md Digest
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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COLUMN
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.