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First Semester 
Teaching style
Lingua Insegnamento

Informazioni aggiuntive

Course Curriculum CFU Length(h)


Attending classes, the student will learn:
- Knowledge and understanding
Knowledge and understanding of the needed steps to develop a mathematical model for a system. Knowledge and understanding of numerical method to solve a mathematical model.
- Applying knowledge and understanding
Understanding the problems related to the modeling and simulation of the main units present in process industry.
- Making judgments
Skills in judge the need to model and simulate a real process.
- Communication skills
Communication skills acquired in-group work.
- Learning skills
Ability to independent study and analysis of technical books on the course arguments.


Knowledge: An adequate knowledge of the fundamental methodological aspects of the basic sciences (calculus, geometry, physics), applied science (thermodynamics, reaction system) and operation units (distillation column and reactors).
Skills: Be able to solve systems of algebraic equations, how to derive and integrate functions. Knowing how to formulate a process model.


Course overview. Model definition. Error types (3 hours).
Programming (6 hours of practice).
Steady state mono-dimensional nonlinear models. Numerical solution methods: bisection, Newton and secant (9 hours + 6 hours of practice).
Steady state multi-dimensional nonlinear models, Numerical solution of nonlinear systems (9 hours + 6 hours of practice).
Integral system models. Numerical solution methods: trapeze, Simpson and Gauss (9 hours + 6 hours of practice).
Nonlinear dynamic systems: mono- and multi-dimensional. Numerical solution methods: Eulero (explicit and implicit), Heun and Runge-Kutta (12 hours + 3 hours of practice).
System described by second order differential equations, Numerical solution methods: finite difference, orthogonal polynomials (9 hours + 6 hours of practice).
System described by partial differential equations. Numerical solution methods: finite difference, orthogonal polynomials (9 hours + 6 hours of practice).

Teaching Methods

60 hours of class and 30 hours of practice, the student is invited to work with the colleagues for finding the solutions of the assigned problems. The teachers is in the class to give support.

Verification of learning

The final exam consists in delivering written reports for the home works, analogous to the one carried out in class, and a final project.
The student, to pass the exam, should be able to:
- derive a mathematical model of chemical processes and able to numerically solve it;
- analyze the process and choose the appropriate model to simulate it;
- able to understand the scientific literature in order to acquire the needed knowledge to derive a mathematical model;
- write a brief report on the obtained results.
The student is evaluated according to the following criteria:
- demonstrated knowledge and understanding: 18/30-21/30;
-demonstrated knowledge and understanding and ability of applying knowledge: 23/30-26/30;
- demonstrated knowledge and understanding, ability of applying knowledge and ability to deliver exhaustive reports: 27/30-30/30.


V. Comincioli, Analisi Numerica, McGraw-Hill Italia.

More Information

Course note are available (in italian).

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