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# Calculus II

 Code 8541 Year 1 Semester S2 ECTS Credits 6 Workload TP(60H) Scientific area Mathematics Entry requirements There is no entry requirement. Mode of delivery Presential classes Work placements Not applicable Learning outcomes With this Curricular Unit, it is intended that the students acquire basic knowledge of Differential and Integral Calculus of functions of several variables. At the end of this Curricular Unit the student must be able to:1) Compute limits of functions of several variables;2) Study the continuity of functions of several variables;3) Derive functions of several variables;4) Apply the derivatives to compute the extremes of functions of several variables;5) Integrate functions of several variables;6) Use integral calculus to determine areas and volumes.7) Formulate and solve problems using the differential and integral calculus of functions with several variables Syllabus 1- Functions of several variables.1.1 Brief notions of topology in R^n1.2 Functions from R^n in R^m1.3 Limits1.4 Continuity2- Differential calculus in R^n2.1 Partial and directional derivatives2.2 Differentiability of functions of R^n in R^m2.3 Derivative of a composition of functions2.4 Derivatives of higher order; Schwarz's Theorem2.5 Implicit function theorem2.6 Absolute extremes and local extremes2.7 Conditional extremes: Lagrange multiplier method3- Integral calculus in R^n3.1 Riemann integral3.2 Properties of integrable functions3.3 Coordinate change3.4 Applications4- Line Integrals4.1 Paths and lines4.2 Line integral of a scalar field4.3 Line integral of a vector field4.4 Green's Theorem5. Surface integrals5.1 Parameterization of surfaces5.2 Surface integrals of scalar fields; area of a surface5.3 Surface integrals of a vector field5.4 Gauss and Stokes theorems Main Bibliography 1. Stewart, James, "Cálculo", Volume II, 5ª edição Thomson Learning, 2001.2. Lang, S., "Calculus of Several Variables", Undergraduate Texts in Mathematics, Third Edition, Springer-Verlag,1987.3. Apostol,T.M., "Calculus",Volume II, John Wiley & Sons, 1968.4. H. Anton, I. Bivens e S. Davis, Calculus, (Eight Edition), John Wiley & Sons, 2006. Language Portuguese. Tutorial support is available in English.

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Electrical and Computer Engineering
Last updated on: 2021-09-06

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