Calculus II

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 tutorial lessons are taught in a computer room for treating the subjects in the MATLAB environment. There is a laboratorial component in this course unity where a test is made in the computer, having a weight of 2.5 values in the final score.
Continuous Assessment: two tests during the semester with a final score of 17.5 values. It will be assigned the mark corresponding to the rounding arithmetic average of the two tests.
Assessment by final examination: There are two final examination terms, both marked to 17.5 points. Students have also the opportunity of repeating the MATLAB test. 

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.

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.

NAO