Thesis (MSc)--Stellenbosch University, 1993. / ENGLISH ABSTRACT: Formal methods aim to apply the rigour of mathematical logic to the problem ofguaranteeing that the behaviour of (critical) software conforms to predetermined requirements. The application of formal methods during program construction centers around a formal specification of the required behaviour of the program. A development attempt is successful if the resulting program can be formally proven to conform to its specification. For any substantial program, this entails a great deal of effort. Thus, some research efforts have been directed at providing mechanical support for the application of formal methods to software development. E.W. Dijkstra's calculus of weakest precondition predicate transformers [39,38] represents one of the first attempts to use program correctness requirements to guide program development in a formal manner. / AFRIKAANSE OPSOMMING: Formele metodes poog om die strengheid van wiskundige logika te gebruik om te waarborg dat die gedrag van (kritiese) programmatuur voldoen aan gegewe vereistes. Die toepassing van formele metodes tydens programontwikkeling sentreer rondom a formele spesifikasie van die verlangde programgedrag. 'n Ontwikkelingspoging is suksesvol as daar formee1 bewys kan word dat die resulterende program aan sy spesifikasie voldoen. Vir enige substansiële program, verteenwoordig dit ‘n aansienlike hoeveelheid werk. Verskeie navorsinspoging is gerig op die daarstelling van meganiese ondersteuning vir die gebruik van formele metodes tydens ontwikkeling van sagteware. E. W. Dijkstra se calculus van swakste voorkondisie (“weakest precondition”) predikaattransformators [39,38] is een van die eerste pogings om vereistes vir programkorrektheid op ‘n formele en konstruktiewe wyse tydens programontwikkeling te gebruik.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O presente trabalho tem como objetivo auxiliar professores de Educação Básica a abordar alguns conceitos básicos de Cálculo Diferencial e Integral no terceiro ano do ensino médio, utilizando os softwares wxMaxima e Geogebra. Nossa proposta visa resgatar o ensino do Cálculo no âmbito escolar, mas de uma maneira diferente da tradicional, utilizando a tecnologia em nosso favor, como uma ferramenta facilitadora no processo ensino-aprendizagem de conceitos de limites, derivadas e integrais. A ideia é que toda a parte algébrica e gráfica, que exige conhecimentos matemáticos específicos, seja feita pelos softwares e que os estudantes aprendam a interpretar as soluções que as ferramentas nos fornecem e a conhecerem um pouco mais sobre a matemática e suas aplicações. / The present work aims to help Basic Education teachers to approach some basic concepts of Differential and Integral Calculus in the third year of high school using the software wxMaxima and Geogebra. Our purpose is to recover the teaching of Calculus in the school context, but in a different way from the traditional one, using the technology in our favor, as a facilitating tool in the teaching-learning process of boundary, derivative and integral concepts. The idea is that all the algebraic and graphic part, which requires specific mathematical knowledge, is done by software and that students learn to interpret the solutions that the tools provide us and to know a little more about mathematics and its applications.