Computational Methods for Biomedicine

Year
2
Academic year
2022-2023
Code
01019217
Subject Area
Biomedical Sciences
Language of Instruction
Portuguese
Other Languages of Instruction
English
Mode of Delivery
Face-to-face
Duration
SEMESTRIAL
ECTS Credits
6.0
Type
Compulsory
Level
1st Cycle Studies

Recommended Prerequisites

Computers and Programming.

Teaching Methods

The theoretical classes have the aim of demonstrating and explaining the numerical methods that are used in Biomedicine. In these classes it is stimulated the understanding and integration of the new topics with the previously acquired knowledge.
In the practical classes the students implement computationally in MatLab the algorithms learnt in the theoretical classes. The practical classes promote group work and discussion, as well as stimulate the autonomous work.

Learning Outcomes

- Acquire basic knowledge of numerical and computational methods applied to biology and medicine.
- Apply this knowledge to solving problems in biology.
- Recognize the importance of computational methods in solving complex problems associated to biology.
- Relate the acquired knowledge with the information acquired in previous related courses.

Competence in information management
Competence in critical reasoning
Attention to quality
Competence in practical application of theoretical knowledge
Competence on problem solving.

Work Placement(s)

No

Syllabus

Bases of Numerical Methods:
- Zeros and extrema of a function: bissection, secant and Newton-Raphson methods.
- Numerical differentiation: rules of 2, 3 and 5 points, Richardson Extrapolation.
- Numerical integration: Simpson rule, Romberg integration.
- Linear systems of equations: Gauss elimination, LU factorization.

Important methods in modeling biological systems:
- Solving ordinary differential equations: Euler, Euler-Cromer, Runge-Kutta, predictor-corrector methods;
- Solving partial differential equations (elliptic, hyperbolic and parabolic).
- Monte Carlo methods: numerical integration, Gillespie.

Head Lecturer(s)

José Lopes Pinto da Cunha

Assessment Methods

Continuous assessment
Frequency: 100.0%

Final assessment
Exam: 100.0%

Bibliography

- C. Moler, Numerical Computing with MATLAB, SIAM (2008).

- Alfio Quarteroni e Fausto Saleri, Cálculo Científico com MATLAB e Octave, Springer, 2007.

- Stanley M. Dunn, Alkis Constantinides e Prabhas V. Moghe, Numerical Methods in Biomedical Engineering, Academic Press, 2005.

- Jaan Kiusalaas, Numerical Methods in Engineering with Python, Cambridge University Press (2010).

-Morten Hjorth-Jensen, Computational Physics, University of Oslo (2010).

- Tao Pang, An Introduction to Computational Physics, Cambridge University Press (2006).

- William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, 3rd Edition (2007).