Bachelor’s degree in Engineering Physics

Universitat Politècnica de Catalunya · BarcelonaTech

Bachelor's degree in Engineering Physics

Barcelona School of Telecommunications Engineering (ETSETB)

The bachelor’s degree in Engineering Physics, the first of its kind in Spain, is aimed at students with a strong aptitude for physics and mathematics who wish to apply the principles of these basic sciences to technological problems in a multidisciplinary environment, and who accept the challenge of inventing the technology of the future and pursuing research that will transform the world. You will learn about fundamental concepts of physics as they are applied in various branches of engineering, gaining knowledge that will enable you to understand basic scientific principles and their application in the key emerging technologies that will drive development in the years ahead: photonics, nanotechnology, micro- and nanoelectronics, advanced materials and biotechnology. With this grounding, you will be able to pursue any master’s degree offered worldwide that is related to physics and new technologies, as well as others master's degrees in engineering disciplines such as telecommunications engineering, electronic engineering, industrial engineering and bioengineering. Graduates may be employed in industry, technology companies, research and development centres and laboratories, universities and public administrations, where they may occupy posts of greater or lesser responsibility depending on their experience, aptitudes and personal interests, or they may become entrepreneurs.

Duration
4 years
Study load
240 ECTS credits (including the bachelor's thesis). One credit is equivalent to a study load of 25-30 hours.
Delivery
Face-to-face
Language of instruction

Check the language of instruction for each subject (and timetable) in the course guide in the curriculum.

Information on language use in the classroom and students’ language rights.

Fees and grants
Approximate fees per academic year: €1,107 (€2,553 for non-EU residents). Consult the public fees system based on income (grants and payment options).
Location
Barcelona School of Telecommunications Engineering (ETSETB)
Official degree
Recorded in the Ministry of Education's degree register
Places
44
Registration and enrolment
What are the requirements to enrol in a bachelor's degree course?
Legalisation of foreign documents
All documents issued in non-EU countries must be legalised and bear the corresponding apostille.
Professional opportunities

Graduates may go on to become researchers; specialists, including heads of projects, areas and departments; and entrepreneurs, in the following settings:

  • High-tech industry
  • Electronics and nanotechnology industry
  • Telecommunications companies
  • Biotechnology, biomedicine and pharmaceutical companies
  • Companies that design systems and services based on new technologies
  • Technology consultancies
  • Technology centres
  • Research and development centres
  • Research centres and laboratories
  • Universities and research
  • Teaching
Within the framework of the courses offered by the Interdisciplinary Higher Education Centre (CFIS)
You can also take an interdisciplinary double degree coordinated by the CFIS at two UPC schools.
Further information on the CFIS website

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