Syllabus |
1. NUMERICAL AND POWER SERIES Nature of a series Comparison, limit, D'Alembert, Cauchy and Leibniz's tests Absolute convergence Power series
2. FUNCTIONS FROM R^n TO R^m Topological notions Functions Limits Continuity
3. DIFFERENTIAL CALCULUS IN R^n Partial derivatives Gradient, laplacian, jacobian, divergence and rotational Derivative in a point in the direction of a vector Differentiabiity Tangent hyperplane Linear approximation Chain rule Schwarz and implicit function's theorems Local and global extremes Lagrange multipliers
4. INTEGRAL CALCULUS in R^n Riemann integral Fubini's theorem Integrals in general sets Polar, cylindrical and spherical coordinates Areas and volumes
5. LINE INTEGRALS Line integrals of scalar and vectorial fields Green's theorem
6. SURFACE INTEGRALS Surface integrals of scalar and vectorial fields Gauss and Stokes's theorems
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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, 1983
Additional 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
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