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Students can manipulate 650 interactive figures, including graphs of functions, derivatives, and integrals, as they learn the basics of calculus.
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Next we recall the basics of the calculus of interval-valued functions on time scales (see [10]).
While the papers [8, 10] present the introduction to fractional q-derivatives and q-integrals, the paper [9, 11] discusses the basics of fractional difference calculus.
Although [2] and [15] are good sources to study the basics of time scale and quantum calculus, we just state some definitions, important results, and notations necessary for our article.
We expect participants to have some familiarity with at least the basics of molecular biology; elementary probability theory, calculus and differential equations; and some facility in at least one programming language and/or mathematical modeling.
The basic ideas of calculus can be explained without limits.
All the basic techniques of calculus for finding integrals work in this manner.
Without access to the power of analytic geometry, classical Greek mathematicians such as Archimedes (c. 285 212/211 bc) solved special cases of the basic problems of calculus: finding tangents and extreme points (differential calculus) and arc lengths, areas, and volumes (integral calculus).
MATH 1110-1120 followed by MATH 2130 (spring only) or MATH 2310 (fall only) is a good choice for students who need to master the basic techniques of calculus but whose majors will not require a substantial amount of math.
For the basic theories of calculus on time scales, one can see [13].
For the basic theories of calculus on time scales, see [10].
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