Métodos Computacionais em Biomedicina

Calculus I and Calculus II.

The teaching of the curricular unit consists of theoretical (T) and practical-laboratory (PL) classes.
The T aim to study models and teach numerical analysis techniques, as students need tools to solve each of the problems, computationally applied to the field of Biomedicine. These classes encourage understanding and integration of knowledge.
PL classes are computational practices using MatLab, which allow the implementation and practical application of the studied methods, and promote group work and discussion.

– Acquire knowledge of mathematical modeling applied to biological systems and biomedicine.
– Provide the student with numerical tools that enable the obtaining of one or more approximate solutions to problems whose resolution cannot be carried out analytically.
– Apply this knowledge in solving, by computational means, problems in the field of biomedicine.
– Recognize the importance of computational methods in solving complex problems in areas associated with biological and medical processes.
– Strengthen programming skills and understanding of the specifics of algorithms studied for the resolution of specific problems in the field of biomedical engineering
– Develop critical thinking and analysis of results.

1.    Mathematical models studied using Numerical Analysis techniques:
1.1.    Mathematical models of population growth
1.2.    Mathematical ecosystem models
1.3.    Epidemiological models
1.4.    Mathematical Model for Immunotherapy
1.5.    Drug release models
1.6.    Nerve impulse propagation model
1.7.    Cardiovascular Model
2.    Numerical analysis bases:
2.1.    Polynomial interpolation.
2.2.    Numerical differentiation.
2.3.    Numerical integration: Trapeze and Simpson rules.
2.4.    Roots of nonlinear equations: bisection and Newton-Raphson methods.
2.5.    Linear systems of equations: numerical resolution – iterative methods.
2.6.    Numerical resolution of nonlinear systems: Newton’s method.
2.7.    Numerical resolution of ordinary differential equations and systems of differential equations: Euler, Runge-Kutta and predictor-corrector methods.

The assessment will consist of two assignments, worth a total of 8 points, and a final exam worth 12 points – with a minimum passing grade of 5.00 (to be taken during regular and/or resit periods and special periods). The final grade will be the sum of the assignments (there is no minimum grade requirement) and the exam grade, if the student achieves the minimum passing grade on the exam.

This course unit uses a distributed assessment system, composed of:

1.  Assignment 1: 4 points
2. Assignment 2: 4 points
3. Written exam: 12 points, with a minimum of 5.00 points (taken during the regular, resit, and/or special exam periods)

The final grade is the sum of (1) + (2) + (3), provided the student obtains a minimum of 5.00 points on the exam.

Passing requires a final grade of 10 points or higher.

 Assignments and laboratory classes

•  The completion/submission of both assignments is mandatory.
•  Each assignment will include questions/assessments in class, as part of the laboratory classes (PL).
• Attendance at PL classes is mandatory, with a minimum attendance of 11 classes throughout the semester.
• Failure to meet the minimum attendance requirement for PL classes will result in a penalty of up to 2 points on the grade for each assignment.
• Each assignment is carried out in groups of 2 students, with the grade assigned individually.
• The assignments must be submitted in report format, containing: presentation of the problem; relevant concepts; numerical solution in Matlab using the codes developed in class; presentation and discussion of results; conclusions.
• There are no minimum requirements for the assignments.

Grade Defense 

Students with a grade higher than 17 at any time of evaluation may be required to take a written exam to defend their grade.

NAO