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Faltung equations (closed cycle type) have a wide range of biological applications, nonetheless, they are poorly studied. We use a Volterra‐Kostitzin model (which is a Faltung equation) to study the dynamics of a certain species, where the integral term represents a residual action. The complexity of resolution of this non‐linear equation using classical numeric methods is here solved with the Adomian decomposition method. Our method provides the same graphic solution as others do, such as the numeric method Miladie. However, the decomposition method of Adomian has the advantage that neither time nor space are considered discontinuous and that it gives an analytical solution with a reliable approximation.

After World War II, an educational modernization process gained ground worldwide. International organizations such as UNESCO began to play a key role in the creation, development and dissemination of a new educational vision in different countries. This article examines the origin and development of this modernization process under the dictatorship of Franco. More specifically, we will show how the adoption of this conception in Spain must be understood from the perspective of the interaction between UNESCO and Franco's regime, and how the policies of the dictatorship converged with the proposals suggested by this international organization. Our principal argument is that the educational policies carried out in Spain throughout the second half of the 20th century can be better understood when inserted into a transnational perspective in education.

This article uses documents from archives that until now were unpublished or scarcely known. We have also analyzed materials published in the preeminent educational journals of the dictatorship, such as the Revista de Educación, Revista Española de Pedagogía, Bordón and Vida escolar, as well as documents published by the Spanish Ministry of National Education.

Franco's dictatorship built an educational narrative closely aligned with proposals put forward by UNESCO on educational planning after World War II. The educational policies created by the dictatorship were related to the new ideas that strove to link the educational system with economic and social development.

This article is inspired by a transnational history of education perspective. On the one hand, it traces the origins of educational modernization under Franco's regime, which represented a technocratic vision of education that is best understood as a result of the impact that international organizations had in the second half of the 20th century. On the other hand, it follows the intensifying relationship between the dictatorship and the educational ideas launched by UNESCO. Both aspects are little known and studied in Spain.

The purpose of this paper is to analyze the circumstances that have conditioned the development of education in Spain from the enlightenment to the present day.

Multidisciplinary scientific approach that combines the interpretation of the legal texts with the revision of the doctrinal and theoretical contributions made on the issue.

From the beginning of the nineteenth century, the history of education in Spain has been marked by constant fluctuations between the reactionary instincts, principally maintained by the Catholic Church and the conservative social classes, and the progressive experiments, driven by the enlightened and the liberals first, and the republicans and the socialists later. As a consequence of that, the fight for finishing with illiteracy and guaranteeing universal schooling underwent permanent advances and retreats, preventing from an effective modernization of the Spanish educative system. On the one hand, renewal projects promoted by teachers and pedagogues were inevitably criticized by the ecclesiastical hierarchy, obsessed with the idea of preserving the influence of religion on the schools. On the other hand, successive governments were weak in implementing an educational policy which could place Spain at the level of the other European and occidental nations.

At the dawn of the twenty-first century, although the country has overcome a good part of its centuries-old backwardness, increasing economic difficulties and old ideological splits keep hampering the quality of teaching, gripped by neoliberal policies which undermine the right to education for all. The reading of this paper offers various historical clues to understand this process.