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# Calculus II

 Code 15754 Year 1 Semester S2 ECTS Credits 6 Workload TP(60H) Scientific area Mathematics Entry requirements N.A. Learning outcomes The students approved in this course will be able to: 1. Compute limits of functions of several variables2. Investigate the continuity of functions of several variables3. Investigate the differentiability of functions with several variables4. Apply the derivatives to compute maximuns and minimuns5. Integrate functions of several variables6. Apply integral calculus to compute areas and volumes7. Compute line and surface integrals Syllabus 1. Improper integrals 2- Real functions of several real variables: limits and continuity2.1 Basics in R^n: algebra, geometry and topology2.2 Domain, range, graph, curves and level surfaces2.3 Limits2.4 Continuity3- Differential Calculus in R^n3.1 Partial derivatives and directional derivatives3.2 Differentiability3.3 Derivative of the composite function3.4 Higher order derivatives; Schwarz's Theorem3.5 Implicit Function Theorem3.6 Local extremes and absolute extremes3.7 Conditioned extremes: Lagrange multipliers4- Integral calculus in R^n4.1 Double and triple integrals: definition, examples and properties4.2 Change of coordinates4.3 Applications5- Line integrals5.1 Paths and lines5.2 Line integral of a scalar field5.3 Line integral of a vector field5.4 Green's Theorem 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. Teaching Methodologies and Assessment Criteria The teaching methodology is based on theoretical-practical lessons. The theoretical part is carried out through the explanation of the subjects, accompanied by examples and dialoguing with the students to whom written notes are provided. The practical part is based on the resolution of assignments both with guidance and autonomously. Assessment undertaken throughout the teaching-assessment period will consists of three written tests. The student will also be given the possibility of a final exam. Language Portuguese. Tutorial support is available in English.

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Electromechanical Engineering
Last updated on: 2024-02-25

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