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Differential and integral proportional calculus: how to find a primitive for

Campillay Llanos, William; Guevara, Felipe; Pinto Jiménez, Manuel; Torres, Ricardo (Taylor & Francis, 2020)

We present a type of arithmetic called Proportional Arithmetic. The main properties and objects that emerge with this way of operating quantities are exposed. Finally, the antiderivative and the indefinite integral are ...

Research on calculus: what do we know and where do we need to go?

San Diego State University; Portland State University; Universidade Estadual Paulista (UNESP) (2014-08-01)

In this introductory paper we take partial stock of the current state of field on calculus research, exemplifying both the promise of research advances as well as the limitations. We identify four trends in the calculus ...

Internal program extraction in the calculus of inductive constructions

Severi, Paula; Szasz, Nora (UR. FI – INCO., 2002)

Based on the Calculus of Constructions extended with inductive definitions we present a Theory of Specifications with rules for simultaneously constructing programs and their correctness proofs. The theory contains types ...

k-Fractional trigonometric functions

Cerutti, Rubén A.; Luque, Luciano Leonardo (Hikari Ltd, 2014)

Based on the k-Mittag-Lefler function and the k- -Exponential Function we introduce families of functions that allows us define new fractional trigonometric functions that contain the classical trigonometric functions ...

k-Fractional trigonometric functions

Cerutti, Ruben Alejandro; Luque, Luciano Leonardo (Hikari Ltd, 2014-08)

Based on the k-Mittag-Lefler function and the k-α-Exponential Function we introduce families of functions that allows us define new fractional trigonometric functions that contain the classical trigonometric functions ...