What Is Calculus Definition and Practical Applications

Calculus is a branch of mathematics that involves the study of rates of change. Before calculus was invented, all math was static: It could only help calculate objects that were perfectly still. But the universe is constantly moving and changing. No objects—from the stars in space to subatomic particles or cells in the body—are always at rest. Indeed, just about everything in the universe is constantly moving. Calculus helped to determine how particles, stars, and matter actually move and change in real time. Calculus is used in a multitude of fields that you wouldnt ordinarily think would make use of its concepts. Among them are physics, engineering, economics, statistics, and medicine. Calculus is also used in such disparate areas as space travel, as well as determining how medications interact with the body, and even how to build safer structures.  Youll understand why calculus is useful in so many areas if you know a bit about its history as well as what it is designed to do and measure. Key Takeaways: Fundamental Theorem of the Calculus Calculus is the study of rates of change.Gottfried  Leibniz and  Isaac Newton, 17th-century mathematicians, both invented calculus independently. Newton invented it first, but Leibniz created the notations that mathematicians use today.There are two types of calculus: Differential calculus determines the rate of change of a quantity, while integral calculus finds the quantity where the rate of change is known. Who Invented Calculus? Calculus was developed in the latter half of the 17th century by two mathematicians, Gottfried  Leibniz and  Isaac Newton. Newton first developed calculus and applied it directly to the understanding of physical systems. Independently, Leibniz developed the notations used in calculus. Put simply, while basic math uses operations such as plus, minus, times, and division (, -, x, and à ·), calculus uses operations that employ  functions and integrals  to calculate rates of change. Those tools allowed Newton, Leibniz, and other mathematicians who followed to calculate things like the exact slope of a curve at any point. The Story of Mathematics  explains the importance of Newtons fundamental theorem of the calculus: Unlike the static geometry of the  Greeks, calculus allowed mathematicians and engineers to make sense of the motion and dynamic change in the changing world around us, such as the orbits of planets, the motion of fluids, etc. Using calculus, scientists, astronomers, physicists, mathematicians, and chemists could now chart the orbit of the planets and stars, as well as the path of electrons and protons at the atomic level. Differential vs. Integral Calculus There are two branches of calculus:  differential and integral calculus. Differential calculus studies the derivative and integral calculus studies...the integral, notes the Massachusetts Institute of Technology. But there is more to it than that. Differential calculus determines the rate of change of a quantity. It examines the rates of change of slopes and curves. This branch is concerned with the study of the rate of change of functions with respect to their variables, especially through the use of derivatives and differentials. The derivative is the slope of a line on a graph. You find the slope of a line by calculating the rise over the run. Integral calculus, by contrast, seeks to find the quantity where the rate of change is known. This branch focuses on such concepts as slopes of tangent lines and velocities. While differential calculus focuses on the curve itself, integral calculus concerns itself with the space  or area under the curve. Integral calculus is used to figure the total size or value, such as lengths, areas, and volumes. Calculus played an integral role in the development of navigation in the 17th and 18th centuries because it allowed sailors to use the position of the moon to accurately determine the local time. To chart their position at sea, navigators needed to be able to measure both time and angles with accuracy. Before the development of calculus, ship navigators and captains could do neither. Calculus — both derivative and integral — helped to improve the understanding of this important concept in terms of the curve of the Earth, the distance ships had to travel around a curve to get to a specific location, and even the alignment of the Earth, seas, and ships in relation to the stars. Practical Applications Calculus has many practical applications in real life. Some of the concepts that use calculus include motion, electricity, heat, light, harmonics, acoustics, and astronomy. Calculus is used in geography, computer vision (such as for autonomous driving of cars), photography, artificial intelligence, robotics, video games, and even movies. Calculus is also used to calculate the rates of radioactive decay in chemistry, and even to predict birth and death rates, as well as in the study of gravity and planetary motion, fluid flow, ship design, geometric curves, and bridge engineering. In physics, for example, calculus is used to help define, explain, and calculate motion, electricity, heat, light, harmonics, acoustics, astronomy, and dynamics. Einsteins theory of relativity relies on calculus, a field of mathematics that also helps economists predict how much profit a company or industry can make. And in shipbuilding, calculus has been used for many years to determine both the curve of the hull of the ship (using differential calculus), as well as the area under the hull (using integral calculus), and even in the general design of ships. In addition, calculus is used to check answers for different mathematical disciplines such as statistics, analytical geometry, and algebra. Calculus in Economics Economists use calculus to predict supply, demand, and maximum potential profits. Supply and demand are, after all, essentially charted on a curve—and an ever-changing curve at that. Economists use calculus to determine the  price elasticity of demand. They refer to the ever-changing supply-and-demand curve as elastic, and the actions of the curve as elasticity. To calculate an exact measure of elasticity at a particular point on a supply or demand curve, you need to think about infinitesimally small changes in price and, as a result, incorporate mathematical derivatives into your elasticity formulas. Calculus allows you to determine specific points on that ever-changing supply-and-demand curve. Source Calculus Summary. Massachusetts Institute of Technology, January 10, 2000, Cambridge, MA.

Cross Cultural Interview Interview of an African-American...

As I entered the home to conduct my interview, I was immediately greeted by very soft spoken female. She’s a 42 yrs old African American female, who’s married with two children. She migrated from the south 30 years ago along with her mother and sister. She’s currently working for the Department of Education as a substitute teacher with aspiration of becoming a child psychologist. The subject was eager to be interviewed. She thought it would be great to sure her views and perspectives of her culture. Culture is defined by Webster’s Dictionary as , the total of the inherited ideas, beliefs, values, and knowledge, which constitute the shared bases of social action. To me culture is rich and fascinating filled with family, traditions, memories, and many dialects. Our subject is an African American female. The historical roots of the African American family are in Africa and as a result the family can trace its origin to a distinct culture and society. Since the family’s origins are in Africa they came from a society with different norms and values. A society composed of many different tribes, each with their own language, customs and traditions. They placed a strong emphasis on the family and kinship ties. Their communities depended on cooperation, assistances and well maintained social order. When a woman was married, she was considered the wife of the family not just the husband (Franklin, 1967-28-31). In today’s world there are many stereotypes that plague the AfricanShow MoreRelatedThe Concept of Gender and Gender Identity1223 Words   |  5 Pagesthe baby is. Parents get ready months in advance to set up the baby room for their boy or girl. Yet sex and gender are two different things. Sex is referring to a person’s genitals while gender is more in the line of the social and cultural aspects of being a man or a woman. 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Computer Benefits free essay sample

Science and technology Adv of technology First of all, technologies play a very important role in society because it makes life easier to live on and less time consuming. Technology has the ability to create shortcuts in working. People do not have to do all the hard labor anymore. For example, microwave ovens cook food easily without using any stoves and making a big mess. Some decade ago, there were no gas or electric stoves, people have to get firewoods and lighting them up for cooking. Technology makes things very easy to use comparing it in the old fashion way. Moreover, medical science is very progressive and saves many innocent lives. Medical treatment has been going well with the help of technology. Nowadays, hospitals use technology as the assistance for the operation. Doctors use machines to produce medicine to cure sickness and the discovery of x-ray enable doctors to treat some kinds of diseases. We will write a custom essay sample on Computer Benefits or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page On the otherhand, the application of science leads to the development of technology. Technology comes from the Greek word tekne, which means art, craft or skill. Technology is the art craft and skill of harnessing scientific knowledge. Technology has improved the quality of life in many ways. DNA Analysis is now used to solve crimes. Packaged livelihood technologies produce goods and provide work and income. Nuclear research has brought about technologies fro treating cancer, preserving food and providing energy. Harnessing energy from the sun has brought about solar powered batteries for calculators and watches. The aqualung allowed man to explore the ocean depths thereby opening the underwater world for deeper exploration. In addition to this, science and technology influences our lives. These inventions that have changed the world are products of genuises who altogether make up only a small percentile of the millions of people who inhabit the earth. Disad of tech However, there is always a down side to everything. As a saying goes, there is no such thing as free lunch. Technological advancement has its own negative effects. For example, the burning of fossil fuels is primarily to energize the modern worldand to power cars. However, it has degraded the quality of air we breathe and has caused other environmental hazards with health threatening effects that adversely affect life. On the contrary, technology also brings harm to our society. The booming of industrialization and development causes pollutions to our world. For example, the smoke from the vehicles and machines affects the quality of air and destroy the ozone layer. As a result, people suffer illness like cancers. In addition, technologies also create financial problems in families because most of the technologies are expensive like computers. People that cannot afford to buy this kind of technology will live in a stressful life. For example, people that do not have washing machine will have to wash clothes by hand which is time consuming Computer benefits free essay sample In todays modern world, computers are needed everyday. Around the world, children use computers from the time they are little. Its true that children should have fun when they are young; however, in my opinion, a child who knows how to use the computer will be more successful in the future. My reasons for this view are personal, academic and professional. From a personal point of view, computers can help young people to learn more about the world. For example, some children use the Internet to find information on different subjects. In this way, they learn to find answers by themselves. By using the computer when they are little, children feel more comfortable around computers. They also know how to use the computer for different reasons. From an academic viewpoint, children have to learn how to use this new invention. For instance, when I was in college, many students used to bring their laptops to class. We will write a custom essay sample on Computer benefits or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page They used to take notes, do research and share information. They wrote their essays, made presentations and created useful lists. Children who can use the computer when they are young have more confidence than other children. From a professional perspective, the computer is found in every kind of office. Today, employers will still hire people who cannot use computers and give them computer training. But tomorrow, companies will expect people to have these skills already. As a result, by encouraging children to use the computer for a short time every day, parents are preparing their children for future jobs. In conclusion, it is clear that computers are now a part of our regular life. Children who can use computers easily and confidently will do better in the future.

The Valley Essays - Political Culture, Social Agreement,

The Valley 1. There are several instances in The Valley that show that customs and traditions pass on through different generations. The first example takes place with the first sketch, Jehu. Where Hinojosa describes how a girls hand in marriage is traditionally asked for. Hinojosa weaves in two different generation performing the same tradition, Roque Malacara, asking for Tere, and Braulio Tapia taking in retro-spect about his own experience, when he too had to face his father-in-law and ask for his wives hand in marriage. Another example of traditions is the giving of nicknames, or apodos. From making the name easier, to naming them for a characteristic, nicknaming is seen through out the different generations, families, and cities. Like Vicky for Eduviges, Panchita for Francisca, Chedes for Mercedes, and Rafa for Rafael. Nicknames were also give for other reasons like physical or personality characteristics, such as Hoarsey because his voice was that, or Mion because he happen to pee in his pants. Yet another example of traditions and customs through out different generations, is the oral tradition. Jehu and Rafa both narrate part of their story, the same way the viejiots did about the Revolution. The same way their children with talk about their own experience. The oral tradition is one of the ways customs or traditions are kept alive through out the years. Creative Writing