Cálculo 2 - Conceitos, Exercícios e Aplicações

Este livro pretende fornecer aos estudantes dos cursos de Engenharia um texto que seja, simultaneamente, elementar e rigoroso e que lhes permita aprender os conceitos básicos do cálculo infinitesimal e as suas aplicações. Conscientes da vastidão de possíveis caminhos a seguir na apresentação das matérias, os autores optaram por seguir uma sequência simples que tivesse em linha de conta os atuais ajustes dos objetivos da unidade curricular em que esta temática se enquadra, face à atual tendência para a diminuição dos tempos letivos e incentivo à utilização de software MATLAB. Neste sentido, este livro está organizado em três capítulos, ao longo dos quais se procurou obedecer a uma estrutura evolutiva em torno do rigor e da formalidade, mas sem excessos de nomenclatura. No primeiro capítulo estudam-se as funções reais de variável real, o segundo capítulo incide sobre o estudo da natureza de séries numéricas e funcionais e o terceiro capítulo destina-se ao cálculo integral. Em cada capítulo é proporcionado um conjunto de exercícios variados e não repetitivos, em número suficiente e equilibrado, apresentando-se alguns deles já resolvidos, propondo-se outros para resolução e ilustrando algumas aplicações práticas de integração de conhecimentos, recorrendo a software de cálculo algébrico e numérico.

Disposable immunosensor using a simple method for oriented antibody immobilization for label-free real-time detection of an oxidative stress biomarker implicated in cancer diseases

This work proposes a novel approach for a suitable orientation of antibodies (Ab) on an immunosensing platform, applied here to the determination of 8-hydroxy-2′-deoxyguanosine (8OHdG), a biomarker of oxidative stress that has been associated to chronic diseases, such as cancer. The anti-8OHdG was bound to an amine modified gold support through its Fc region after activation of its carboxylic functions. Non-oriented approaches of Ab binding to the platform were tested in parallel, in order to show that the presented methodology favored Ab/Ag affinity and immunodetection of the antigen. The immunosensor design was evaluated by quartz-crystal microbalance with dissipation, atomic force microscopy, electrochemical impedance spectroscopy (EIS) and square-wave voltammetry. EIS was also a suitable technique to follow the analytical behavior of the device against 8OHdG. The affinity binding between 8OHdG and the antibody immobilized in the gold modified platform increased the charge transfer resistance across the electrochemical set-up. The observed behavior was linear from 0.02 to 7.0 ng/mL of 8OHdG concentrations. The interference from glucose, urea and creatinine was found negligible. An attempt of application to synthetic samples was also successfully conducted. Overall, the presented approach enabled the production of suitably oriented Abs over a gold platform by means of a much simpler process than other oriented-Ab binding approaches described in the literature, as far as we know, and was successful in terms of analytical features and sample application.

New molecularly-imprinted polymer for carnitine and its application as ionophore in potentiometric selective membranes

Carnitine (CRT) is a biological metabolite found in urine that contributes in assessingseveral disease conditions, including cancer. Novel quick screening procedures for CRT are therefore fundamental. This work proposes a novel potentiometric device where molecularly imprinted polymers (MIPs) were used as ionophores. The host-tailored sites were imprinted on a polymeric network assembled by radical polymerization of methacrylic acid (MAA) and trimethylpropane trimethacrylate (TRIM). Non-imprinted polymers (NIPs) were produced as control by removing the template from the reaction media. The selective membrane was prepared by dispersing MIP or NIP particles in plasticizer and poly(vinyl chloride), PVC, and casting this mixture over a solid contact support made of graphite. The composition of the selective membrane was investigated with regard to kind/amount of sensory material (MIP or NIP), and the need for a lipophilic additive. Overall, MIP sensors with additive exhibited the best performance, with near-Nernstian response down to ~ 1 × 10− 4 mol L− 1, at pH 5, and a detection limitof ~ 8 × 10− 5 mol L− 1. Suitable selectivity was found for all membranes, assessed by the matched potential method against some of the most common species in urine (urea, sodium, creatinine, sulfate, fructose and hemoglobin). CRT selective membranes including MIP materials were applied successfully to the potentiometric determination of CRT in urine samples.