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 
Vectors and Tensors in Engineering Physics (FTP_Tensors)

The course starts with an overview of classical engineering physics with special emphasis of balance and constitutive equations (i.e., continuity equations and material laws). The basic concepts of vector analysis are applied to electrodynamics, various transport phenomena, mechanical elasticity and piezo-electric effects. The concept of tensors enables the description of important anisotropic effects of solid state physics. These effects are present in crystals as well as in layered material systems, which are more and more used in modern technology. The given overview facilitates the student’s understanding and application of numerical simulation methods (e.g., FEA, multiphysics).


  • Physics, analysis, linear algebra at Bachelor’s level ,
  • The mathematical prerequisites are covered by the chapter 7-9 of [4]. The summaries of these chapters are in the appendix of this document.

Learning Objectives

  • Students are familiar with the most important basic laws of engineering physics for isotropic materials in general view form, recognize analogies between different application areas and exploit these for analyzing systems
  • Students know about the generalization of the laws for anisotropic materials and can interpret these, especially with regard to application in numerical simulation
  • Students master vector analysis and the algebra of tensors together with the standard notation conventions
  • Students understand the basics of electrodynamics and transport phenomena for anisotropic systems
  • Students understand mechanical elasticity with 3D strain and stress states and are familiar with the material laws in general form for isotropic and anisotropic bodies
  • Students understand the piezo-electric effect and its applications in engineering (sensors and actuators)

Contents of Module

  • Recapitulation of isotropic material laws (Ohm, Hook, electric polarization, heat conduction)
  • Introduction to vector and tensor calculation: scalar, vectorial and tensorial parameters, tensor algebra,
  • Transformation behavior of vectors and tensors
  • Hands-on calculation of vector analysis and tensoralgebra: electrodynamics and anisotropic transport phenomena
  • Elasticity theory with emphasis on 3D stress states
  • Piezo-effect: physical fundamentals




Introduction, motivation, repetition of fundamental physical laws from engineering physics


Scalars, vectors, divergence, gradient, curl


Integral theorems and applications of vector analysis in physics


Maxwell I: Electro- and magnetostatics


Fundamental mathematical properties of tensors, transformations of tensors


Transport phenomena, Ohm’s law,  heat conduction and diffusion


Elasticity: stress and distortion tensor, thermal expansion


Elasticity: Hooke’s law, tensors of the fourth rank, engineering diagram


Elasticity: 3D stress and distortion states


Elasticity: 3D stress and distortion states




Maxwell II: Electrodynamics


Maxwell III: Waves, Maxwell



Teaching and Learning Methods

Frontal teaching (approx. 60 %)
Presentation and discussion of case studies and problems, individual problem solving (approx. 40 %)


[1] R.E. Newham, Properties of Materials, Oxford, 2005

[2] J.F. Nye, Physical Properties of Crystals, Oxford Science Publication, 2004

[3] J.Tichy, Fundamentals of Piezoelectric Sensorics, Springer 2010

[4] E. Kreszig, Advanced Engineering Mathematics, 10th edition, Wiley, 2011

Download full module description