Fundamental Theorem of Calculus The Fundamental Theorem of Calculus evaluate an antiderivative at the upper and lower limits of integration and take the difference. This theorem is separated into two parts. The first part is called the first fundamental theorem of calculus and states that one of the antiderivatives of some function may be obtained as the integral of the function with a variable bound of integration. The second part of the theorem, called the second fundamental theorem of calculus, states that the integral of a function over some interval can be computed by using any one of its infinitely many antiderivatives. The fundamental theorem of calculus along curves states that if has a continuous infinite integral in a region containing a parametrized curve for then The first fundamental theorem of calculus says that if is a continuous on the closed interval and is the indefinite integral of on , then The second fundamental of calculus holds for a continuous function on an open interval and any point in and states that if is defined by then at each point . Before we explain the fundamental theorem of calculus in details let’s talk about the origin of this theorem. The mathematician who discovered what we call the fundamental theorem of calculus is Isaac Newton. For him, this theorem was virtually self-evident, as Victor Katz states on the book “A History of Mathematics”. Isaac Newton was born in England on January 4,1643 and is a known as…
The Mandelbrot and Filled Julia Sets The Mandelbrot and Filled Julia Sets are sets of numbers that are composed of complex numbers that do not diverge for varying conditions of the function fc(z)=z²+c. For the Mandelbrot set, the function is iterated from z=0. The filled Julia set holds c constant for any complex number to look at the behavior of the iterated functions for each value of z in the complex plane. Both sets are derived from the iterations of simple functions in the complex plane,…
Abstract: This paper is a report on the development of algebra throughout time. It’s slow, but nevertheless, unyielding progression brings us to the algebra we know today. However, it was not always based on the abstract, rather, it was born out of necessity. The need to calculate unknown quantities gave rise to algebraic methods and techniques practiced and taught even today. And, even though nowadays, algebra is a rather abstract mathematics, this was not always the case. It was through…
social environments, numbers surround me. Over many years, I have learned how to derive meaning from them or use them to help me figure things out. During this unit, I have learnt, re-learnt and applied various areas of mathematics to help me achieve the outcomes and find solutions to each ‘Thinking Time Problem’ [TTP] presented. These relate to the Australian Curriculum- Mathematics proficiency strands of problem solving and reasoning, while the ‘What I Know About’ [WIKA] activities relate to…
Ms. Caldwell definitely deserves being teacher of the year. If you ask me why I will say many things, for example, math wasn’t a subject I valued until I had Ms. Caldwell for Algebra 1. She always helped us and made sure she answered the questions we had. She would make my classmates and I go early in the mornings to her office so we could explain what we had done wrong and if we didn’t understand the material she would explain the material in detail and say why the answer is right. Her…
Different number were even believed to have a cosmic significance or magical powers. However the main thrust of Chinese mathematics came from the Empire’s desire to have administrators that were well versed in mathematics. Therefore in order to educate, a textbook called, “Nine Chapters on the Mathematical Art” was written. This important text became a vital part of Chinese education. This tool provided hundreds of problems in taxation, engineering and payment of wages. The text served as a…
done alright with that mentality until I began studying for myself. I would look into books for biology, and algebra. Algebra was interesting to me because it was simple equations with letters. You would have to just make a letter equal a number, or another letter. For example: 4=x+1; in turn the answer would be x=3. It would then get more complex later on, where the teachers would throw things like, “X=8b+4” which would take longer to solve. The year was a breeze for me. The next year was not…
relate to logistics, supply chains and warehousing. Business math differs from other types of math’s because it consists of more advanced mathematics such as matrix algebra, linear programming and mathematics of finance. Thus, it is perfect to use in the business management field. Not only is Business math a very important type of mathematics but so is Financial Mathematics because they two form important branches of math that are directly applied to business and economics. Examples of these…
I continued on in high school with geometry, a second year of algebra, precalculus, trigonometry, and calculus. Thus far, my math courses in college have also been easy for me. My least favorite teacher was my calculus teacher, and it was not solely because of the tough subject matter. He was an engineer who took up teaching after retirement. He very simply could not teach well. He would stand in front of the board and talk through the problem at a pace that was almost impossible to follow. I…
The unit that will be transformed is a unit is The Building Blocks of Algebra (eMath Instructional Inc., 2016). This unit is in need of a transformation because of the lack of differentiation. Although there is plenty of scaffolding of the new content (Van de Walle, Karp, & Bay-Williams, 2013, p. 23), the approach does not vary very much in its representation (Van de Walle et al., 2013, p. 22-24). The majority of the unit structure is to be straightforward with the content and not deviate from…