*Period 1, 2014-2015*

(456402.0)

## Description

This course aims to provide an introduction to the entire computational modeling process, from the formulation of a qualitative model, to its quantitative formulation, to model fitting and validation, model analysis, and model predictions. We focus on the various computational methods that can be employed for modeling and especially on the advantages (and disadvantages) of each approach. We discuss in the course modeling with difference equations, differential equations, and with stochastic processes. The examples we follow throughout the course are mainly from biology and ecology, but the applicability of the methods covered in the course is very broad and it includes dependability issues in complex systems, resource availability, but also applications in economy, chemistry, and social sciences.

This course is primarily meant for Master and PhD students in computer science, computer engineering, information systems, and applied mathematics.

## Content

- Computational modeling: generalities
- Basic modeling techniques: modeling change, proportionality and geometric similarity
- Model fiting
- Modeling with ordinary differential equations
- Basic numerical techniques for ODE-based models: steady state analysis, sensitivity analysis, flux control analysis
- Parameter estimation methods
- Modeling with stochastic processes

**Course book:** F.R. Giordano, M.D.Weir, W.P. Fox: A first course in mathematical modeling, Thomson, 2003.

**Credits: **5 study points.

**Components: **28h lectures, final examination.

**Time schedule: S**eptember 1 – October 22, 2014. Lectures will be given every Monday 13-15 and Wednesday 10-12. Exercises sessions will take place on Mondays 15-17. First lecture: September 1, 2014.

**Lecture room:** Catbert (B3028), ICT.

**Exercise room**: Cobol (B3040), ICT.

**Prerequisites:** Basic courses in algorithmics and data structures.

**Lecturer:** Ion Petre, *Department of IT, Abo Akademi University, ipetre’AT’abo.fi*.

**Teaching assistant:** Cristi Gratie, *Department of IT, Åbo Akademi University, cgratie’AT’abo.fi.*

**Course webpage:** http://www.users.abo.fi/ipetre/compmod/

**Lecture slides ****(tentative list; to be uploaded throughout the course):**

- Lecture 1 (1.9.2014): Introduction
- Lecture 2 (3.9.2014): Modeling change
- Lecture 3 (8.9.2014): Modeling change (2). Modeling using proportionality and geometric similarity
- Lecture 4 (10.9.2014): Model fitting
- Lecture 5 (15.9.2014): Empirical model building (interpolation)
- Lecture 6 (17.9.2014): Discrete probabilistic modeling
- Lecture 7 (22.9.2014): Discrete optimization modeling (1)
- Lecture 8 (24.9.2014): Discrete optimization modeling (2)
- Lecture 9 (29.9.2014): Dimensional analysis
- Lecture 10 (1.10.2014): Modeling with ODEs
- Lecture 11 (6.10.2014): Modeling with systems of ODEs
- Lecture 12 (8.10.2014): Continuous optimization modeling

**Exercises** (to be added throughout the course):

- Exercise set 1: due 8.9.2014
- Exercise set 2: due 15.9.2014
- Exercise set 3: due 22.9.2014
- Exercise set 4: due 6.10.2014
- Exercise set 5: due 13.10.2014

**EXAM:** There will be two course exams, on October 24 and on November 7, 2014. Both exams will take place in the ICT Building starting at 12 in one of the auditoriums on the ground floor (most often Gamma).

**Last updated:** October 6, 2014