# Physics for Mathematicians

## Prerequisites

The subject Physics, to be delivered in the first course of the Bachelor of Mathematics at Universitat Autonoma de Barcelona, has the official
code 100090. With 12 ECTS is a 1-year term subject divided in two semesters. The first one is mostly focused on what is called classical mechanics,
the second one comprise electromagnetism and special relativity.

The professor in charge of the theory part for the first semester is Jorge Segovia (jorge.segonza@gmail.com / IFAE@UAB) and for the second semester
is Joaquim Matias (joaquim.matias@uab.cat / IFAE@UAB). \textcolor{blue}{For explaining the associated problems is not yet clear. However, for the first
semester, Alba Cervera Lierta (a.cervera.lierta@gmail.com / BSC-CNS) is, for sure, the professor [missing second semester and people in charge of the seminars]}.

Any prior knowledge beyond the level of {\it Bachillerato} in Mathematics and Physics is not needed. However, it is advisable that the student has some
elemental ability in both subjects:

- Mathematics: function theory, derivation, integration and concepts and operations with vectorial quantities and scales.
- Physics: not indispensable since the subject starts from the elemental principles to a zero level. However, students who have followed a course in Physics in "Bachillerato" have an important advantage.

Concerning the first part of the course (first semester), it is focused on classical mechanics. The majority of students who have received a training in Physics in the {\it Bachillerato} will be familiar with this part. Therefore, our main concern here will be to increase the rigor of the concepts that we are going to see:

Introduction. Units systems. Kinematic particular cases of movement. Concept of relative movement. Dynamical laws of Newton. Inertial and non-inertial reference systems. Forces and moments. Work and kinetic energy. Conservative forces and potential energy. Mechanical energy and conservation theorem. Simple, dampened, forced harmonic oscillators, forced in 1-dimension. Movement in 2 or 3 dimensions. Introduction to vector analysis. Central forces Gravitation Kepler Laws. Newton's universal law of gravitation. Particle systems. Mass center Collisions Solid and Fluid Mechanics. Waves on a rope. Rotating reference systems. The Coriolis theorem.

In the second part, the objective is to present the laws that govern the electrical and magnetic fields, using some of the concepts introduced in the first part. Finally, the third major topic of this course is (special) relativity. This is new material for all students and therefore, there is no prior knowledge required, in addition to the concepts of inertial reference systems and transformations of Galileo that are dealt with in the first part of the course.

## Main Goal

Someone could have asked the question: why does a mathematician needs to learn a basic course of physics? Usually, are physicists that need
mathematics in order to describe the way in which Nature is working. This is because the language for science is mathematics and thus the only
way of speaking science is writing in mathematics. However, from my point of view, mathematics reach its total powerful when it is applied to
human deaylife more than one uses it for abstract concepts. Examples are: data science, investments and stocks, consulting... The most easy way
of applying mathematics to real life problems for an undergraduate student is Physics and that is why this course appear natural here.

While it is true that Mathematics are more necessary for those who want to approach Physics that is the other way round, there is no doubt that
Physics is a very important test ground for mathematicians. Not only to enrich and test mathematical concepts from a practical but also epistemological
point of view. That is why it is so important that future graduates in Mathematics have a training in Physics.

## Skills

## Learning outcomes

## Methodology

Two types of teaching methodology are presented in this subject: one for the theoretical part and the other for problems.

The theoretical part of the subject will be organized in master classes. They will be dynamic with a double objective: i) present,
discuss and demonstrate in detail the subject and ii) ask students about their previous knowledge and about their progress in the subject. This
will be particularly important for a first-year subject, taking into account the wide sample of students who have different levels of knowledge.

The practical part of the course will be structured in the classes of problems and seminars. During the seminars, organized in small groups of
students (one third of the total), the students will work alone or in small groups of 2 or 3 students and will face the proposed problems by consulting
the bibliography and the notes of the theoretical classes. The teacher will have an active and individualized role, as far as possible, to see which are the
most important conceptual difficulties encountered by students. During the seminar, when considered necessary, some smaller simple problems will also be presented
that exemplify some of the aspects that have been presented to the theory class. In the lectures of problems, the most complex and important problems that have been
proposed will be solved in detail, emphasizing the relevant theoretical aspects. These training activities are complemented by a series of hihg-level problems that will
be proposed to solve by the student. He/she will deliver one of them in pre-established dates. The objective of these problems will be to make a personal in-depth analysis
of some of the most relevant aspects of the subject presented.

## Evaluation

The score of the course will be composed during the first semester by 70\% with the score of exam(s) (one or more) and 30\% in the continuous evaluation (delivery of problems, problems made in class, etc.). In the second semester, the same rule will be followed, 70\% with the exam(s) and 30\% with the continuous evaluation focused on the delivery of proposed problems. The final grade will be the average of both notes for each semester. The "Matriculas de honor" will be awarded in terms of this final note (without waiting for the 2nd opportunity exam). The 2nd opportunity exam consists of two parts (one per semester). Both parts must be done if the two semesters are suspend or just the part corresponding with the failed semester. The average in the latter case will be between the note of the approved semester and the note from the part of the 2nd opportunity exam (if approved).

## Bibliography

**Note**that volumes I and II are appropiate for the first and second semester, respectively.