Sentence examples for calculus such as from inspiring English sources

In the same section, we solve the existing optimization problem in a systematic manner by the techniques in variational calculus such as gradient-descent based methods.

For the reader seeking more familiarity with concepts of stochastic calculus such as Ito or Stratonovich integration there are applied approaches [3] and rigorous treatments [37] as well.

For example, basic tools from calculus such as Fermat's theorem, Rolle's theorem and the intermediate value theorem may not necessarily hold.

Earlier forms of the epsilon calculus (such as that presented in (Hilbert 1923)) use a dual form of the epsilon operator, in which εx A returns a value falsifying A x).

Many mathematical models of real problems arising in various fields of science and engineering were established with the help of fractional calculus, such as viscoelastic systems, dielectric polarization, electrode-electrolyte polarization, and electromagnetic waves [4 7].

In the last few years, many problems in science and engineering can be modeled accurately in the form of fractional calculus such as multi-scale problems that span a wide range of time or length scales.

More recent additions to the process calculus family, such as the π-calculus, have added the capability for reasoning about dynamic topologies.

The results in Theorems 1 to 4 can be easily reduced to yield some corresponding formulas involving simpler factional calculus operators such as the Erdélyi-Kober fractional calculus operators.

CORDIC structure does not use any calculus method such as rational or polynomial functions.

These expansions are obtained by using some fractional calculus theorems such as the generalized Leibniz rules for the fractional derivatives and the Taylor-like expansions in terms of different functions.

Since each CAS has interfaces that can execute algebraic calculus operations such as derivative, integral, matrix, and determinant, they can be regarded as a kind of calculating machine that provides convenience for mathematicians.