challenging subject and we’ve faced it ever since we started on our education. We never knew how old we are if we weren’t taught how to count nor do basic operations like addition,subtraction,multiplication and division, before we knew, it already became part of our daily lives . Math have many branches that is meant for different purposes and are based by their classifications and one of them is basic calculus.
NEWS EDITOR Dan Esclamado
PHOTO EDITOR Danica Althea N. Villarosa
COLUMN
OPINION EDITOR Zhanel Javelosa
LAYOUT AND GRAPHICS EDITOR Lance Joshua P. Satojito
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role in our daily living. FEATURE May it be in measuring things or anything that includes numbers. People. Students especially might find it hard to Linking Limits and Physics study but time passes by and you’ll realize it’s acby Lance Joshua P. Satojito and Ariane Diane I. Tagulalap tually fun and amusing. Trying to understand the limit and continuity aximum, calculation definitions. is not just to help us pass boundaries, in basic calculus. If we he derivative is know how to apply them restraints. Limits best defined as the in real life who knows are a way to place rate of curve shift. If what other things we can value on a number you have ever graphed use them too. There’s no or equation that has an equation, you can limit to everything as variables. Math geeks long as you continuousrecognize the rate can find the value ly search for answers. at which the slope of a certain number increases. You may or equation as the also pinpoint unique variable approaches positions on the graph Realtalk. determined values. and also assess the rate Limits are important of change. You can because they are used also find derivatives often in advanced for the rate of change concepts of calculus. Who is the real problem? Math? or You? in 3-dimensional But for most students, graphs. pre-calculus is not passion in learning, the mandatory math Math is not difficult. terest it is hard for them to learn about he lack of interclass they would have or instance, the subject because est in the subject to take. Most students measuring when you have no makes it difficult for who participate in pre- temperatures of ice interest, it is hard to us to focus. If we athematics take calculus are doing so that has sunk in a obtain information. lose focus we lose time, effort, to prepare for college. warm glass of water, track of our lessons and dedication to be Irrespective of the which is why we have mastered. It proves it alone, is a limit. motivation, if we’re a hard time keep- to be one of the Other examples n my opinion, tar- ing up with math. most, if not the most, doing pre-calculus, may be measuring diness of oneself Our lack of motiva- difficult subject acit’s undoubtedly that the strength of an is the reason why tion in studying the cording to the opinwe’re on a course that electric, magnetic majority of students subject math is the ion of the students you’ll have to take or gravitational This find it difficult when thing that is mak- worldwide. higher calculus levels field. These limits it comes to solv- ing the subject hard, is because it takes afterwards. ing mathematical not the subject itself. up a lot more time are used every time and attention than equations. Majority for ordinary people most subjects do. of people portray and scientists alike imit is a way to set mathematics as borto approach to a real ing which makes he difficulty of a value to a number solution. Astronauts, them show a lack of the subject Math or equation that has aerospace engineers, interest to it. There- vary depending astering matha variable in it. You mathematicians, fore, the reason why on the person. The ematics is a will find the value a majority people is complexity of Math tough task in itself. software developers, of a given number having a hard time depends on the ded- Having 6 more subteachers, economists, or equation as it, the during mathemat- ication and willing- jects to learn at the and chemical variable, approaches ics is because they ness of a person to same time is even engineers are making find it boring and learn more about harder. This is why predefined values. use of these concepts they don’t give the the subject. Most students are shying Limits are important to further the progress effort and time be- people may say the away from the chalbecause they are of humanity. ing to engage math- subject itself is hard lenge that is known often used in advance ematical problems. but when you have as Mathematics. digital recording device is used to record yourself singing in the shower. The song comes out as a continuous function. It is also used in scales of measurement, like the ratio scale, and also in physics. It is an essential tool in solving other areas in calculus.
in physical sciences. Just for example, measuring an ice cube’s temperature sunk in warm glass of water is a limit. Another example of a limit is a chemical reaction started in a beaker in which two different compounds react to form a new compound. Now as time approaches infinimits on the oth- ity, the quantity of the er hand are not just new compound formed. restricted to calculus operations to define derivatives and integrals. They also have a broad ikewise, math in any range of practical utility forms still plays a big
L ontinuity of a funcC tion is the secret behind digital recording, including CDs and DVDs. Just like how a
FEATURE EDITOR Ariane Diane I. Tagulalap
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in fields that you never think would make use of, concepts like physics, engineering, economics, statistics, and medicine. It can also be used in areas of space travels or how medicines interact with the body and how to build safer structures. Calculus deals with a lot of topics. Part of this includes the limits and continuity of a function.
IKALAWANG PATNUGOT Lance Joshua P. Satojito
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asic Calculus is the B study of rates of change. Calculus is used
EDITOR-IN-CHIEF Ariane Diane i. Tagulalap
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PROBLEM SOLVING: V
Perspective by Zhanel Javelosa
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he subject Math is complicated and easy at the same time. It depends on the effort that you give in order to gain more knowledge about the subject. It requires concentration and dedication in order to learn Math easily and properly.
he reason why T majority of students find Math hard
is because of the effects of the negative ideas they hear from other people about the subject. The negative ideas they hear about Math causes them to lose interest about the subject. When they lose in-
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