Power Flow Studies Using MATLAB

Power Flow Studies Using MATLAB Executive Summary The report aims to show the differences between Newton-Raphson and Gauss-Seidel methods by using them to analyse a power flow system. During the study in a two-bus system, with a slack bus and PQ bus, two convergence tolerances were used. The case study 1 compares the iterative process…

Correlation the Number of the Students’ College Applications and Consumption of Caffeine

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 to find…

Equation to Model a Cooling Cup of Coffee

MATHEMATICS 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…

Mathematical Modeling of Diseases: Varicella Infection Rates

To what extent can varicella be eradicated with the usage of vaccines? Mathematical Modeling of Diseases: Varicella Infection Rates Table of Contents: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .…

Derivation and Geometry of the Catenary Curve

Mathematics 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…

How does the jump of a horse affect its performance in showjumping competitions?

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 mathematics of…

Mathematical Basis of Big Bang Cosmology

How did the universe begin?   Table of Contents: Abstract………………………………………………………………………………………….1 Introduction……………………………………………………………………………………..1 Rise of the Big Bang Model…………………………………..……………………………….2 Mathematical Basis of Big Bang Cosmology………………………………………………..3 Friedmann-Robertson-Walker(FRW) Metric………………..………………………..3 Friedmann Equations……………………………………………….………………….4 3 Pillars of the Big Bang Model……………………………………..…………………………5 Hubble’s Law……………………………………………………………………………..6 Cosmic Microwave Background Radiation(CMBR) …………………………………7 Big Bang Nucleosynthesis………………………………………………………………8 Implications(?) of the Big Bang Model Conclusion Bibliography   Abstract  …

How Does the Idea of Limits Make the Calculus Precise?

How 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. The Calculus controversy…

Using Mathematics to Solve Crime

Typically, when people ask me why I want to go into Law Enforcement, I shut down. It’s a simple question, really, but the answer isn’t so straightforward. But this essay is living proof that I want to solve crimes; this is proof that I desire to become a sleuth like Nancy Drew. Definitely. Of course,…

Using Game Theory to Predict Brexit Outcomes

“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…

Concepts of Gender and Mathematics

Introduction 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…

Tristram Shandy’s Paradox According to an Encyclopedia entry on NationMaster.com (2009) it is generally considered that the publications of Laurence Sterne’s The Life and Opinion of Tristram Shandy, Gentleman had a dominant effect on literature of that time. Like his contemporary writers, Sterne debated publicly upon the boundary between literature and philosophy, that’s why his…

Accounting Ratio Analysis for Finances

Ratio analysis is a useful tool for analyzing financial statements. Calculating ratios will aid in understanding the company’s strategy and in understanding its strengths and weaknesses relative to other companies and over time. They can sometimes be useful in identifying earnings management and in understanding the effect of accounting choices on the firm’s reported profitability…

Mathematical Learning in the Early Years

Introduction 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…

The Concept of Probability in Mathematics

Probability is a way of expressing knowledge or belief that an event will occur or has occurred. The concept has been given an exact mathematical meaning in probability theory, which is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about the likelihood of potential events…

The Algorithm of Gaussian Elimination

In linear algebra, Gaussian elimination is an algorithm for solving systems of linear equations, finding the rank of a matrix, and calculating the inverse of an invertible square matrix. Gaussian elimination is named after German mathematician and scientist Carl Friedrich Gauss. GAUSS / JORDAN (G / J) is a method to find the inverse of…

The Pigeonhole Principle Forms

PIGEONHOLE PRINCIPLE. Student redefine this as common sense behind this basic idea of this mathematical principle; if there are n objects to be positioned in m receptacles (with m < n), at least two of the items must go into the same box. Whereas the idea is commonsensical, in the hands of a capable mathematician…

Explanation of the Gantt Chart

Its 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…

Types of Mathematics and Engineering

Engineering: 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…

Correlation of Mathematics With Other Subjects

“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…

Models of Lesson Planning for Mathematics

Introduction 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…

Maths Teaching Guide: Geometrical Constructions

12 Geometrical Constructions You know using various instruments of the geometry box-ruler, compass, protractor, divider, set square etc. construction of lines and angles. construction of perpendicular and perpendicular bisector to a line construction of angle bisectors. Construction of special angles like 15°,30°,45°,60°,75°,90°,105°,120°,135°,150°,175° You will learn construction of parallel lines using different techniques- paper folding, set square…

Maths Teaching Guide: Algebraic Expressions

6 Algebraic Expressions You know to write the terms, coefficients and factors of an algebraic expression. to classify an algebraic expression as monomial, binomial, trinomial. to identify like terms. to add and subtract algebraic expression. You will learn multiplication and division of given polynomials. the difference between an identity and an equation. algebraic identities and…

Cracking Ciphers Through Mathematics

Math Exploration: Cracking different Ciphers Rationale From the ancient times to the modern day cryptography has played an important role in our lives. This mathematics exploration is going to look at different ciphers ranging from Monoalphabetic to machine driven cipher. The main use of ciphers is to protect sensitive information when it is being send on…

Overview of Famous Mathematicians

Mathematicians’ Manifesto A young man who died at the age of 32 in a foreign land he had travelled to, to pursue his craft. A clumsy eccentric who could visualize his complete work in his head before he put it to canvas. A Russian who shuns the limelight and refuses recognition for his work. A…