Course aims:

The general aim related to this course consists in getting knowledge which helps the students to use the mathematical concepts together with a specific software to model phenomena from various fields as medicine, physics, chemistry, economy, sociology etc..
A specific aim is related to the use of Matlab and Excel software to model various reality-based problems with mathematical tools.
Besides the knowledge of basics mathematical modeling aided by software products, the course is focused also on the development of an open minded approach of the interdisciplinary matter.

Course Entry Requirements:

Recommended but not mandatory: 1. Probability and mathematical statistics 2. Mathematical software CSE206 3. Numerical calculus 4. Differential and partial derivatives equations

Course contents:

I. Elements of mathematical modeling and simulation 1. Introduction 2. Process of mathematical modeling 3. Models obtained through the translation of the problem in mathematical language 4. Simulation techniques and random numbers II. Models based on statistical techniques 1. Simple linear regression model 2. Polynomial regression model 3. Other simple regression models 4. Multiple linear regression models 5. Other multiple regression models 6. Dynamic models III. Models based on optimization techniques 1. Elements of mathematical programming 2. Transportation problems 3. Problems related to production and stocking 4. Problems of mixtures (dietary optimization, alloy mixture optimization) 5. Problems of cutting-stock 6. Problems from games theory 7. Other optimization problems IV. Deterministic models based on equations 1. Problems of populations’ dynamic 2. Deterministic models in epidemiology 3. Deterministic models in physics

Teaching methods:

Lecture, discussion, exemplification.

Learning outcomes:

• Identifying the appropriate models and methods for solving real-life problems; • Giving the interpretation of mathematical and computer science (formal) models; • Using the simulation in the study of the behavior of developed models and evaluation of results; • Embedding the formal models in specific applications in various domains.

Learning outcomes verification and assessment criteria:

Practical project – 50%; continuous assessment – 50%.

Recommended reading:

E.A. Bender, An introduction to mathematical modeling techniques, Dover Books, New York, 2000, -.
N. Breaz, Mathematical modeling and simulation, theory and applications, Electronic version in the university library, Alba Iulia, 2009, -.
D. J. Higham, N. J. Higham,, MATLAB Guide, 2nd edition, SIAM, -, 2005, -.
M. P. McLaughlin, A tutorial on Mathematical Modeling, www.causascientia.org/math_stat/Tutorial.pdf, -, 1999, -.
Cleve Moler, Numerical Computing in MATLAB, SIAM, -, 2005, -.