You need to activate javascript for this site.

# Calculus II

 Code 16140 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 field4.4 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 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. Language Portuguese. Tutorial support is available in English.

### Course

Computational Mechanical Engineering
Last updated on: 2024-03-01

The cookies used in this website do not collect personal information that helps to identify you. By continuing you agree to the cookie policy.