Calculus II

Code	8481
Year	1
Semester	S2
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	-
Mode of delivery	Face-to-face
Learning outcomes	The students approved in this course will be able to: 1. Compute limits of functions of several variables 2. Investigate the continuity of functions of several variables 3. Investigate the differentiability of functions with several variables 4. Apply the derivatives to compute maximuns and minimuns 5. Integrate functions of several variables 6. Apply integral calculus to compute areas and volumes 7. Compute line and surface integrals
Syllabus	1- Real functions of several real variables: limits and continuity 1.1 Basics in R^n: algebra, geometry and topology 1.2 Domain, range, graph, curves and level surfaces 1.3 Limits 1.4 Continuity 2- Differential Calculus in R^n 2.1 Partial derivatives and directional derivatives 2.2 Differentiability 2.3 Derivative of the composite function 2.4 Higher order derivatives; Schwarz's Theorem 2.5 Implicit Function Theorem 2.6 Local extremes and absolute extremes 2.7 Conditioned extremes: Lagrange multipliers 3- Integral calculus in R^n 3.1 Double and triple integrals: definition, examples and properties 3.2 Change of coordinates 3.3 Applications 4- Line integrals 4.1 Paths and lines 4.2 Line integral of a scalar field 4.3 Line integral of a vector field 4.4 Green's Theorem 5- Surface integrals 5.1 Parameterizations 5.2 Surface integrals of scalar fields 5.3 Surface integrals of vector fields 5.4 Gauss' and Stokes' theorems
Main Bibliography	[1] Stewart, J., Cálculo, Volume 2, Tradução da 7.ª edição Norte-Americana, Cengage Learning Edições Ltda, 2014 [2] Marsden and Tromba, Vector Calculus, 6th Edition, W.H. Freeman, 2011 [3] Adams, R., Essex, C., Calculus, A Complete Course, 9th Edition, Pearson, 2018 [4] Anton, H., Bivens, I., Cálculo, Volume 2, Stephen Davis, 8.ª Edição, Bookman, 2007 [5] Apostol, T., Cálculo, Volume 2, Reverté, 1994 [6] Pires, G., Cálculo Diferencial e Integral em R^n, IST Press, 2012 [7] Kreyszig, Advanced Engineering Mathematics, 10th Edition, John Wiley & Sons, Inc, 2011 [8] Salas, Hille, Etgen, Calculus: One and Several Variables, 6th Edition, John Wiley & Sons, Inc, 2007.
Language	Portuguese. Tutorial support is available in English.