MSE Master of Science in Engineering

The Swiss engineering master's degree

Ogni modulo equivale a 3 crediti ECTS. È possibile scegliere un totale di 10 moduli/30 ECTS nelle seguenti categorie: 

  • 12-15 crediti ECTS in moduli tecnico-scientifici (TSM)
    I moduli TSM trasmettono competenze tecniche specifiche del profilo e si integrano ai moduli di approfondimento decentralizzati.
  • 9-12 crediti ECTS in basi teoriche ampliate (FTP)
    I moduli FTP trattano principalmente basi teoriche come la matematica, la fisica, la teoria dell’informazione, la chimica ecc. I moduli ampliano la competenza scientifica dello studente e contribuiscono a creare un importante sinergia tra i concetti astratti e l’applicazione fondamentale per l’innovazione 
  • 6-9 crediti ECTS in moduli di contesto (CM)
    I moduli CM trasmettono competenze supplementari in settori quali gestione delle tecnologie, economia aziendale, comunicazione, gestione dei progetti, diritto dei brevetti, diritto contrattuale ecc.

La descrizione del modulo (scarica il pdf) riporta le informazioni linguistiche per ogni modulo, suddivise nelle seguenti categorie:

  • Insegnamento
  • Documentazione
  • Esame
Ordinary Differential Equations and Dynamical Systems (FTP_OrdDiff)

In this module, students learn which class of dynamical phenomena can be described with systems of ordinary differential equations. They learn to recognize the fundamental behavior patterns of these systems and also to develop simulation models for them.

Requisiti

Knowledge and abilities at the level of a completed Bachelor's degree in:

  • Differential and integral calculus
  • Ordinary differential equations
  • Matrix calculus
  • Complex numbers

Obiettivi di apprendimento

  • Description of dynamical phenomena with differential equations
  • Analysis of system behavior
  • Knowledge of fundamental behavior patterns, understanding the connection with system structure
  • Development and simulation of models for dynamical systems
  • Knowledge of numerical methods for solving systems of differential equations

Contenuti del modulo

  • Topic 1: Modeling physical systems with differential equations, analysis of dynamical systems by way of example
  • Topic 2: Analytical and numerical methods
  • Topic 3: Systems of differential equations, state diagram, block diagrams
  • Topic 4: Trajectories, equilibria, linear stability analysis, eigenmodes, the example of linear, time-invariant (LTI) systems
  • Topic 5: Non-linear systems, bifurcation, chaos, discrete dynamical systems

Metodologie di insegnamento e apprendimento

Lecture units: lecture, working on and discussing short exercises
Tutorial units: working on and discussing set exercises
Private study: study of the literature, working on assignments and exercises

Bibliografia

[1] Differential Equations, An Introduction to Modern Methods and Applications, J. R. Brannan and W. E. Boyce,John Wiley and Sons, 2015

[2] Nonlinear Dynamics and Chaos, S.H. Strogatz, Westview press, 2014

[3] Differential Equations, Dynamical Systems, and an Introduction to Chaos, M. W. Hirsch, S. Smale, R. L. Devaney. Academic Press, 2012

[4] Differential Equations, A Dynamical Systems Approach, J.H. Hubbard, B.H. West, Springer,1997

Scarica il descrittivo completo del modulo

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