How has calculus improved our way of life and aided in the advancement of technology?
354212
Caculus is an accurate description of some natural phenomenon. For example work is defined as the integral of force times incremental distance. Speed is decribed as the derivative of position verses time. Current is the derivative of charge with respect to time. I can go on and on. It is an aid to study and predict nature and phenomenom. It turns out that a lot of nature can be described in calculus terms. Engineers use it to analyze things. For example if you didn't know calculus it would take many trials and error tests to get anything product (building, airplane, car) fine tuned to operate more efficiently. In conclusion without caculus engineers and scientest would not be able to be as precise and would take more time designing/testing.
894057
Differentiation and integration are mathematical operations applied to polynomial functions.\n\nThe first is differential calculus, which is concerned with the instantaneous rate of change of quantities with respect to other quantities, or more precisely, the local behavior of functions. This can be illustrated by the slope of a function's graph. The second is integral calculus, which studies the accumulation of quantities, such as areas under a curve, linear distance travelled, or volume displaced. These two processes act inversely to each other, as shown by the fundamental theorem of calculus.\n\nThese operations are frequently used solve complex scientific problems, for instance, in the physics area. fundamental advances in calculus during the 17th and 18th century had a deep impact on the ensuing development of physics. Today, calculus is used in every branch of the physical sciences, in computer science, in statistics, and in engineering; in economics, business, and medicine; and as a general method whenever the goal is an optimal solution to a problem that can be given in mathematical form.
1116918
In Calculus of Varations deals with minimization problems the most elementary of which is the Brachistochrone.  This is the problem of the shape of a wire which provides the fastest path between two points for a marble sliding down it.  I don't know what applications of differentiation is.
872930
No. Archimedes did not know Calculus, but he knew heuristics which resemble integral calculus. The Western World learnt about calculus only during the time of Newton (England) and Leibnitz (Germany) who discovered calculus independent of each other. The terminology that we use in school/college is that of Leibnitz.\n\nIn India, the mathematician-astronomer Aryabhata in 499 used infinitesimals and expressed an astronomical problem in the form of a basic differential equation. Manjula in the 10th century elaborated on this differential equation in a commentary. This equation eventually led Bhaskara in the 12th century to develop a number of ideas that are foundational to the development of modern calculus, perhaps including an early form of the theorem now known as "Rolle's theorem". He was also the first to define the notion of the derivative as a limit. In the 14th century, Madhava, along with other mathematician-astronomers of the Kerala School, studied infinite series, power series, Taylor series, differentiation, integration, and the mean value theorem. Yuktibhasa, which some consider to be the first text on calculus, summarizes these results.
207713
Ordinary differential equations are equations to be solved in which the unknown element is a function, rather than a number, and in which the known information relates that function to its derivatives. Few such equations admit an explicit answer, but there is a wealth of qualitative information describing the solutions and their dependence on the defining equation. \n\nThe solutions to many classic differential equations, particularly linear second-order differential equations, cannot be expressed in terms of the elementary functions. This includes Bessel functions, Whittaker functions, Airy functions, and so on.\nBuilding on tradition going back to the ancient Greek philosophers, Leibniz and Newton invented calculus in the late 17th century and thereby laid the foundation for the revolutionary development of science and technology that is shaping the world today. Calculus is a method for modeling physical systems mathematically by relating the state of a system to its neighboring states in space-time using differential and integral equations. Because calculus is inherently computational, this revolution began to accelerate tremendously in the 1940s when the electronic computer was created. Today, we are seeing what is essentially a ``marriage'' of calculus and computation in the creation of the field of computational mathematical modeling. \n\nActually, Leibniz himself sought to realize a unification of calculus and computation, but failed because the mechanical calculator he invented was not sufficiently powerful. The next serious effort was made in the 1830s by Babbage, who designed a steam powered mechanical computer he called the Analytical Engine. Again, technical difficulties and low speed stopped his ambitious plans. \n\nThe possibility of realizing Leibniz' and Babbage's visions of a universal computing machine came with the invention of the electronic valve in the 1930s, which enabled the construction of high speed digital computers. The development took a leap during the World War II spurred by the computing demands of the military. Until this time, large scale computations were performed by rooms of people using mechanical adding machines. The war provided an immediate pressure to speed up the process of scientific development by using mathematical modeling to hone a physical problem down to a manageable level, and mathematicians and physicists became interested in the invention of an electronic computing device. The logical design of programmable electronic computers was developed by the mathematician von Neumann, among others. By the late forties, von Neumann was using the first ENIAC (Electronic Numerical Integrator And Calculator) computer to address questions in fluid dynamics and aerodynamics. \n\nThe subsequent development of computer power that has resulted in desktop computers of far greater power than the ENIAC, has been paralleled by the rapid introduction of computational mathematical modeling into all areas of science and engineering. Questions routinely addressed computationally using a computer include: What is the weather going to do in three days? Will this airplane fly? Can this bridge carry a load of ten trucks? What happens during a car collision? How do we direct a rocket to pass close by Saturn? How can we create an image of the interior of the human body using very weak X-rays? What is the shape of a tennis racket that has the largest "sweet spot"? What is a design of a bicycle frame that combines low weight with rigidity? How can we create a sharp picture from a blurred picture? What will the deficit be in Sweden in the year 2000? How much would the mean temperature of the earth increase if the amount of carbon dioxide in the atmosphere increased by 20 percent? \n\nThe physical situations behind these kinds of questions are modeled by expressing the laws of mechanics and physics (or economics) in terms of equations that relate derivatives and integrals. Common varia
342662
there are a lot of people who contirbuted parts to calculus, but Leibniz and Newton pulled these ideas together into a coherent whole and they are usually credited with the probably independent and nearly simultaneous "invention" of calculus.
838806
I studied Calculus when I was a senior in high school.  Calculus is hard, but you learn along the way.
97676
Of course, math is the foundation of advancement.
655103
Are you suggesting that with improving technology we are living less long?\nIf so I can think of nowhere to find evidence to say you are correct.\nGenerally, improving technology goes hand in hand with greater lifespans, although the relationship is far from causal in every case.
303750
i'm an accountant and i've never had to use calculus...\n\nthat's more mathematics and physics i think...
781528
Definitely any advanced Math courses you can take (Algebra, Calculus, Trigonometry, etc.) I think would be helpful, especially Calculus.
1105564
Don't know try it and tell us.  \n\nWould you sniff this?\n\nhttp://plaza.ufl.edu/kbeaz/severe_calculus.jpg
95619
yes.As we know, mathematics plays an important role in our life. Plus, when we think about it, everything around us use mathematical theory. This proves that english can saves our soul. Without it, we may live in stoneage.
626773
Calculus has been mostly subsumed by topology, differential geometry and cohomology at the (pure) research level. The language of these topics is much more concise and powerful than that of classical analysis. If you're looking for recent advancements in analysis (the formal name for calculus), these are the fields you should be familiar with. Basically, these fields examine every type of object that one could do analysis on, in a way similar to what one does with basic calculus (continuity, limits, curvature, etc.).\nSee http://xxx.lanl.gov/archive/math for new research in these areas, as well as classical areas.
839779
Technology has made our world so much smaller. It is through this wonderful thing called the internet that we are able of discuss religion with monks in tibet and rock music with hippees in england all without leaving our homes.\nTechnology has allowed us to keep a close knit family relationship cheaply and more easily despite the impedances of distance. Through advances such as webcams and cellular phones I am able to talk to my dad in California for a fraction of what it would have cost just ten years ago.\nTechnology is modelling our society into one without boundaries. It is ever bringing us closer to one another. Whether we want to be close or not.
1087357
Math is used all the time in the engineering sciences.  Many physical phenomena, including fluid flow, heat transport, and diffusion can be described by appropriate partial differential equations.  In order to solve these equations and make predictions, you need to be good at calculus.\n\nIf you limit yourself to addition, subtraction, multiplication, and division, you would be stuck with linear models for everything.  This means that any more complicated relationship between two variables could not be modeled continuously, and you would never be able to extrapolate with any confidence.  Thus development of new technology would be strictly trial and error (and you wouldn't even have a good trial and error system without statistics).\n\nHang in there!  Get through that math.  You don't have to like it, but you will inevitably appreciate the developments that math has enabled.
3254
"The Calculus of One Variable" by I. A. Maron is a good book for self-study.