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Syllabus |
1. Topology and Geometry in R^n.
Inner product, norm, and distance. Cross product. Lines and planes. Quadratic forms. Basic topological notions.
2. Differential Calculus in R^n.
Scalar- and vector-valued functions.
Graphs and level sets. Continuity. Partial and directional derivatives. Tangent plane. Differentiability. Higher-order derivatives. Derivative of a composite function (chain rule). Taylor’s formula. Local and constrained extrema. Implicit Function Theorem.
3. Multiple Integrals.
Definition, Fubini’s theorem, and change of variables.
Double integrals: Cartesian and polar coordinates.
Triple integrals: Cartesian, cylindrical, and spherical coordinates. Applications.
4. Vector Calculus.
Line and surface integrals.
Green’s theorem, Stokes’ theorem, and Gauss’ theorem.
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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] Salas, Hille, Etgen, Calculus: One and Several Variables, 6th Edition, John Wiley & Sons, Inc, 2007
[4] Adams, R., Essex, C., Calculus, A Complete Course, 9th Edition, Pearson, 2018
[5] Kreyszig, Advanced Engineering Mathematics, 10th Edition, John Wiley & Sons, Inc, 2011
[6] Anton, H., Bivens, I., Cálculo, Volume 2, Stephen Davis, 8.ª Edição, Bookman, 2007
[7] Apostol, T., Cálculo, Volume 2, Reverté, 1994
[8] Pires, G., Cálculo Diferencial e Integral em R^n, IST Press, 2012
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Teaching Methodologies and Assessment Criteria |
1. Classes are theoretical-practical. The teaching method consists of the exposition of concepts, theoretical results, examples and applications to engineering, whenever possible. Problem solving and individual work are encouraged, based on exercises suggested by the teacher.
2.1. The assessment can take place during the class period or in the final exam.
2..2. The assessment of knowledge throughout the teaching-learning period will be periodic and will consist of two written tests, each lasting two hours and rated at ten (10) points.
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