MSE Master of Science in Engineering

The Swiss engineering master's degree

Each module contains 3 ECTS. You choose a total of 10 modules/30 ECTS in the following module categories: 

  • 12-15 ECTS in technical scientific modules (TSM)
    TSM modules teach profile-specific specialist skills and supplement the decentralised specialisation modules.
  • 9-12 ECTS in fundamental theoretical principles modules (FTP)
    FTP modules deal with theoretical fundamentals such as higher mathematics, physics, information theory, chemistry, etc. They will teach more detailed, abstract scientific knowledge and help you to bridge the gap between abstraction and application that is so important for innovation.
  • 6-9 ECTS in context modules (CM)
    CM modules will impart additional skills in areas such as technology management, business administration, communication, project management, patent law, contract law, etc.

In the module description (download pdf) you find the entire language information per module divided into the following categories:

  • instruction
  • documentation
  • examination 
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.

Prerequisites

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

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

Learning Objectives

  • 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

Contents of Module

  • 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

Teaching and Learning Methods

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

Literature

[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

Download full module description

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