Computing Methods for Biomedicine

Recommended Prerequisites

N.A.

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.

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.

Work Placement(s)

No

Syllabus

Bases of Numerical Methods:
- Numerical interpolation
- Numerical differentiation: rules of 2, 3 and 5 points, Richardson Extrapolation
- Numerical integration: Simpson rule, Romberd integration.
- Zeros of a function: bissection, secant and Newton-Raphson methods
- Linear sistems of equations: Gauss elimination, LU factorization
- Conjugated gradient method
- Linear and nonlinear regression

Important methods in modeling biological systems:
- Monte Carlo methods: numerical integration, gillespie
- Solving differential equations: Euler, Euler-Cromer, Runge-Kutta methods; stiff equations
- Solving partial differential equations.

Head Lecturer(s)

João Carlos Lopes Carvalho

Assessment Methods

Continuous evaluation
Continuous evaluation: 100.0%

Bibliography

S. Dunn, Numerical methods in Biomedical Engineering, Academic Press (2005)
P. DeVries, J. Hasbun, A First Course in Computational Physics, Jones & Bartlett Publishers (2010)
C. Moler, Numerical Computing with MATLAB, SIAM (2008)
G. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, Clarendon Press (1985)
J. Faires, R. Burden, Numerical Analysis, Brooks/Cole (2005)