Razmadze wrote the first textbooks in Georgian on analysis and integral calculus. |
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The problem of calculating loxodromes is exactly the problem of the fundamental theorem of calculus. |
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He demanded a retraction saying that he had never heard of the calculus of fluxions until he had read the works of Wallis. |
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Other examples are negative numbers, complex numbers, trigonometry, raising to powers, logarithms, and the beginnings of calculus. |
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Gibbs and Heaviside had been early exponents of the vector calculus while its chief opponents had been Tait. |
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His work is almost exclusively on calculus, in particular differential equations and functions of a real variable. |
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The only place calculus is used is to compute the linearization of the map, and it involves only derivatives. |
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This language, the language of the predicate calculus, is what Russell called the perfect language. |
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In the classical predicate calculus only conjunction, negation and the universal quantifier are needed. |
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Girls cut calculus to get their eyelashes done, and boys distributed roofies during softball practice. |
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The fundamental theorem of calculus becomes almost obvious once the nonstandard terminology is invoked and interpreted in its full literality. |
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Many who once visualized that they would be taking calculus shortly afterward instead make precalculus into their final mathematics course. |
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One of the first topics he studied, which developed from his early work on electromagnetism, was a new topic, now called the fractional calculus. |
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Berkeley's arguments are directed chiefly against the Newtonian fluxional calculus. |
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The mathematics curriculum grew accordingly to include algebra, trigonometry, and sometimes even Newton's fluxional calculus. |
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He integrated Leibniz's differential calculus and Newton's method of fluxions into mathematical analysis. |
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We're going to look at one example of how they let us extend calculus and allow us to integrate some very odd functions! |
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From 1852 to 1858 he taught algebra and geometry, while from 1860 to 1862 he taught differential and integral calculus. |
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Also in 1786 he again worked on his ideas for the differential and integral calculus, giving a new treatment of infinitesimals. |
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Since his work made its appearance just before the dawn of calculus, infinitesimals will be used in the sequel. |
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And of course there was Bentham with his felicific calculus of pleasure and pain, to say nothing of Jefferson and Franklin. |
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They fall squarely within the tradition of classical word problems and are designed for use in a traditional calculus course. |
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Thousands of TV commercials go on their merry way, oblivious to dire circumstances outside the calculus of huckstering. |
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Hermann Grassmann is chiefly remembered for his development of a general calculus for vectors. |
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Thompson's compact book also stands as a rebuke to the hefty, overstuffed volumes lugged around by today's college calculus students. |
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Newton's work in calculus was all to work out the dynamics of motion, so there was really no difference. |
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There are cheat codes to the universe, as anyone who's cracked a book on differential calculus can tell you. |
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He corresponded with Gabriel Cramer on mechanics, geometry, probability, number theory and the differential and integral calculus. |
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Mason's research interests lay in differential equations, the calculus of variations and electromagnetic theory. |
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In this way, Bradley had a significant, if indirect, impact on predicate calculus. |
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Radon applied the calculus of variations to differential geometry which led to applications in number theory. |
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There he taught courses on advanced algebra, the calculus of variations, mechanics, Fourier series, and synthetic geometry. |
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In particular he studied the role of these curves in the calculus of variations and in mechanics. |
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Pure mathematics became Clebsch's main research topic when he began to study the calculus of variations and partial differential equations. |
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His steady stream of publications is testimonial to his authority in the fields of Riemannian geometry and the calculus of variations. |
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However, in this case the trauma sustained to the lumbar region probably dislodged a calculus from the renal parenchyma into the left ureter. |
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The most likely cause of retrieval failure was that the calculus was fixed to the duct wall. |
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The calculus is rough and causes plaque to accumulate more rapidly increasing the problem. |
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If plaque is not regularly removed the flora evolves, and plaque may calcify, forming calculus. |
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It is thought that the catheter balloons burst as they were pushed against the calculus as the bladder contracted during bladder emptying. |
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The calculus may be extracted through the fistula site and if needed, sialodochotomy could help in delivering the calculus to the oral cavity. |
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In all other patients, including those in whom a urinary calculus is not detected, intravenous contrast medium should be injected. |
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Expectation is an experiential calculus through which the abstracted possibilities of the event are rendered subculturally consistent. |
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I've sat in on these liver distribution meetings, and it's a grim calculus. |
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This discussion is kept concise by the use of an elegant calculus of closure operations on group properties. |
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In the final calculus of course, these are issues that are best settled empirically. |
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Newton was one of the inventors of the branch of mathematics called calculus. |
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There are shorter methods for summing an infinite number of terms in calculus and other branches of advanced mathematics. |
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He worked on the four colour problem and also published books on calculus, differential equations, complex variable and Fourier series. |
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He became a physics major but differential equations and calculus just didn't excite him. |
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By integrating the function using calculus we can compare the sum of the series with the integral of the function and draw conclusions from this. |
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He made decisive and formative contributions to geometry, calculus and number theory. |
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Continuity is the mathematics of calculus and physics but there's never been a theory of computation that deals with this continuum. |
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Simion was soon teaching college-level courses such as multivariate calculus and differential equations to the most advanced math students. |
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Shtokalo worked mainly in the areas of differential equations, operational calculus and the history of mathematics. |
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All this depended in turn on mathematical progress, notably calculus developed by Newton and Leibniz, which allowed for actuarial calculations. |
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During that year Moore also set about reading calculus because he enjoyed mathematics and wanted to extend his studies. |
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It builds on the classical results in the calculus developed by Hilbert and his students. |
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It would take a team of NASA scientists to calculate when a no-knock entry or a brief wait would be appropriate using this calculus. |
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These are equations involving the rate of change of quantities either in time, or in space, or in both, and are a part of calculus. |
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It was one of the earliest variational problems and its investigation was the starting point for the development of the calculus of variations. |
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Problems remained, however, which Kirchhoff solved using variational calculus. |
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Perhaps his most important contribution was to the calculus of several variables. |
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The brachistochrone problem was one of the earliest problems posed in the calculus of variations. |
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But the most depressing reality in this morbid calculus is the unequal value of lives. |
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Nina's new guy is way more enticing than 9 a.m. calculus... but can she blow off class again? |
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Indians also added to our knowledge of even more complicated branches of mathematics such as trigonometry and calculus. |
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Support for the Vietnam conflict also mirrors the ends-and-means calculus reflected in the Korean War. |
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In 1816 the Analytical Society produced a translation of a book of Lacroix in the differential and integral calculus. |
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This, like calculus or reading Milton, is something the undergraduates have studied and learned to do from their elders and betters. |
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But is education limited to calculus, literature, microbiology, and quantum physics? |
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Celestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry. |
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The main research topics which Genocchi worked on were number theory, series and the integral calculus. |
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Any book on calculus will contain many similar examples and exercises for you to practice. |
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Expectation is a calculus of futurity, an extrapolation of narrativised past events into the future. |
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In his last years he worked on a new absolute differential calculus and a geometry of Hilbert spaces. |
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He also wrote on applications of the symbolic calculus to mathematical physics. |
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Numbers are better manipulated as calculus stones or abacus beads than in human memory. |
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This made calculus a lot cleaner, and it makes the conceptualization of a circle as an infinite-sided polygon possible. |
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Not all were captivated by the application of differential calculus to human activity. |
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Later on, in 1858, Bellavitis included the system of quaternions into his geometric calculus. |
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I don't know that it's something we could be made to understand, as if it were jet propulsion or differential calculus. |
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I seemed to hit the limits of my mathematical abilities after differential calculus in 1986, my first year of university. |
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I've never learned enough about the details of his calculus ratiocinator to determine the answer. |
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Students can use graphing calculators or computers to solve calculus problems and to explore many different kinds of mathematical behavior. |
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However when I learned calculus a whole new appreciation for kinematics blossomed. |
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Its used in all sorts of things in calculus where recursion is necessary, like differential equations. |
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If plaque is not thoroughly removed, salts from the saliva cause it to become hard and form scale or dental calculus. |
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The book contained the elements of geometry and algebra in addition to the calculus. |
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His most important work was on differential projective geometry where he used the absolute differential calculus. |
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By their fourth year students were studying the differential and integral calculus. |
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Chronic periodontitis may be a sequel of chronic gingivitis, usually because of accumulation of plaque and calculus. |
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For more information on calculus textbooks written in the nineteenth century, see the authoritative article by George Rosenstein. |
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The fundamental lemma of the calculus of variations is named after him. |
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With other emerging allies the calculus is trickier and leaves less margin for error. |
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This calculus is loaded with all kinds of assumptions about the ongoing prejudices of white America. |
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Advanced calculus gives us a strong tool for finding the change in the area of a given shape under continuously differentiable transformations-namely, the Jacobian. |
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By examining the limits of sums, products and quotients of variable quantities, Mengoli was setting up the basic rules if the calculus thirty years before Newton and Leibniz. |
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Whether convening meetings between scientists and sociologists or converting calculus to algebra, he brings his own agility to medical problem-solving. |
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Hongkongers aren't asking to secede from China, but Beijing's faulty calculus is only alienating the city. |
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But now we have a more, uh, self-confident right wing, and consequently we have a new and different calculus. |
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In the last scene, he uses his calculus of flow to rescue an Iraqi boy from a fast-moving, wind-buffeted river. |
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Perhaps the most famous example of this is Stokes' theorem in vector calculus, which allows us to convert line integrals into surface integrals and vice versa. |
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It's hard to conceive of a successful blogger of any persuasion who would allow considerations of gender to enter into the linking calculus I have just described. |
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Many engineers of his age felt similar, a computer could be used to do calculus and arithmetic, but not do then daunting tasks such as communications and process control. |
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Problems cover the spectrum from basic arithmetic to calculus. |
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But for practical effect, you'd be better off trying to explain the fundamentals of tensor calculus. |
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Still, he is teaching calculus to guys who struggled with long division. |
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She jumped at the chance to watch RT, or jumped at the chance to skip calculus homework. |
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Of course, the political calculus of extending the outreach to appointments is not inconsiderable. |
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The Evangelical calculus attempts to console and convert grieving relatives and witnesses by redefining such loss as a means to the measureless prize of eternal life. |
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Instead we should view promises, and other people's rights, as of such towering importance that they are basically invulnerable to the calculus of social interests. |
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In the pursuit of pseudo-scientific tractability, neoclassical economics neglects the dynamic aspects of the social realm and delivers a static utilitarian calculus. |
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William's father wrote a number of successful textbooks on arithmetic, calculus and trigonometry, which brought in a comfortable income for the family. |
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There he gave courses on astronomy, celestial mechanics, the differential and integral calculus, the theory of probability, geometry and trigonometry. |
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If overcrowding was also part of their calculus, there was no mention of it on the site. |
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Between 1917 and 1919 he worked on the variational calculus. |
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Putnam will still be around to explain how they change the political calculus. |
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When I started teaching again I made quite a fuss doing my calculus courses constructively, making a point of presenting my epsilon-delta's as explicit, calculable, functions. |
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We must make the course accessible to students whose common background includes only the freshman and sophomore courses in calculus and differential equations. |
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The Dutch clockmaker's discovery was all the more striking because he arrived at his results before the advent of the calculus of Newton and Leibniz. |
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There he taught courses on analytic functions and functional calculus. |
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Each such language, he holds, includes analytic rules which provide a calculus for reasoning and a conceptual framework for describing its subject-matter. |
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This is, I think, the moral calculus at the heart of the argument, a calculus that folks on that side of the cultural divide very much want to preserve. |
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Above all else, the mammoth South Asian fan base needs to start seeing cricket as a pursuit of shared enjoyment, not as a calculus of honour and shame. |
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Once calculus has formed you cannot remove this yourself and is essential that your dentist or hygienist carries out scaling for you on a regular basis. |
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He has interests in differential equations, the calculus of variations, and functions of a real variable which he would work on for the rest of his life. |
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Bernoulli greatly advanced algebra, the infinitesimal calculus, the calculus of variations, mechanics, the theory of series, and the theory of probability. |
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Immediately after his return Bolza continued teaching and research, in particular on function theory, integral equations and the calculus of variations. |
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Osgood's main work was on the convergence of sequences of continuous functions, solutions of differential equations, the calculus of variations and space filling curves. |
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Jacob Bernoulli and Johann Bernoulli invented the calculus of variations where the value of an integral is thought of as a function of the functions being integrated. |
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The hermeneutics used in the historicists' calculus of exploitation and oppression are less hermetic than those of new criticism and theory, but they are just as schematic. |
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Beyond some point, the disutility of additional work surely offsets the value, both internal and external, of this work, even in the idealized felicific calculus. |
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With clear definition of real numbers formulated at the end of the 19th century, differential and integral calculus had developed into an authentic mathematical system. |
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There he was to receive a good understanding of basic mathematics studying differential and integral calculus, analytic geometry and the foundations of analysis. |
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The curriculum of all schools will be inverted so that high-school seniors are taught finger painting and kindergarten students are educated in calculus and chemistry. |
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In 1887 he published a famous paper in which he developed the calculus of tensors, following on the work of Christoffel, including covariant differentiation. |
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Yet the development of the general theory of relativity introduced Einstein to the power of abstract mathematical formalisms, notably that of tensor calculus. |
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What you are saying is that, strictly speaking, a proof is valid if it is written out in predicate calculus and has the right structure according to the rules of logic. |
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Such a calculus is like a machine which, fed with certain raw materials, manufactures a determinate product in an exact, orderly, and unvarying manner. |
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In his reply Leibniz gave some details of the principles of his differential calculus including the rule for differentiating a function of a function. |
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Maclaurin appealed to the geometrical methods of the ancient Greeks and to Archimedes' method of exhaustion in attempting to put Newton's calculus on a rigorous footing. |
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Plaque not removed daily hardens into crustlike calculus, or tartar, which forms around the edges of the gum tissues and irritates them further. |
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As with the formula for the area of a circle, any derivation of this formula inherently uses methods similar to calculus. |
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In technical language, integral calculus studies two related linear operators. |
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Newton developed the ideas of universal gravitation, Newtonian mechanics, and calculus, and Robert Hooke his eponymously named law of elasticity. |
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Differential calculus is the study of the definition, properties, and applications of the derivative of a function. |
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Limits were the first way to provide rigorous foundations for calculus, and for this reason they are the standard approach. |
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From this point of view, calculus is a collection of techniques for manipulating infinitesimals. |
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Applications of integral calculus include computations involving area, volume, arc length, center of mass, work, and pressure. |
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Applications of differential calculus include computations involving velocity and acceleration, the slope of a curve, and optimization. |
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The development of calculus was built on earlier concepts of instantaneous motion and area underneath curves. |
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These symbolic directions became popular, as operational calculus, and pushed to the point of diminishing returns. |
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Reference to Lagrange in calculus terms marks out the application of what are now called formal power series. |
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It was also during this period that the ideas of calculus were generalized to Euclidean space and the complex plane. |
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Newton had been reluctant to publish his calculus because he feared controversy and criticism. |
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In calculus, foundations refers to the rigorous development of the subject from axioms and definitions. |
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One of the first and most complete works on both infinitesimal and integral calculus was written in 1748 by Maria Gaetana Agnesi. |
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Most modern historians believe that Newton and Leibniz developed calculus independently, although with very different notations. |
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Since the time of Leibniz and Newton, many mathematicians have contributed to the continuing development of calculus. |
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Today, both Newton and Leibniz are given credit for developing calculus independently. |
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If we wanted logic, we'd have become fans of propositional calculus instead. |
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Newton was the first to apply calculus to general physics and Leibniz developed much of the notation used in calculus today. |
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Subsequent thinkers struggled with the same tension and proposed different solutions to it as the case of infinitesimal calculus illustrates. |
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It was during these visits that he came up with the design for a calculating machine as well as the infinitesimal calculus. |
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He referred to the effort to value the results of an act, whether positive or negative, as the felicific calculus. |
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Leibniz and Newton are usually both credited with the invention of calculus. |
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The book presupposes a good knowledge of advanced calculus and Boolean logic. |
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He is now regarded as an independent inventor of and contributor to calculus. |
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What avails it to make a shine in Greek if the next hour one does a barney in calculus. |
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Microfossils in calculus demonstrate consumption of plants and cooked foods in Neanderthal diets. |
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Differently, here we consider strong solutions of problems of the calculus of variations on time scales. |
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According to her Web site, her research focuses on calculus of variations and symmetry methods for differential equations. |
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Many notations from the lambda calculus have been adopted in the EP data model.The pure lambda calculus is a well-known untyped system. |
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This calculus assumes, based on evidence of various kinds, that school hours lost to snow days equal lost student learning. |
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As a Jew committed to halakhah, I admit I do not understand this calculus. |
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More significantly, the calculus of holding territory has now changed. |
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A validity study for the CLEP introductory calculus subject examination at the University of IIIinois. |
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To help pay her tuition, the college student began to tutor high school students in calculus and physics. |
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These axiom schemata are also used in the predicate calculus, but additional logical axioms are needed to include a quantifier in the calculus. |
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In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became calculus. |
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Economists have further criticized comparative negligence as not encouraging precaution under the calculus of negligence. |
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In mathematics, calculus, statistics, logic, vectors, tensors and complex analysis, group theory and topology were developed by Westerners. |
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Bonaventura Cavalieri's works anticipated integral calculus and popularized logarithms in Italy. |
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Urinary tract infection with septicaemia due to Staphylococcus saprophyticus in a patient with a ureteric calculus. |
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The calculus of 30mm x 20mm x15mm was extracted successfully and end to end urethroplasty was performed. |
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Intravenous urography showed a nonvisualized left kidney with calculus and a normal right kidney. |
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Four hundred years ago, Gauss taught calculus and differential equations at the University of Gottingen in Germany. |
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The calculus was immediately evident on rigid nephroscopy and removed with duckbill graspers. |
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Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus. |
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Newton also made seminal contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus. |
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For shapes with curved boundary, calculus is usually required to compute the area. |
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In Chapter IV, Bentham introduces a method of calculating the value of pleasures and pains, which has come to be known as the hedonic calculus. |
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In 1734, he published The Analyst, subtitled A DISCOURSE Addressed to an Infidel Mathematician, a critique of calculus. |
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This paper will demonstrate that this same calculus has been duplicated in the ancillary powers approach to police powers. |
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For formulations using tensor calculus or differential forms, see alternative formulations. |
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The district has not purchased textbooks to teach CPM in higher-level math courses, such as precalculus and calculus, he said. |
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Generally, modern calculus is considered to have been developed in the 17th century by Isaac Newton and Gottfried Leibniz. |
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There is no consensus, however, as to which part should be eliminated from the predicate calculus. |
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Newton had previously invented the calculus, of mathematics, and used it to perform the mathematical calculations. |
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The calculus for peak oil has changed with the introduction of unconventional production methods. |
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Bentham suggested a procedure for estimating the moral status of any action, which he called the Hedonistic or felicific calculus. |
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Economists draw on the tools of calculus, linear algebra, statistics, game theory, and computer science. |
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Reformulations of calculus in a constructive framework are generally part of the subject of constructive analysis. |
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Over the years, many reformulations of calculus have been investigated for different purposes. |
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He invented his Operational calculus method for solving linear differential equations. |
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In the realm of medicine, calculus can be used to find the optimal branching angle of a blood vessel so as to maximize flow. |
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Chemistry also uses calculus in determining reaction rates and radioactive decay. |
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Maxwell's theory of electromagnetism and Einstein's theory of general relativity are also expressed in the language of differential calculus. |
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Heaviside did much to develop and advocate vector methods and the vector calculus. |
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Starting from knowing how an object is accelerating, we use calculus to derive its path. |
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The fundamental theorem of calculus states that differentiation and integration are inverse operations. |
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Among the topics are functions and models, applications of differentiation, techniques of integration, parametric equations and polar coordinates, and vector calculus. |
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In ancient times, the method of exhaustion was used in a similar way to find the area of the circle, and this method is now recognized as a precursor to integral calculus. |
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Bentham's felicific calculus, that policy should be concerned with the greatest happiness of the greatest number, gradually confined beauty to a preserve of elites. |
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The formal study of calculus brought together Cavalieri's infinitesimals with the calculus of finite differences developed in Europe at around the same time. |
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It is given a bicovariant differential calculus on the superspace. |
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This argument is actually a simple application of the ideas of calculus. |
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A thoracolith is an intrapleural benign fibrotic structure with a necrotic fat core also described as a pleural stone, intrathoracic calculus or pleurolith. |
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This hands-on guide also covers sequences and series, with introductions to multivariable calculus, differential equations, and numerical analysis. |
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His work on the subject usually referred to as fluxions or calculus, seen in a manuscript of October 1666, is now published among Newton's mathematical papers. |
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Differential calculus is used to model the behaviour of nuclear decay. |
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They assume students to be familiar with techniques of analyzing power systems and with calculus, matrix algebra, and Laplace and Fourier transforms and the Fourier series. |
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Without a teacher, it took him many years to master calculus. |
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A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. |
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Limits are not the only rigorous approach to the foundation of calculus. |
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Joining Bethe at Cornell after the war, Feynman labored intensely to apply a new type of calculus he had developed to fundamental puzzles in quantum electrodynamics. |
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In modern mathematics, the foundations of calculus are included in the field of real analysis, which contains full definitions and proofs of the theorems of calculus. |
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One of the reasons identified for this attrition has been students' underperformance in calculus classes and their inadequate preparation in precalculus content. |
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In modern logic, the role of universal grammar is entrusted to a formal calculus representing the mental operations which are expressed in discourse. |
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Students should be comfortable with at least one-variable calculus, vector algebra in the plane, mathematical induction, and elementary set theory. |
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There are many students who are required to study data analysis without any exposure to calculus, let alone probability theory or the theory of statistics. |
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In the 14th century, Indian mathematician Madhava of Sangamagrama and the Kerala school of astronomy and mathematics stated components of calculus. |
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The foundations of differential and integral calculus had been laid. |
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The main existence theorems in calculus are the Intermediate Value Theorem, the Extreme Value Theorem, Rolle's Theorem, and the Mean Value Theorem. |
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Not one of us leaves calculus behind on purpose, so to be able to meticulously debride the roots in the furcations and 'visualize' root abnormalities is extraordinary. |
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Inspired by the success of the new mathematics, some thinkers, Leibniz included, sought to reduce much or all of human experience to a purely logical calculus. |
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Typically in such cases, an ultrasound or conventional sialogram would be requested in seeking obstructed or dilated ducts, a ductal calculus or an abscess within the gland. |
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This is another reformulation of the calculus in terms of infinitesimals. |
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This led Abraham Robinson to investigate if it were possible to develop a number system with infinitesimal quantities over which the theorems of calculus were still valid. |
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The ancient period introduced some of the ideas that led to integral calculus, but does not seem to have developed these ideas in a rigorous and systematic way. |
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The linear independence of this new basis is easily proved using our theorem involving Hopf algebra calculus, while we have not been able to find an elementary proof of it. |
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In economics, calculus allows for the determination of maximal profit by providing a way to easily calculate both marginal cost and marginal revenue. |
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This advanced math, including statistics and multivariable calculus, makes possible the solution to such complex dynamic situations as space vehicle reentry. |
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The calculus preview in each chapter focuses on a single calculus concept, such as algebra and limits, the are problem and the hyperbolic functions. |
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Today, calculus has widespread uses in science, engineering and economics. |
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These ideas were arranged into a true calculus of infinitesimals by Gottfried Wilhelm Leibniz, who was originally accused of plagiarism by Newton. |
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Several studies have demonstrated the reduction of calculus formation by dentifrices that contain combinations of pyrophosphates combined with sodium fluoride. |
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We submit that a wooden spoon of our day would not be justified in calling Galileo and Napier blockheads because they never heard of the differential calculus. |
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In a formulation of the calculus based on limits, the notation. |
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Despite this, Turing continued to show remarkable ability in the studies he loved, solving advanced problems in 1927 without having studied even elementary calculus. |
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By Newton's time, the fundamental theorem of calculus was known. |
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Dental hygienists are used to removing plaque, calculus and stains from tea or coffee, but what about removing red stains caused by chewing paan all day? |
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In this paper the authors proposed alternative methods for calculus of position of the central axis and the centrifugal moments, based on the coordinates of centers of mass. |
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Integral calculus is the study of the definitions, properties, and applications of two related concepts, the indefinite integral and the definite integral. |
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