Base Knowledge
Calculus, Math Analysis
Teaching Methodologies
In the lectures it is made a theoretical exposition of each topic which is complemented by studying practical examples. Problem solving related with the acquired knowledge is performed in the tutorial lessons. Some lessons are taught using the software MATLAB to solve practical problems.
Learning Results
Understand and apply the basic concepts of differentiation and integration of functions with several variables;
Find the derivatives and integrals of functions with several variables;
Understand and apply the basic concepts of vector analysis;
Recognize the importance of the material taught in the area of biomedical engineering;
Use the MATLAB software in the numerical treatment of the subjects and compare, with criticism, the results obtained by computational means with the ones obtained analytically;
Base problem solving on mathematics;
Select appropriately the available information (from monographs, textbooks, internet, …).
Expose the problems’ solution in a clear and simple way;
Show interest and autonomy in teamwork.
Program
1. Functions with several variables and their derivatives.
Conics and quadrics; Domain, level curves and graphic; Limits and continuity; Partial derivatives;
Differentiability; Directional derivative and the gradient vector; Maximum and minimum values. Using the MATLAB in the treatment of functions with two variables.
2. Multiple Integrals.
Double Integrals: Definition; Properties; Geometric meaning; Evaluation and Applications.
Triple Integrals: Definition; Properties; Geometric meaning; Evaluation and Applications.
3. Vector Analysis.
Parametric coordinates; Line integrals and applications; Vector fields; rotational and divergent.
Curricular Unit Teachers
Internship(s)
NAO
Bibliography
Howard Anton (1999). Cálculo um novo horizonte, Volume 2, Bookman.
João R. Cardoso (2013). Apontamentos de apoio às aulas de Cálculo II, DFM, ISEC.
P. M. Silva, P. Rosa, R. Rodrigues (2015). Conceitos e Animações – Plataforma de e-learning, https://www2.isec.pt/~ppr/
Finney, Weir, Giordano (2003). Cálculo, Volume 2, Addison Wesley.
João R. Cardoso (2013). Actividades de apoio às aulas de MATLAB, DFM, ISEC.
Larson, Hostetler, Edwards (2006). Cálculo, Volume 2, McGrawHill, 8ªEd.
James Stewart (2008). Calculus – Early Transcendentals, Thomson, 6ªEd.