You need to activate javascript for this site.
Menu Conteúdo Rodapé
  1. Home
  2. Courses
  3. Electromechanical Engineering
  4. Calculus II

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 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. Improper integrals
2- Real functions of several real variables: limits and continuity
2.1 Basics in R^n: algebra, geometry and topology
2.2 Domain, range, graph, curves and level surfaces
2.3 Limits
2.4 Continuity
3- Differential Calculus in R^n
3.1 Partial derivatives and directional derivatives
3.2 Differentiability
3.3 Derivative of the composite function
3.4 Higher order derivatives; Schwarz's Theorem
3.5 Implicit Function Theorem
3.6 Local extremes and absolute extremes
3.7 Conditioned extremes: Lagrange multipliers
4- Integral calculus in R^n
4.1 Double and triple integrals: definition, examples and properties
4.2 Change of coordinates
4.3 Applications
5- Line integrals
5.1 Paths and lines
5.2 Line integral of a scalar field
5.3 Line integral of a vector field
5.4 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.
Last updated on: 2024-02-25

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