Mathematica in the classroom: new tools for exploring precalculus and differential calculus

Prémio de Melhor Artigo de Jovem Investigador atribuído pela empresa Timberlake, apresentado na 1ª Conferência Nacional sobre Computação Simbólica no Ensino e na Investigação - CSEI2012, que decorreu no IST nos dias 2 e 3 de Abril.

Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144: 13-29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green's theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.

A treatise on the differential calculus; with numerous examples

Mode of access: Internet.

Outlines of a theory of algebraical equations, deduced from the principles of Harriott, and extended to the fluxional or differential calculus,

Mode of access: Internet.

A Treatise on the differential calculus and the elements of the integral calculus : with numerous examples /

Mode of access: Internet.

An elementary treatise on the differential calculus : containing the theory of plane curves, with numerous examples /

Includes index.

The elements of the differential calculus, comprehending the general theory of curve surfaces, and of curves of double curvature. Intended for the use of mathematical students in schools and universities.

Available on demand as hard copy or computer file from Cornell University Library.

An elementary treatise on the differential calculus, in which the method of limits is exclusively made use of,

Mode of access: Internet.

The principles of the differential calculus; with its application to curves and curve surfaces ...

Mode of access: Internet.

A treatise on infinitesimal calculus, containing differential and integral calculus, calculus of variations, applications to algebra and geometry, and analytical mechanics.

Vol. 3 and 4 form the author's Treatise on analytical mechanics.

Calculus

Word notes for a first year university calculus course

Beispiele über die Lehren des Differential-, Integral- und Variations-Kalkul's und Aufgaben über deren Anwendung /

No more published?

Notes on intrinsic calculus /

Mode of access: Internet.

Concepts from tensor analysis and differential geometry.

Mode of access: Internet.

L.A. Sohncke's Sammlung von aufgaben aus der differential- und integralrechnung /

th. 1. Differentialrechnung.--th. 2. Integralrechnung.