Overall objectives:

O1 - Approach (aspects of) mathematical models employed in various areas of natural sciences, humanities and engineering.
O2 - Show how some of these mathematical models can be introduced within the context of mathematical education at the high school level (third cycle or secondary).
O3 - Consolidate and broaden concepts that were acquired during the undergraduate course in Mathematics, showing how they arise in different areas and / or in different contexts of science and engineering.
O4 - Show that there are problems which apparently appear to be different, but share a similar mathematical structure (mathematical model).

Syllabus:

P1 - Introduction to Mathematical Modelling: topics on the construction, study, validation and use of mathematical models. Different kinds of mathematical models.
P2 - Mathematical models involving Linear Algebra: application of linear algebra concepts (e.g. matrices, linear applications, linear systems) in mathematical models related to electrical circuits, traffic flow, social networks, chemical reactions, geometric optics, computer science, economics and biology.
P3 - Discrete mathematical models: modelling examples using different types of sequences. Examples of application in biology, economics, games and other everyday situations.
P4 - Continuous mathematical models: examples of modelling using real functions of a real variable (e.g. polynomial, rational, exponential, logarithmic, trigonometric functions) with applications in Physics (kinematics, radioactive dating,...), Biology, Economics, Geology, Astronomy and Geography (demography).

Literature/Sources:

Murray, J.D , Mathematical Biology , Springer
M. M. Meerschaert , 1999 , Mathematical Modelling , Academic Press
J. F. Matos, W. Blum, S. K. Houston, S. P. Carreira , 2001 , Modelling and mathematical education , Horwood Publishing Limited
Erwin Kreyszig , 1988 , Advanced Engineering Mathematics , John Wiley & Sons
P. A. Tipler & R. A. Llewellyn , 2003 , Modern Physics , W. H. Freeman Company
Clive Dym , 2004 , Principles of Mathematical Modeling , Elsevier Science Publishing Co Inc

Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
Teaching: Use of the whiteboard for presentation, explanation of subject material and problem solving. Use of the computer and projector to help visualize and better understand the concepts. The use of slides to introduce concepts may be used promptly (in this case the exposed material should be provided to students, in detail, through a Booklet or other supporting documents). Evaluation: Two tests each one with a weight of 35%, and a practical work (in report or article format) to be delivered at the end of the semester (weight of 30%). This work is to motivate students to do research and obtain results on their own initiative (always counting on the support / guidance of the teacher). The work also has the purpose of creating good writing habits in Mathematics. The evaluation during the appealing season and the special season should be done in agreement with the current Regulation for the Evaluation of Student Learning at the University of Madeira.