Mathematical Modelling and Programming

Course topics: calculus in one and more variables, with particular reference to optimization problems in one and more variables, free and constrained with applications. Differential and difference equations with application to continuous and discrete time dynamic systems

1. Knowledge and understanding:
a.1) Ability to understand the basic elements of functions, in one or more variables, optimization included
a.2) Ability to understand the basic elements of System Dynamics

2. Applying knowledge and understanding:
b.1) Ability to solve real world problems with calculus tools
b.2) Ability to build and analyze static dynamic models of real world phenomena

3. Making judgements
c.1) Ability to evaluate limits and potentiality of mathematical models

Set theory. Algebra and analytic geometry. Equations and inequalities. It is understood that the student must have at least a basic knowledge of the fundamental elements of calculus, such as functions and their properties, limits, derivatives, monotone and convexity, graphs, and elements of integral calculus. Knowledge of linear algebra will also be required, with particular reference to vectors, matrices and their properties, systems of linear equations and solutions by means of linear algebra techniques.
IT IS FUNDAMENTAL THAT THE STUDENT ARRIVES AT THE BEGINNING OF THE COURSE WITH SUCH KNOWLEDGE.

Eigenvalues and eigenvectors
R language elements
Functions in one variable, optimization and applications
Multi-variable functions, free and constrained optimization, with applications
Differential and finite difference equations
Elements of continuous and discrete time dynamic systems
Stability of dynamic systems, even in the non-linear case

Required readings
Material distributed by the Lecturer during the seminars and some recommended books (which will be specified during the course)
Recommended readings
Some books will be recommended during the course
R statistical software https://www.r-project.org/

Final written exam, and possible oral exam. Appropriate verification tests will also be possible during the course.

Traditional with slides. Student's presentation.

English

Attendance is required. Daily preparation is also required; suitable tests during the course will constitute part of the exam.

written