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# Calculus II

 Code 10346 Year 1 Semester S2 ECTS Credits 6 Workload TP(60H) Scientific area Mathematics Entry requirements Does not have. Mode of delivery Theoretical/Practical Work placements Not applicable. Learning outcomes In this Curricular Unit the students will obtain the basic knowledge of series and of differential and integral Calculus of functions of several variables.At the end of this Curricular Unit the students should - determine the nature of a numerical series; - compute the interval of convergence of a power series; - compute limits of functions of several variables; - study the continuity of functions of several variables; - compute partial derivatives of functions of several variables; - apply the derivatives to compute maximums and minimums; - integrate functions of several variables; - apply integrals to compute areas and volumes; - compute line integrals; - apply Green's Theorem; - compute surface integrals; - apply Gauss and Stokes's theorems. Syllabus 1. NUMERICAL AND POWER SERIESNature of a seriesComparison, limit, D'Alembert, Cauchy and Leibniz's testsAbsolute convergencePower series2. FUNCTIONS FROM R^n TO R^mTopological notionsFunctionsLimitsContinuity3. DIFFERENTIAL CALCULUS IN R^nPartial derivativesGradient, laplacian, jacobian, divergence and rotationalDerivative in a point in the direction of a vectorDifferentiabiityTangent hyperplaneLinear approximationChain ruleSchwarz and implicit function's theoremsLocal and global extremesLagrange multipliers4. INTEGRAL CALCULUS in R^nRiemann integralFubini's theoremIntegrals in general setsPolar, cylindrical and spherical coordinatesAreas and volumes5. LINE INTEGRALSLine integrals of scalar and vectorial fieldsGreen's theorem6. SURFACE INTEGRALSSurface integrals of scalar and vectorial fieldsGauss and Stokes's theorems Main Bibliography Main bibliography - Apostol, T.M., Cálculo, Vol. 1 e 2, Reverté, 1993 - Sarrico, C., Cálculo Diferencial e Integral, Esfera do Caos, 2009 - Swokowski, E. W., Cálculo com Geometria Analítica, Vol. 2, McGrawHill, 1983Additional bibliography- Dias Agudo, F.R., Análise Real, Vol. I e II, Escolar Editora, 1989- Demidovitch, B., Problemas e exercícios de Análise Matemática, McGrawHill, 1977- Lima, E. L., Análise Real, Vol. 2, Colecção Matemática Universitária, IMPA, 2004- Lima, E. L., Curso de Análise, Vol. 2, Projecto Euclides, IMPA, 1989- Mann, W. R., Taylor, A. E., Advanced Calculus, John Wiley and Sons, 1983- Stewart, J., Calculus (International Metric Edition), Brooks/Cole Publishing Company, 2008 Language Portuguese. Tutorial support is available in English.

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Aeronautical Engineering
Last updated on: 2023-06-13

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