Classical Mechanics
Code: 107842Credits: 6
| Degree programme | Type | Course |
|---|---|---|
| Mathematics | FB | 1 |
Contact lecturer
- Name :
- Marcel Alguero Casas
- Email :
- marcel.alguero@uab.cat
Teaching staff
- Gabriel Jover Mañas
Group languages
You can consult this information at the end of the document.
Prerequisites
As a first-year course in the Mathematics degree program, it should not require any prior knowledge beyond that acquired in high school. However, it is advisable for students to have some basic skills in function theory, differentiation, integration, and the use and manipulation of vector and scalar quantities.
As for Physics knowledge, it is not strictly necessary, since the course begins with the fundamental principles at an introductory level. Nevertheless, students who have taken Physics in high school will have a significant advantage. Therefore, it is recommended that students who have not studied Physics at that level take an initial look at the books listed in the bibliography in order to become familiar with and gain some exposure to the topics that will be covered in the course.
Objectives
While it is true that Mathematics is generally more necessary for those wishing to approach Physics than vice versa, it is undeniable that Physics provides a very important testing ground for mathematicians. It not only allows mathematical concepts to be enriched and tested from a practical perspective, but also from an epistemological one. For this reason, it is important that future Mathematics graduates receive a basic education in Physics.
The aim of this course is to provide students with the fundamental concepts of Classical Mechanics, many of which will already be familiar to those who have studied Physics in high school. The main focus, however, will be to develop a more rigorous understanding of these concepts.
Learning outcomes
- CM03 (Formulate physical problems, identifying the relevant physical principles and their mathematical formulation.) Formulate physical problems, identifying the relevant physical principles and their mathematical formulation.
- CM04 (Apply mathematical tools to the resolution of elementary problems in the field of Physics.) Apply mathematical tools to the resolution of elementary problems in the field of Physics.
- KM05 (Identify the main foundations of Physics, as well as its mathematical formulation.) Identify the main foundations of Physics, as well as its mathematical formulation.
- KM06 (Identify the principles of particle, fluid and wave motion.) Identify the principles of particle, fluid and wave motion.
- SM04 (Solve elementary Physics problems based on their mathematical formulation.) Solve elementary Physics problems based on their mathematical formulation.
- SM05 (Analyse experimental data and observations in the context of Physics, identifying patterns, relationships, and conclusions.) Analyse experimental data and observations in the context of Physics, identifying patterns, relationships, and conclusions.
- SM06 (Properly express fundamental physical information using the relevant mathematical language and the magnitudes and units associated with the basic concepts.) Properly express fundamental physical information using the relevant mathematical language and the magnitudes and units associated with the basic concepts.
Contents
Introduction. Systems of units. Kinematics. Motion in 2 or 3 dimensions. Introduction to vector analysis. Special cases of motion. Concept of relative motion. Dynamics. Newton’s Laws. Inertial and non-inertial reference frames. Forces and torques. Centre of mass. Work and kinetic energy. Conservative forces and potential energy. Mechanical energy and conservation theorem. Simple, damped, and forced harmonic oscillators in 1 dimension. Central forces. Gravitation. Kepler’s Laws. Newton’s universal law of gravitation. Systems of particles. Collisions. Waves.
Learning activities and methodology
| Title | Hours | ECTS | Learning outcomes |
|---|---|---|---|
| Problem-solving sessions | 14 | 0.56 | CM04, SM04, SM05, SM06 |
| Theory sessions | 30 | 1.2 | CM03, CM04, KM05, KM06 |
| Lab sessions | 6 | 0.24 | SM05, SM06 |
| Personal study | 80 | 3.2 |
This course proposes two types of teaching methodology: one for the theoretical part and one for the practical part.
On one hand, the theoretical part of the course will be organised through lectures. These will be dynamic and have a dual objective: i) to present, discuss, and demonstrate in detail the material covered in the syllabus, and ii) to use the classes as a tool, through questions to students, to get a direct sample of their level, both in terms of prior knowledge and of their progress through the course.
This will be particularly important for a first-year course, given the varied range of knowledge levels among students. The practical part of the course will be structured around problem-solving sessions and laboratory sessions. In the problem sessions, the most complex and important problems assigned will be solved in full detail, with emphasis on the most relevant theoretical aspects. Finally, in the laboratory sessions, students will be given a series of standard experimental practicals in which measurements are taken and compared with the theoretical work done. The objective will be to write a report at the end of each session describing the problem posed, the methodology followed, the data processing carried out, as well as the challenges encountered and proposals for improving the experimental practical. Since the practicals will be done in groups of 2 or 3 students, one report per group must be submitted. In addition, these formative activities are complemented by a series of higher-level problems that will be assigned and that students will submit on set dates. The aim of these problems is to provide a personal in-depth exploration of some of the most relevant aspects of the material presented.
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| Lab Reports | 20% | 9 | 0.36 | SM05, SM06 |
| Resit | 100% | 3 | 0.12 | CM04, KM05, SM04 |
| Exam (test; partial) | 40% | 3 | 0.12 | CM04, KM05, SM04 |
| Exam (test; partial) | 30% | 3 | 0.12 | CM04, KM05, SM04 |
| Problem set | 10% | 2 | 0.08 | CM03, CM04, KM05, KM06, SM04 |
The course grade will be composed of synthesis tests and continuous assessment. The synthesis tests will consist of a mid-term exam and a final exam, contributing 30% and 40% of the course grade respectively. Continuous assessment will consist of problem submissions and attendance and submission of lab reports, corresponding to 10% and 20% of the first semester grade respectively. Distinctions (Matrícula d’Honor) will be awarded based on the final grade (without waiting for the resit).
This course offers a single-assessment option. This assessment, which will take place concurrently with the second partial exam and will therefore have a duration of three hours, will consist of the submission of two problem sets, four laboratory assignments and their corresponding reports, as well as the completion of a final exam.
Bibliography
- P.A. Tipler, G. Mosca. Física para la Ciencia y la Tecnología (vol I). Ed. Reverté, 6a. edició, Barcelona, 2010.*
- H. Young, R. Freedman, Física universitaria (vol I i II), Addison-Wesley, Pearson Education, Decimosegunda edicion, Mexico 2009*
- R. P. Feynman, R. B. Leighton, M. Sands. The Feynman Lectures on Physics. Addison-Wesley, 1964.*
*Note: available online.
Software
- LaTeX
Since the syllabus of this course does not contemplate the need to use Artificial Intelligence (AI) tools in any of its phases, their use is prohibited. Any work containing AI generated parts will be considered an act of academic dishonesty and may result in a partial or total penalty on the activity grade. In severe cases, more serious sanctions may be considered.
Course groups and languages
The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE
| Type of teaching | Group | Language | Semester | Shift |
|---|---|---|---|---|
| (TE) Theory | 1 | Catalan | first semester | morning-mixed |
| (PAUL) Classroom practices | 1 | Catalan | first semester | morning-mixed |
| (SEM) Seminars | 1 | Catalan | first semester | morning-mixed |
| (SEM) Seminars | 2 | Catalan | first semester | morning-mixed |
| (SEM) Seminars | 3 | Catalan | first semester | morning-mixed |