Cálculo II

Mathematics and Calculus I.

In theoretical classes, a theoretical exposition of each subject is made, which is complemented in the theoretical-practical classes by the study of practical examples and by solving exercises to apply the knowledge acquired. The practical-laboratory classes are taught, if possible, in a computer room to deal with the subjects using MATLAB software – the use of software will allow a deepening of the concepts and a better understanding by the student, allowing solving  more complexes problems.

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. Ordinary differential equations
1.1. Introdution and motivation
1.2. First order differential equations
1.3. First order linear equation
1.4. Bernoulli’s equation
1.5. Separable variable equation
1.6. Zero degree homogeneous equation
2. Functions with several variables and their derivatives
2.1. Conics and quadrics
2.2. Domain
2.3. Level curves and graphic
2.4. Limits and continuity
2.5. Partial derivatives
2.6. Differentiability
2.7. Directional derivative and the gradient vector
2.8. Maximum and minimum values
2.9. Using the MATLAB in the treatment of functions with two variables.
3. Multiple Integrals
3.1. Double Integrals: Definition; Properties; Geometric meaning; Evaluation and Applications
3.2. Triple Integrals: Definition; Properties; Geometric meaning; Evaluation and Applications.
4. Vector Analysis
4.1. Parametric coordinates
4.2. Line integrals and applications
4.3. Vector fields
4.4. Rotational and divergent.

The course unit follows the following distributed assessment methodology:

1. Activity carried out in PL classes, worth 4 points (using Matlab software), with no minimum passing grade.

2. Test, worth 6 points, with no minimum passing grade.

3. Written exam, worth 10 points, with a minimum passing grade of 4 points (to be taken during the regular, resit, and/or special exam periods).

The final grade will be the sum of (1)+(2)+(3). A passing grade on the activity requires attendance in PL classes, with a minimum attendance of 10 classes throughout the semester. Otherwise, the grade will be zero.

A student passes the course unit if they obtain a minimum final grade of 9.5 points, under any of the assessment modalities.

An oral examination may be required in cases of suspected fraud. Students who obtain a grade higher than 17 points, in any of the assessment periods, may be required to sit a written grade defense examination.

Students covered by regulations or statutes that explicitly mention exemption from class attendance (such as the Legal Regime for Working Students, expressed in articles 89 to 96 of the Labor Code, approved by Law No. 7/2009, of February 12), are not subject to minimum attendance requirements in the laboratory component, but must still complete the laboratory work in order to obtain a grade in this component.

NAO