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Calculus
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Calculus is a way to study shapes and lines using numbers. It uses numbers to show how things change. Engineers use calculus to make things. Scientists use calculus to study the world and understand nature.
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Calculus&Mathematica is a computer-based calculus reform project developed at the University of Illinois and Ohio State University. It uses Mathematica to teach calculus to high school and college students at over 30 institutions around the world.
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All sections of Calculus 250 take two common 1-hour exams during the quarter and a common 2-hour final exam during final exam week. The course syllabus (distributed in class) lists the dates for the 1-hour exams and describes the material covered by each. The time and place for the final exam will be announced during the fifth or sixth week of the course. It usually occurs early in the week, but that is not always possible. A grading curve is established for each common exam, based on the results from all sections, and that curve is used in each section. Use of calculators is not allowed on any of the common exams.
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Written as a textbook, Calculus is used both for theoretical calculus courses and for "Introduction to Analysis" courses in several U.S. universities. It is ... used (in rather larger numbers) in quite a few Canadian universities, as well as in a few universities overseas. Because of this, sales of the Answer Book, which are intended for instructors of the courses, are normally restricted.
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Calculus is usually developed by manipulating very small quantities. Historically, the first method of doing so was by infinitesimals. These are objects which can be treated like numbers but which are, in some sense, "infinitely small". On a number line, these would be locations which are not zero, but which have zero distance from zero. No non-zero number is an infinitesimal, because its distance from zero is positive. Any multiple of an infinitesimal is still infinitely small, in other words, infinitesimals do not satisfy the Archimedean property. From this viewpoint, calculus is a collection of techniques for manipulating infinitesimals.
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Calculus is widely employed in the physical, biological, and social sciences. It is used, for example, in the physical sciences to study the speed of a falling body, the rates of change in a chemical reaction, or the rate of decay of a radioactive material. In the biological sciences a problem such as the rate of growth of a colony of bacteria as a function of time is easily solved using calculus. In the social sciences calculus is widely used in the study of statistics and probability.
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