Abstract: This paper describes the Laplace transform used in solving the differential equation and the comparison with the other usual methods of solving the differential equation. The method of Laplace transform has the advantage of directly giving the solution of differential equation with given boundary values without the necessity of first finding the general solution…

Read MoreINTRODUCTION A complex number is a number comprising area land imaginary part. It can be written in the form a+ib, where a and b are real numbers, and i is the standard imaginary unit with the property i2=-1. The complex numbers contain the ordinary real numbers, but extend them by adding in extra numbers and…

Read MoreApplication of matrix in daily life Matrices are used much more in daily life than people would have thought. In fact it is in front of us every day when going to work, at the university and even at home. Graphic software such as Adobe Photoshop on your personal computer uses matrices to process linear…

Read MoreApplications of Mathematics in Real Life Situations 1.0 Application of Matrices Matrix concepts can be applied in various fields such as: Quantum Mechanics 3D Games Animations Cryptography and Others. We shall analyze the last one which is Encryption in further details. Encryption is indeed an important measure of security when there are transactions of data between parties.…

Read MoreShare this: Facebook Twitter Reddit LinkedIn WhatsApp We begin our discussion with a common daily embarrassing moment. Suppose that in one’s dresser drawer, he has socks of three different colours (all placed in messy order). Having to get up early in the morning while it is still dark, how does he ensure that he gets a matching pair of same…

Read MoreResearch into topological solitons began in the 1960s, when the fully nonlinear form of the classical field equations, were being thoroughly explored by mathematicians and theoretical physicists. Topological solitons were first examined when the solutions to these equations were interpreted “as candidates for particles of the theory” [1]. The particles that were observed from the…

Read MoreCharlotte Angas Scott was an English mathematician born on June 8, 1858 in Lincoln, England. She was the 2nd child of seven to Caleb, a minister in a Congregational Church, and Eliza Ann Exley Scott (Encyclopedia of World Biography, 2010). In addition to his ministry, Caleb Scott was an educator and in 1865 became the…

Read MoreGeorg Cantor was born in St Petersburg, Russia. His birthday was March 3, 1845. Him and his family lived in St Petersburg Russia until he was 11 years old. They moved to Frankfurt Germany. They moved there because dad’s health was getting bad so he couldn’t take cold winters. Get Help With Your Essay If…

Read MoreINTRODUCTION Calculus, which is one of the foremost branches of Mathematics, studies about the rates of changes. It was invented by Isaac Newton and Gottfried Leibniz in the latter half of the 17th century. It is now used in different fields and subjects such as science, economics, and engineering (Wikipedia, 2019). For example, in Physics, calculus…

Read MoreShare this: Facebook Twitter Reddit LinkedIn WhatsApp INTRODUCTION: The control systems are based up on the behaviour of the dynamics systems and it is also a branch of the engineering and mathematical model of the process. The desired output of the system is called as reference. A controller is device which observes and outcome the changes in the output that…

Read MoreIntroduction This is a well known fact that the early years of a child’s life are very important in terms of their emotional and social development, their general well being and their intellectual, emotional and physical growth. Almost all the children develop at different paces and what they learn takes place in the first three…

Read MoreShare this: Facebook Twitter Reddit LinkedIn WhatsApp What are that iteration methods compare different iterative method? What are the iteration methods? An iterative method is a powerful device of solving and finding the roots of the non linear equations. It is a process that uses successive approximations to obtain more accurate solutions to a linear system at each step. Such…

Read MoreLouise Scupham This essay will explore the Turing machine and its relationship with computable numbers and an introduction to real numbers of various types. I will offer an explanation of the reasons why a number may or may not be considered computable through the use of the concept of countable sets and what makes a…

Read MoreConic Section The names parabola and hyperbola are given by Apolonius. These curve are infact, known as conic sections or more commonly conics because they can be obtained as intersections of a plane with a double napped right circular cone. These curves have a very wide range of applications in fields such as planetary motion,…

Read Moremost branches of economics such as calculus and probability theory. The concept that I have talked about in my project are the real number system. 2 Definitions Natural numbers Natural numbers are the fundamental numbers which we use to count. We can add and multiply two natural numbers and the result would be another natural…

Read More“No subject is ever well understood and no art is intelligently practiced, if the light which the other studies are able to throw upon it is deliberately shut out.” – RAMONT What is correlation? The meaning of term ‘correlation’ in simplest form is “connect” or “to be connected”. More precisely, ‘Correlation’ means mutual relation of two or…

Read MoreShare this: Facebook Twitter Reddit LinkedIn WhatsApp Correlation the Number of the Students’ College Applications and Consumption of Caffeine Introduction and statement of intent: Students are exposed to a lot of stress during the college admissions process. These increased stress levels come with some negative consequences like the increase in consumption of caffeine. The objective of this academic project is…

Read MoreDEFINITE INTEGRAL Integration is an important concept in mathematics which, together with differentiation, forms one of the main operations in calculus. Given a function ƒ of a real variable x and an interval [a, b] of the real line, the definite integral, is defined informally to be the net signed area of the region in…

Read MoreMathematics SL Derivation and Geometry of the Catenary Curve Table of Contents Introduction 1 The Catenary Curve 1-2 Geometry and Defining Variables 3-5 Derivation 5-7 Application 8-9 Conclusion 9 Bibliography 9-10 Introduction ————————————————— My biggest interest has always been art and design. Both my brother and my dad work in construction which introduced me to…

Read MoreIntroduction Mathematics, a subject of problem solving skills and applications, has wide usage in all the fields. Basic skills of mathematical applications in number systems used even in day – to – day life. Though calculators and computers have greater influences in calculations, still there is a need to find new easy methods of calculations…

Read MoreIntroduction Planning the word it contains more weightage as compared to any other word. We can only achieve any target often a proper planning strategy. In planning what is target to achieve is our goal with the available resources. Planning also plays an important role in teaching-learning process. While, doing a proper planning in teaching…

Read MoreI. Introduction The main role of digital signature primitive is to preserve the data integrity of electronic document and to accomplish the requirement of authentication and verification. Only one signer using his/her private key generates an ordinary digital signature scheme. However, in some practical application, a document requires all group members to generate a signature…

Read MoreINTRODUCTION TO DIRECT AND ITERATIVE METHOD Many important practical problems give rise to systems of linear equations written as the matrix equation Ax = c, where A is a given n × nnonsingular matrix and c is an n-dimensional vector; the problem is to find an n-dimensional vector x satisfying equation . Such systems of…

Read MoreDISLIKE OF MATHEMATICS AMONGST SECONDARY STUDENTS 1. INTRODUCTION Why do kids, students and adults seem dislike mathematics? It is quite common for small children to say “I love numbers”. Do they really know exactly what mathematics is? Get Help With Your Essay If you need assistance with writing your essay, our professional essay writing service…

Read MoreBernard Opoku qCarl Friedrich Gauss, born into a poor working class family in Brunswick, now lower Saxon, Germany and died in Gottingen, Germany. He was a child prodigy with genius that did not impress his father who called him a “star-gazer.” His mother, Dorothea Gauss was the exact opposite of his father as she collaborated…

Read MoreEngineering: Engineering is the word that does not have proper definition. Every person thinks with different point of view so create different definition but most commonly used definition of engineering is, this is the practical application of science to commerce or industry. As we know that the work of scientist is to know, the engineer…

Read MoreMATHEMATICS SL Internal Assessment Mathematically Determining an Equation to Model a Cooling Cup of Coffee I. Introduction After having spent countless hours completing assignments and projects, I have too often found my coffee to be cold by the time I get around to drinking it. As a result, I began to question the reasoning behind…

Read MoreShare this: Facebook Twitter Reddit LinkedIn WhatsApp Equity and Social Justice in the teaching and learning of Mathematics Equity and Social justice are important issues in Mathematics teaching. This essay explores the relevance of how Mathematics Education may be a necessary factor in determining the social justice of a child’s upbringing, and consider how equity can be used to ensure…

Read MoreSummary Euler Totient theorem is a generalized form of Fermat’s Little theory. As such, it solely depends on Fermat’s Little Theorem as indicated in Euler’s study in 1763 and, later in 1883, the theorem was named after him by J. J. Sylvester. According to Sylvester, the theorem is basically about the alteration in similarity.…

Read MoreHistory of matrix had to be going back to the ancient times, because it is not applied until 1850. Matrix is the Latin word for womb, and is same in English. It can also mean something is formed or produced. Matrix was introdeced by James Joseph Sylvester,who have brief career at the University of Virginia,…

Read MoreThere are only a handful of Egyptian mathematical texts that are still in existence today. It is amazing how these ancient texts can survive for thousands of years so we can continue to study them and understand the minds of ancient Egyptians. Egyptians were more scientifically and mathematically advanced than one might think. The most…

Read MoreThe Fencing Problem. A farmer has exactly 1000 metres of fencing and wants to fence off a plot of level land. She is not concerned about the shape of the plot, but it must have a perimeter of 1000m. Which shape, with a perimeter of 1000m has the maximum possible area? Let us start off…

Read MoreSome aspects of mathematics can be dull and tedious from start to end, much of it however is intriguing and inspiring, when you truly see the beauty and the relevance. This is why I would like to bring to your attention the magic of the Fibonacci numbers. If you have ever looked at a sheet…

Read MoreHow Does the Fibonacci Sequence Relate to Nature and Other Math Processes? Nature is all around us, and because I spend a lot of time outside I have been able to enjoy and observe all that nature has to offer. Due to the fact that I love science and discovering how everything around me functions…

Read MoreCalculating the number of folds and the hypothetical size of a piece of paper so that its thickness equates to the distance from the Earth to Saturn. As a physics student doing the option on astrophysics, I have become very interested in the immensity of the universe. I decided it would be intriguing to combine…

Read More“Consider the negotiations over Brexit between the UK and the EU. Use Game Theory to describe the players’ strategies, their payoffs and how the game is played. Solve your model to predict the outcome(s).” The essay thesis is that due to Brexit, the EU will achieve more of its aim and objectives during negotiations than…

Read MoreIts use a simple logic calculations to identify the critical path, it does include: – A sequence of activities has a timing duration. – Adding the timing durations from the start till the end (forward pass), it helps to determine the early and late start. – Deduct the timing durations from the end to the…

Read MoreIntroduction Gas sensors based on semiconducting metal oxides are being widely used for sensing gases and vapors. The initial momentum was provided by the findings of Seiyama et al. in metal oxide-gas reaction effects in 1962. It was shown that the electrical conductivity of ZnO can be changed by the presence of reactive gases in…

Read MoreMany computer related vision technology, it is critical to identify moving objects from a sequence of videos frames. In order to achieve this, background subtraction is applied which mainly identifies moving objects from each portion of video frames. Background subtraction or segmentation is a widely used technique in video surveillance, target recognitions and banks. By…

Read MoreIntroduction In 1896 Charles Darwin wrote “The chief distinction in the intellectual powers of the two sexes is shewn by the man’s attaining to a higher eminence, in whatever he takes up, than can women…….if men are capable of a decided pre-eminence over women in many subjects the average mental power of a man must…

Read MoreIn this project I will talk about starting of history of the algebra which is one of most important branches of arithmetic and Founder of the algebra and meaning of algebra and its benefit of our daily life, how we can learn and teach best way. History of algebra Algebra is an ancient and one…

Read More180 BC Hypsicles: Number Theory Hypsicles was born in 190 B.C. in Alexandria Egypt. He was a mathematician and astronomer. He wrote the “Anaphorikos” or “On the Ascension of Stars,” where he divided the Zodiac into 360° and used arithmetic progression, “a sequence in which each number increases by the same amount over the previous…

Read MorePetros Karayiannis Chapter 0 Introduction Hopf algebras have lot of applications. At first, they used it in topology in 1940s, but then they realized it has applications through combinatorics, category theory, Hopf-Galois theory, quantum theory, Lie algebras, Homological algebra and functional analysis. The purpose of this project is to see the definitions and properties of…

Read MoreReference this Share this: Facebook Twitter Reddit LinkedIn WhatsApp 1. Rationale While looking for an area of maths to delve into my Mathematical Exploration, I took inspiration from my grandfather’s hobby of pottery and glass blowing. In the garage, he would have sheets of glass and clay blocks occupying the shelves. We had a shared past-time where he would make beautiful,…

Read MoreHow does the idea of limits make the calculus precise? In this essay, I will be discussing the topic of differentiation and how the ideas of the calculus were criticised. I will be giving an overview of how calculus can be explained and explaining the idea of limits and the infinitesimal number. Get Help With…

Read MoreShare this: Facebook Twitter Reddit LinkedIn WhatsApp How does the jump of a horse affect its performance in showjumping competitions? 1.0 Rationale: In this Math IA, I am wanting to talk about the different types of horses and their how they jump is better than other animals. My aim of this Internal Assessment is to analyse the…

Read MoreImage Inpainting – Filling in the gaps. Abstract Inpainting is the process of rebuilding lost or damaged parts of images and videos. Image inpainting, also called hole filling, is the technique of image reconstruction by filling or replacing the region where there is damage or intentional removal of objects. The outcome is to make the…

Read MoreWhen Are We Ever Going to Use This? – Imaginary and Complex Numbers The number √-9 may seem impossible, and it is when talking about real numbers. The reason is that when a number is squared, the product is never negative. However, in mathematics, and in daily life for that matter, numbers like these are…

Read MoreHow the Aztec Mathematical System Came to be and Contributed to us Today by Destiny Harrison, Delaney Garcia, Jaysiya Norman, Jewel Samson, Raquel Cruz, Katelyn Woodley, Kalyna Mai and Olivia Nixon For the competition, we were tasked with studying Aztec mathematics. Aztec mathematics was one of the most complicated mathematical writings of any of the…

Read MoreMathematics was man’s first approach to understanding the world around them since the beginning of humanity. The study grew with history in various forms with every human civilization, and as time passed, more discoveries were made that allowed humanity to reach great heights in agriculture, architecture, social structure, and their culture. Great mathematicians continued extensive…

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