Spring is coming... Chicago, March 2014

Physics for Mathematicians

Professors

Jorge Segovia jsegovia@ifae.es
Alba Cervera Lierta a.cervera.lierta@gmail.com

Theory

You can find below the useful documentation of the subject:

Problems

You can find below the associated problems of the subject:

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.
It is advisable for students to take a first look at the books of the bibliography to familiarize themselves with them and get in touch with the topics that will be dealt with, especially in the first part of the course.
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

  • Faced with real situations with a mean level of complexity, ask for and analyze relevant data and information, propose and validate models using appropriate mathematical tools to finally obtain conclusions.
  • Develop a thought and a critical reasoning and to know how to communicate effectively, both in their own languages ​​and in a third language.
  • Distinguish, in the face of a problem or situation, what is substantial from what is purely casual or circumstantial.
  • Demonstrate to possess and understand knowledge in a study area that is based on the general secondary education base, and is usually found on a level that, while supported by advanced textbooks, also includes some aspects which involve knowledge from the forefront of their field of study.
  • Know how to apply their knowledge to their work or vocation in a professional way and possess the skills that are usually demonstrated through the elaboration and defense of arguments and the resolution of problems within their area of ​​work or study.
  • Have the ability to gather and interpret relevant data (usually within their area of ​​study) to issue judgments that include a reflection on relevant issues of a social, scientific or ethical nature.
  • Recognize the presence of Mathematics in other disciplines.
  • Learning outcomes

  • Understand basic physical phenomena.
  • Develop a critical thinking and reasoning and know how to communicate effectively, both in their own languages ​​and in a third language.
  • Formulate and address physical problems, identifying relevant physical principles and using estimates of order of magnitude and special limit cases to arrive at a solution that must be presented outlining suppositions and approximations.
  • Introduce yourself to the fundamentals of Physics, including classical mechanics, electromagnetism and relativity.
  • Demonstrate to possess and understand knowledge in a study area that is based on the general secondary education base, and is usually found on a level that, while supported by advanced textbooks, also includes some aspects which involve knowledge from the forefront of their field of study.
  • Know how to apply their knowledge to their work or vocation in a professional way and possess the skills that are usually demonstrated through the elaboration and defense of arguments and the resolution of problems within their area of ​​work or study.
  • That students have the ability to gather and interpret relevant data (usually within their area of ​​study) to issue judgments that reflect on relevant issues of a social, scientific or ethical nature.
  • Use mathematics to describe the physical world, selecting the appropriate equations, constructing suitable models, interpreting mathematical results and comparing them critically with experimentation and observation
  • 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

  • P.A. Tipler, G. Mosca. F\'isica para la Ciencia y la Tecnolog\'ia (vol. I and II). Ed. Revert\'e, 6a. edici\'o, Barcelona, 2010.
  • H. Young, R. Freedman, F\'isica universitaria (vol. I and II), Addison-Wesley, Pearson Education, Decimosegunda edici\'on, M\'exico 2009.
  • E. Mass\'o, Curs de relativitat especial, Universitat Aut\`onoma de Barcelona. Servei de Publicacions, ed.(06/1998), Idioma: Catal\`a, ISBN: 8449012848, Barcelona 1998.
  • A.P. French. Relatividad Especial. Ed. Reverté, 1974.

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