In this course, we introduce vector and Fourier analysis from a hands-on, application-oriented perspective, in coordination with PHY104: Electromagnetism and Light. Vector analysis spans the differentiation and integration of vectors in two and three-dimensional space, eventually culminating with Green’s theorem in the plane and its higher-dimensional generalization, Stokes’ theorem. Changing gears, we introduce the concept of Fourier series, which give an approximation of periodic functions as an infinite sum of cosines and sines. We then use this tool to solve the wave equation on a finite domain. We conclude the course with a gentle introduction to Fourier transforms, viewed as a limit of Fourier series in the limit of infinite periodicity. Besides their intrinsic mathematical interest, these tools are widely used in Physics (Electromagnetism, Fluid mechanics, Quantum mechanics…).

PHY104 provides an overview of numerous physics concepts related to the description of light and of electromagnetic phenomena.

This course introduces the concept of fields in physics, in particular with the electric and magnetic fields, and develops students’ understanding of electrostatics, magnetostatics, geometrical and wave description of light. In addition, students explore concepts such as Coulomb’s law, Lorentz force, Gauss’ law, Ohm’s law, Faraday’s law, and others.

Upon completion of the course, the students will understand how the classical field theory of electromagnetism with the set of Maxwell equations can describe in a unified way many physical phenomena, from the propagation of light to electrostatics, magnetostatics and electromagnetic induction.

For the initial session, student evaluation is continuous throughout the semester with three written exams regularly spaced, and with equal weight. The third exam is at the end of the semester but is part of the continuous assessment. Each written exam has the same duration of 1 hour and 30 minutes, and covers a third of the course content. For these written exams, only a calculator is authorized, everything else is prohibited. To validate the PHY104 course in the initial session, a minimum average of 10/20 for these 3 written exams is required. Additionally, a project and several homeworks, distributed throughout the semester, are graded and count as a bonus added to the final PHY104 grade if the course is validated. The project gives a bonus of maximum one point, and homeworks also give a bonus of maximum one point (for all of them). 

For the remedial session (if the course is not validated in the initial session), students are evaluated by an oral exam of 45 minutes. It is a final assessment consisting of this oral exam only, with a weight of 100%. For this remedial oral exam, only a calculator is authorized, everything else is prohibited. 

In the Beginner’s Physics Lab sessions, students will have the opportunity to apply the knowledge they have acquired in LAB103 in five distinct lab sessions of 4-hour duration. Students will learn basic experimental techniques, data analysis and interpretation, and documentation of experimental work. Students will cover, in-depth: the Lorentz Force and the measurement of the specific charge (e/m) of the electron, quantization of the matter with the Franck-Hertz experiment, geometrical optics and the prism spectrometer, the speed of sound, forces and torques.

Applied Physics (PHY107) provides a combination of lectures and seminars with a clear aim to show the link between advanced engineering and high-level physical/mathematical education. The course will cover selected questions based on fluid mechanics, thermodynamics, optics, electricity and magnetism. Background obtained during courses of general physics and mathematics will be used to understand the principles of rocket propulsion, engines for hypersonic flights, peculiarities of mass-spectrometry in physics/chemistry and biology, the link between optical spectroscopy, molecular analysis and quantum mechanics etc. As a result of the course, students should be able to look at applied physics problems combining deep knowledge in mathematics and physics and to be able to formulate to resolve a set of estimates giving the idea about mechanisms involved in the considered phenomena.