Computational Modeling

Recommended Prerequisites

Computers and Programming; Linear Algebra and Analytical Geometry; Mathematical Analysis III.

Teaching Methods

The theoretical classes have the aim of demonstrating and explaining the numerical methods. 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 Physical Engineering.
- Apply this knowledge to solving problems in Physical Engineering.
- Recognize the importance of computational methods in solving complex problems associated to Physical Engineering.
- 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

Final assessment
Exam: 100.0%

Continuous assessment
Frequency: 100.0%

Bibliography

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

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

- 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).