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This paper aims to study ways of contributing to the development of Calculus through a Project-Based Learning (PBL) approach, which involves students in their first semester of the Integrated Master's program in Industrial Engineering and Management (IEM) at the University of Minho. The study presents the analysis of forty-two interdisciplinary project reports developed by students over a seven-year period. The reports offer good evidence for the application of the requested Calculus learning outcomes, demonstrating that the application of Calculus content occurred during the development of the project. This finding means that PBL was successful as a truly active learning process for Calculus that involves students learning independently through the interdisciplinary resolution of problems related to their engineering professional profiles.

Floral traits are used as signals to attract pollinators and play an important role in species identification and isolation. Nicotiana is a genus with a diverse range of flower morphologies, colours, and pollination systems related to a natural history of hybridization, a driver of speciation in this genus. Nicotiana alata and Nicotiana forgetiana are pollinated by hawkmoths and hummingbirds, respectively, and a putative hybrid population was recently found. This population presents flowers with intermediate phenotypes providing an opportunity to investigate the impact of hybridization on floral trait variation. Here we investigated the floral shape, floral pigments, and nectar traits in a putative hybrid population, hereafter termed atypical populations (AP) compared to phenotypes of allopatric populations of both species. We found a high variation in floral pigmentation in AP plants and observed phenotype segregation in some genotypes. Nicotiana forgetiana and AP plants showed the same flavanol peaks as Nicotiana alata , suggesting the same UV-absorbent phenotype attractive to hawkmoths. The geometric morphometric results showed that the intermediate-coloured flowers had similar floral shape and size to N. alata. Our results suggest that the putative hybrid population would be able to attract the same parental pollinator—hawkmoths and hummingbirds—making backcrossing events possible and attracting other pollinators, such as bees. [ABSTRACT FROM AUTHOR]

Floral shape and size play a role in plant diversification and reproductive isolation. Different floral forms can rise by selective pressures by pollinators/ecological constraints and/or genetic drift. Nicotiana (Solanaceae) has c. 82 currently recognized species grouped in 13 sections. Nicotiana forgetiana and N. alata belong to section Alatae and present different floral traits related to their primary pollinators. These species co-occur in a region of plant endemism in southern Brazil marked by a mosaic between open grasslands and Araucaria forest. Here, we conducted a population-level sampling across the range of N. forgetiana and combined geometric morphometric analyses and ecological niche modelling to shed light on the patterns underlying intraspecific floral shape variation. Corolla shape and size varied significantly across the geographical distribution of N. forgetiana and ' rastroensis ', a putative new species. These floral shape differences were related to variations in temperature, precipitation and elevation. We also observed a range of intermediate floral traits in two populations, and our results of geometric morphometric analyses reveal morphological overlap between N. alata and N. forgetiana. Moreover, we found that habitat suitability for both species was impacted by past climatic oscillations, with severe reduction for N. forgetiana during the Last Glacial Maximum. We discuss the results to shed light on the evolution of N. forgetiana. [ABSTRACT FROM AUTHOR]

Population genetic structure results from the interaction between historical events, current ecological conditions and life traits. The genetic structure and gene flow between populations are important to species dynamics, mainly for rare and endangered species that are more vulnerable to landscape changes and fragmentation. Here we evaluated the genetic diversity, population structure and gene exchange in Petunia bonjardinensis , P. reitzii and P. saxicola , three rare species endemic to subtropical highland grasslands in southern South America. We analysed the genetic diversity and structure considering historical events, such as founder effect and climate changes, and biological traits of each species. We also estimated the conservation status for these three species. We collected samples from all adult individuals and occurrence sites that could be found at the same flowering season and genotyped them for 13 nuclear microsatellite markers. Our results indicate that rarity is probably historical for these species, given that we found no genetic evidence for recent bottlenecks. Petunia bonjardinensis , with the largest occurrence area and population sizes, displayed the higher diversity indices. The other two showed lower genetic diversity and are geographically most restricted. Gene exchange among these species was low, although they share some ancestral genetic polymorphism. Historical migration, founder effects and Pleistocene climate cycles ae the main factors explaining genetic diversity, and this was also influenced by reproductive biology and recent habitat loss, whereas the landscape influences the structure. Based on IUCN criteria, the three species are endangered, and the main risk for their survival is probably anthropic activity in the occurrence area. We recommend an urgent programme for the preservation of these species in situ and ex situ. [ABSTRACT FROM AUTHOR]

Aim: Pleistocene climate oscillations influenced the species distribution and genetic diversity in grasslands, and such climatic changes promoted expansion and contraction cycles, leading to fragmentation and isolation of evolutionary lineages in refuges. This study aimed to infer the evolutionary processes that most influenced the genetic diversity of a South American nightshade Petunia inhabiting subtropical grasslands under the Pleistocene influence. Location: Pampa and Chaco. Taxon: The widely distributed herb Petunia axillaris subsp. parodii (Solanaceae). Methods: We obtained high‐density genome coverage throughout the geographical distribution of Petunia axillaris subsp. parodii. We estimated the genetic diversity and structure to evaluate population differentiation and applied a model‐based demographic analysis to investigate the scenarios that could have influenced the species' evolutionary history. We evaluated the association between neutral and outlier polymorphisms with environmental variables to distinguish the influence of the geographical distance and environmental differences between populations. Results: There are three evolutionary lineages in P. axillaris subsp. parodii. The origin and differentiation of these lineages were related to the Pleistocene refuges and rivers acting as barriers to gene flow. We also identified 496 outlier loci related to adaptation to environmental conditions. Main conclusion: The Pleistocene climate changes drove lineage diversification isolated in micro‐refugia. Rivers and changes in their courses may have also acted on the population divergence, serving as barriers to gene flow or even as corridors for species range expansion. These findings contribute to the knowledge of the evolutionary processes that influenced the lineage diversification of South American subtropical grassland species. [ABSTRACT FROM AUTHOR]

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Block diagrams and signal-flow graphs are used to represent and to obtain the transfer function of interconnected systems. The reduction of signal-flow graphs is considered simpler than the reduction of block diagrams for systems with complex interrelationships. Signal-flow graphs reduction can be made without graphic manipulations of diagrams, and it is attractive for a computational implementation. In this paper the authors propose a computational method for direct reduction of signal-flow graphs. This method uses results presented in this paper about the calculation of literal determinants without symbolic mathematics tools. The Cramer's rule is applied for the solution of a set of linear equations. A program in MATLAB language for reduction of signal-flow graphs with the proposed method is presented. Index Terms--Mason's rule, signal-flow graphs, symbolic calculations, transfer functions.