Calculus Essay Topics & Samples for College Students

Before the onset of the seventeenth century, the Middle East had dominated in the area of mathematical ideas. Many philosophers and scientists came up with compelling ideas in mathematics and proved many formulas in mathematics from the Middle East. Essentially, there were distinct factors that influenced scholars and philosophers from this region to be competent in mathematics and other scientific inventions as they were. However, in the onset of the seventeenth century, Europe replaced the Middle East, which had been vastly associated with mathematical discoveries. Europe thus became the new engine house of mathematical ideas from the seventeenth century . ...

Part 1:

1. This notation means that the limit of a function f(x) as x tends to a is equal to L. In this case, L is a number. a is a number. x is the function. No we cannot conclude anything about f (a). 2.

The three conditions associated with non-existence of a limit are

- Divergence up to infintiy - Oscillations with a frequency increasing with time - Scintillation 3. Limx-a f(x) = ∞means that the limit of the function as x tends to a is infinity while Limx-∞ f(x) = b means that as the limit of the function as x tends to infinity is equal to ...

One of the dark secrets of Newton is his deep curiosity and obsession to religion and his devotion to occult. Another revelation shows that Newton has tried to enter pseudoscience which means he settled on beliefs and practices that are mistakenly known as based on scientific method given that before everything, he believes that everything in this world can be subscribed to scientific understanding. According to Walter Lewin, one of the speakers in the video, Isaac Newton is allergic to criticisms even before that is why he decided on keeping his inventions and even the other earthly manners that ...

1. Integration is a topic within calculus that has been applied in many engineering problems. Sir Isaac Newton and Gottfried Wilhelm von Leibniz first developed integration concepts, while working independently, in the 15th century (Goldman and Foresta, 2005 p. 4). Leibniz used integral calculus to work on sequences of functions while Newton used it to find the area under a curve and consequently overlook the use of indivisibles (Goldman and Foresta, 2005 p. 5). A separate, but similar in concept discoveries, lay the foundation for the two part fundamental theorem of calculus. The first part states that, if f ...

Validity and Scope of Approximate Methods of Integration

Introduction Addition of discrete numbers is pretty straightforward; more than 80% of the human population can make mental calculations instantly. So when integration was introduced as a kind of addition in a continuous domain, I was not very worried. However, it didn’t take me long to realize that understanding integration is more than solving a bunch of problems using well defined techniques. So in my pursuit to understand the topic well, I decided to research upon how some of these techniques (Trapezium Rule and Simpson’s Rule) came about, how they work, and what they really mean. With ...

Since its creation in the 17th century the mathematics of calculus allows different fields of study the ability for measuring change and motion connected with natural and physical science including medical research and proactive applications of medicine. With the onset of the 21st century, the advances in mathematical insights forming definitions and theorems underpin the variety of uses of calculus in medicine. Calculus provides the abstract mathematical understanding of varieties of professional fields. These include economic trends, biological probabilities with ocean currents, meteorologist calculations of upper atmosphere airflow for weather prediction, and space scientists designing remarkable aircraft for space ...

Economics is not Mathematics but mathematics has a great help for economics. It has a dose of reality to some economist according to Michael Edesess, a mathematician. Mathematics from economics has a major difference; there is no mathematician that uses a term in a formula or any statement of any theorem if the said term has defined with accuracy. Economists defined terms such as aggregate demand or economic growth but a thorough study on some real mathematics is suggested to assure an exact definition of the term. Overviews on both subjects are necessary to ensure clarity and depth of ...

Calculus is widely used in various professional fields such as in engineering, statistics, physics, economics and architecture. Calculus is also considered as the language that scientists, engineers and economists use due to its capability to model and also control numerous systems. The tasks performer by these professionals usually has a massive impact on people’s lives such as in communication, medicine, electronics, economy, transport and also in national defense. Calculus is widely applied in the field of engineering in modeling and controlling systems. Electrical engineer often uses integration in determining the precise length of power cables that are required ...

The discovery of calculus, which is a branch within mathematics, is attributed to both Isaac Newton and Gottfried Leibniz. Both Isaac Newton and Gottfried Leibniz made independent contributions towards the development of the foundations of calculus. Instrumental and significant contributions were done by both Newton and Leibniz in a bid to ensure that calculus was developed in order to assist in various concepts and applications of mathematics (Kleiner 139). However, it is important to note that the foundations of calculus developed by Newton differed widely from the foundations of calculus that were developed by Leibniz. There is no doubt ...

Karl Theodor Wilhelm Weierstrass was a German mathematician who is often called as the "father of modern analysis".

Weierstrass was interested in the soundness of calculus, and also made significant advancements in the field of calculus of variations. Among the several significant axioms, Weierstrass established a necessary condition for the existence of strong extrema of variational problems. As we know, Cauchy gave a form of the (ε, δ)-definition of limit, in the context of formally defining the derivative, in the 1820s, but did not correctly distinguish between continuity at a point versus uniform continuity on an interval, due to insufficient rigor. Notably, in his 1821 Cours d'analyse, Cauchy gave a famously incorrect proof that the (pointwise) limit of ( ...

Calculus is a section in mathematics that can also be referred to as infinitesimal calculus that is mainly focused on integrals, infinite series functions and limits. Most of the ideas and notions in the history of calculus were invented by various mathematicians in the seventeenth century. These ideas were closely related hence summarized together to ensure that the current calculus is simple to integrate and calculate. However, much credit is attributed to Isaac Newton and Gottfried Leibniz whose ideas although different but were essential in developing diverse functions in calculus (Stewart 112).

The innovation of calculus is usually related ...

1. The function of Bentham’s hedonistic calculus is to provide a moral theory of what is right and wrong, based on the idea that what gives the most pleasure and happiness and the least pain to the world is the correct action. An example of how to use this theory is for legislators to create laws that would cause more suffering and pain to criminals than the pleasure their crime provided. An advantage of using the calculus is tries to provide the best results for the most people. The inherent problem with the the calculus is that some ...

Isaac Newton also called the father of all science has vastly influenced the science world greatly. He came up with theories and advancements in science that have been used since then to solve problems of the modern day science. His discoveries and theories have had an effect on the fields of mathematics, mechanics, optics, astronomy, alchemy, experimental chemistry, and theology.

Mathematics

Newton at a time worked in Cambridge as a mathematics professor. It was when he was at Cambridge that he came up with calculus which was a new mathematics field. Newton came up with infinitesimal calculus to be exact ...

The ethical quandary in Robert F. Ladenson’s Friends and Lovers presents a situation in which one member of a group of three friends, Claire, must make a decision about how to deal with information she has received intimately concerning her other two friends, Tony and Beth, who are engaged to be married. Tony has revealed he had a brief affair but asked Claire to keep the fact a secret, and Beth has asked Claire if she thinks something is “going on” with Tony. Claire’s decision on how to deal with the situation will differ depending on what ...

Introduction

The worldwide technological revolution has impacted many facets of global systems in a major way (Aaron 1). Technological innovation has improved the archaic traditional methodology of obtaining results. Speed and productivity have been enhanced thanks to this technological advancement. However, compared to other sectors, the education system has lagged behind in incorporating technology in the learning process (Aaron 1). The education system stands to gain a lot if it incorporates technology in the learning models. The most innovative way to do this is the gamification of the learning process. This paper aims to illustrate gamification, how it operates and ...

Biography of Archimedes

Archimedes was born in 287 BC in Syracuse on the island of Sicily. His father Phidias, was astronomer and mathematician; He provided him education in sciences. Archimedes had his studies in Alexandria. Archimedes met the famous astronomer Conon, the astronomer and mathematician Eratosthenes, with whom he maintained in the future scientific correspondence. He worked in a library where he studied Democritus, Eudoxus and other scientists. Archimedes later published several works in mathematics. His work consists of providing the areas of figures bounded by the curves and volumes of bodies bounded by arbitrary planes. He is the one of the ...

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Introduction Ellipse is the locus of points of Euclidean plane for which the sum of the distances to two data points F1 and F2 (called foci) is constant and greater than the distance between the foci. Bulk body is a body of revolution generated by the rotating flat geometrical figure bounded by a curve about an axis lying in the same plane. Volume of the solid formed by rotation around the x axis of the figure bounded function f (x) on the interval [a; b], the x-axis and direct x = a ...

Final Essay: Meditation and Conflict Management

When legal researcher Erin Brockovich blew the whistle on California utility company PG&E in the early 1990s, the subsequent tortfeasor lawsuit Anderson vs. PG&E, resulting in a $333 million landmark settlement to the plaintiffs in 1993, established a new baseline for damages in respect to environmental violations by a corporation (Girardi & Keese). Analysis of the legal representation of 650 residents in the City of Hinkley, California, by Brockovich’s employer, by law firm Girardi and Keese expiates the limitations of mediation and conflict management leading up to litigation of gross negligence cases. The case alleging defendant corporation, PG&E’s ...

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Question A

Find the derivatives of the following: 1) y=cos(x2)e-2x y'=-2xsinx2e-2x-2cosx2e-2x=-2e-2x(xsinx2+cosx2) 2) y=2x2sin3x+4 y'=4xsin3x+4+3cos3x+42x2=2x(2sin3x+4+3xcos3x+4) 3) y=3xsinx22x+1 y'=3sinx2+6x2cosx22x+1-6xsinx22x+12=3sinx2+6x2cosx22x+1- -6xsinx22x+12 4) y=x3+4x2+5x-1 y'=3x2+8x+5

Question B

- What approaches did you take to complete this assignment? - What is the most difficult part of this assignment for you to do? The most difficult part was #4, when I had to find the derivative of the ratio, and there was also a multiplication in numerator. This question requires ...

Mathematics and sciences gave me one of the biggest challenges in my early education life. Having studied in a private school in the US where I was introduced to Everyday Math, I realized that it was not as easy as the tutors would want us to believe. An s early as I can remember, the educators used old and ineffective teaching criteria. Having to count from 0 to 1000 and playing games seemed tedious at the moment but it was as much impractical as I would learn later on. Addition and subtraction facts were scanty, and less emphasized. Until ...

This article is about sleep and its importance to memory. Sleep has been found to assist in the consolidation of memory coming from newly acquired information. Sleep provides the condition for the optimal consolidation to happen. The time and length of the sleep, as well as the conditions under which the learning or passing of the new information takes place will determine the success of the consolidation. Consolidation of memory, on its part, is essential because it has been found to improve both the quality and also the quantity of the memory patterns. This article reviews several other articles ...

Isaac Newton’s story of how an apple falling from a tree that hit his head inspired him to formulate a theory of gravitation is one that all school children grow up hearing about. Newton is arguably one of the most influential scientific minds having ever lived. He has published books such as Arithmetica Universalis, The Chronology of Ancient Kingdoms, Methods of Fluxions, Opticks, the Queries, and most famously, Philosophiæ Naturalis Principia Mathematica. He formulated the three laws of gravitation, discovered the generalized binomial theorem, developed infinitesimal calculus (sharing credit with Gottfried Wilhelm Von Leibniz, who developed the theory ...

Mathematical Modeling

In an analysis of the economic condition of both enterprises and the larger subject of the national economy applies dismemberment problem or situation into smaller questions. This allows the procedure to the study of the logic which is a simulation. In particular, this method is applicable to the social processes that, among others, form the socio- economic system. Thus, we are able to understand the factors that determine the social conscience and the state of the productive forces, the institutional framework of the society. Modeling of social processes is an important part of mathematical methods in economics that highlight ...

Introduction

One of the famous irrational number in mathematics is the number e which has a value: e= 2.71828 18284 59045 23536 02874 71352 66249 77572 47093 69995 The number e was named by the Swiss-German mathematician, Leonhard Euler, in 17th century. It is frequently called Euler's number after his name; however, the letter e stands for the word exponential. The number e is the base of the natural logarithms that is created by John Napier. In the year 1737, Euler employed the symbol for pi to denote the ratio of the circumference to the diameter within a circle. Then, ...

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Marx’s Economic Analysis Theory of Surplus Value Marx’s theory of surplus value proposed that the surplus product (surplus value) remains in the whole social product (net national income) after the production classes (workers) received their compensation (wages) (Mendel n. p.). According to Marx in his theory of classes, it is the ruling class (capitalists and politicians) who appropriates the surplus value that can be found in three different forms: (a) unpaid surplus labor (slave mode of production); (b) goods directly used (product of surplus labor), and; (c) cash.

Fetishism of the Commodity

Created for commodity ...

Chapter 9: Descartes

1. "I find here that thought is an attribute that belongs to me; it cannot be separated from me. I am, I exist, that is certain" (Descartes qtd. in Soccio 260). What does Descartes mean by this statement and why is it so important? Descartes claims that there is no ego without a thought (mind) and this ego does not exist in a thoughtless state. That is one of his most important ideas, which led to a well-known statement - “I think therefore I am”. 2. What is meant to be proven by the wax example? How does Descartes ...

Introduction to Electrical Engineering

Electronic gadgets are in great demands today because of the evolution of high technology and advancement of internet connection. People are always finding something new, so, many companies are giving funds for research. With the help of electrical engineers, companies are providing new gadgets every now and then to surpass the features of the previous gadgets that they have been produced. In order for the students to solve complexities of a problem, electrical engineering program gives an opportunity to learn new things by experimentation and analytic solving. Therefore, this program mainly tackles mathematics and science. Because of experimentation and ...

The nature of utilitarianism helps man make an effort to the question, “what should a man do? Which the answer ought to produce the best results to come forth. It is with this thought that utilitarianism takes the good and the bad caused by the deed. When evaluating this action it takes into account not only the happiness of the individual, but also of everybody touched by it. If such a theory opposes egoism does it seem to be rather “hollow” and rapid to approach? I disagree because it rallies for the common good of every individual. The employ ...

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J. Ernest Wilkins Jr. An African America, the youngest student in the University of Chicago at the age of 13, and a Ph.D. in Mathematics at the age of 19 – that is the genius of Jesse Ernest Wilkins Jr. His work on Multi Variable Calculus, Algebra, Nuclear Physics, and Engineering, have created and contributed extraordinary systems, not only in the fat man and a little boy nuclear explosions, but also in using nuclear energy for the generation of electricity as well Gamma-Ray protection. Unfortunately, he was an African-American, and it impacted him all ...

As a freshman, I am applying for a sophomore transfer, based on a 3.72 GPA my first semester at University of Houston Bauer Honors. I took Human Situation and my English class in Honors at the college. Commuting to UH makes a hassle for me, and I am deprived of several opportunities available outside classrooms on campus. In 2013, I graduated from Stephen F Austin High School in Sugar Land, Texas. Having successfully moved from Karachi, Pakistan, in the middle of my junior year in high school, I still had issues with my credits and coursework transferring, and had ...

Introduction to Engineering Technology

The career that one takes in life is a very crucial thing in life. It is important to choose a career that you were comfortable with since it determines what you will do for the rest of your life. The career that one takes is mostly determined by the passion that you have for a particular kind of work. The job market also determined your career that one takes. For instance, course like engineering and medicine are considered more lucrative. Biotechnology is basically a science based course that deals with the microorganism. The microorganism is used to perform different ...

Urolithiasis refers to the condition where there is the formation of urinary stones as well as their location in the urinary system. While the term urolithiasis refers to those stones that are in the ureter, nephrolithiasis also known as renal calculus refers to those stones that are found in the kidney, and cystolithiasis (vesical calculi) refers to the stones that are formed or located into the urinary bladder (Pearle, Calhoun, & Curhan, 2007). The urinary stones also known as calculi refer to the hardened mineral deposits forming in the kidney. The stones originate as microscopic after which they develop into ...

Executive summary

MathCAD is a crucial tool for applying in mathematics and especially mathematics for engineering. The software provides an environment of inherent interactivity with scratchpad, real math notation, automatic recalculation and fully integrated project components. MathCAD yields results when making crucial calculations. This is achieved through integration of text, math and graphics into a single worksheet. This in turn, is visualized, illustrated and annotated in all the calculations. MathCAD runs in computer operating systems like MS Windows 2000, XP, Vista, Windows 7and windows 8.

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Conclusion 13 Objectives Activity procedures - Load the MathCAD software - s:\ ...

As the authors point out in the opening chapter of Moral Issues in business, "Stories of business corruption and of greed and wrongdoing in high places have always fascinated the popular press, and media interest in business ethics has never been higher" (Shaw et alt, 4). Part of this fascination must stem from humans interest in "bad new" of disasters terrorism and threats to peaceful living. Some of the interest might be a self defense mechanism that seeks to guard against unwanted circumstances that could happen in people's lives through protection themselves of the knowledge of what has happened ...

Social psychology implies by its name that it jumps from the focus being on the individual to how the individual functions within the confines of a society. Morality, or a set code of personal conduct and defined and agreed upon notions of right and wrong are at the center of any societal concern. Kohlberg categorized moral attitudes as “the basic building block of the social psychological theories” (Kohlberg, 1963). Kohlberg agrees with psychologist McDougall that “the fundamental problem of social psychology is the moralization of the individual by the society.” This essay endeavors to explore Kohlberg’s theory of ...

- Problem Statement – Area(s) of Improvement In any educational process the only way for a student to learn is by actually remembering what they have been taught. This is doubly true in any of the more precise subject such as math, science and technology; all of which rely on solid evidence to prove someone’s point and more importantly, numbers. By this very attribute, math has gained the ire of students around the world despite the numerous improvements and possibilities the field has provided to society. In this light, the main problem that this research paper is trying to ...

Bakan notes that privatization of the environment for corporations to have real venture in the environment may form a way of proceeding. Suppose the corporations take charge of the environments or they possess a fiscal venture in it, they would have more inclination into taking care of it, as this is believed to increase its value in resale. Corporations give considerable care for assets which they have chances of reselling unlike the assets that can only be used once (Friedman, 25). As a matter of fact, what has been shown by empirical studies indicate that privatization has resulted to ...

Scientific advancements are generally associated with Europe at a point in history when superstition, fear and absolute devout to religious beliefs got replaced with reasoning and knowledge. Up until a change in people’s view of the world started by the help of the great scientists of history, the whole of Europe and the then discovered world saw its habitation, the Earth, and everything happening in it with the eye of religion, mostly the teachings of the bible, so their values were basically world-denying. Great kings and kingdoms of that age ruled and governed majorly by biblical teachings and ...

The scientific revolution of the 17th century is strongly associated with the name of a genius scholar Isaak Newton. His contribution to the world’s scientific thought can hardly be overestimated. Born in 1642 on the Christmas night in Woolsthhorpe, which is situated in Lincolnshire, England, the child was destined to change the world and become the culminating figure in the revolution of scientific knowledge. A genius as he was, Isaak Newton left his legacy in every fundamental area of that time science: mathematics, mechanics, optics and astronomy. Isaak stepped into this world in the farmer’s family but ...

Mergers and Acquisitions (M & As) have become popular among companies, in the last two decades. The word merger describes a process whereby two or more parties come together resulting in either the creation of a totally new entity or continuance of one of the former entities (Jayesh, 2012). Conversely, acquisition refers to acquiring power over the management or assets of the company without integration of companies (Jayesh, 2012). This question seeks to find out reasons that make board of directors go for mergers and acquisitions (M&A), despite the fact that most companies that use this approach fail. The question ...

Sophie Germain

Learning about women mathematicians and inventors is an instance that presents must scepticism due to the Romanisation that only men in the early years have held interest in math or science. However, there were notable women figures as noted by Osen (1975) in these two fields that have enabled men to understand unfamiliar concepts these women were able to address. One of these women was the Frenchwoman Sophie Germain. Sophie Germain was born to Ambroise Francois and Marie Germain on April 1, 1776. France, in this period, was filled with political conflicts considering the late 18th century France was ...

The ability to motivate oneself and those around a person is a crucial skill in life. Motivation acts a driving engine and a source of strength to make a person to persist at doing something or pursuing a goal. It is through motivation that an individual elicits and holds on to a given conduct. The difference between those who quit doing things in life and those who hold on to the end will depend on their motivational levels. In the movie stand still, the teacher Escalante, defies all odds and decides to introduce calculus at the school. The other ...