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Physics I

Code: EIC0010     Acronym: FISI1

Classification Keyword

Instance: 2014/2015 - 2S

Active? Yes
Web Page: http://def.fe.up.pt/eic0010
Responsible unit: Department of Physics Engineering
Course/CS Responsible: Master in Informatics and Computing Engineering

Cycles of Study/Courses

Acronym No. of Students Study Plan Curricular Years Credits UCN Credits ECTS Contact hours Total Time
MIEIC 195 Syllabus since 2009/2010 1 - 6 56 162

Teaching Staff - Responsibilities

Teacher Responsibility
Jaime Enrique Villate Matiz

Teaching - Hours

Lectures: 2,00
Recitations: 2,00
Type Teacher Classes Hour
Lectures Totals 1 2,00
Jaime Enrique Villate Matiz 2,00
Recitations Totals 9 18,00
Jaime Enrique Villate Matiz 6,00
Victor Hugo Granados Fernandez 4,00
Maria Helena Sousa Soares de Oliveira Braga 4,00
Joana dos Santos Brojo Ascenso 4,00

Teaching language

Suitable for English-speaking students


Physics is the foundation of any Engineering field. With the advent of computers, the kind of physical problems that can be solved in an introductory course has expanded significantly. Computational physics and simulation techniques allow students to get a wider view of physical phenomena without requiring complicated analytical methods. The computational techniques developed to solve mechanics problems have been applied to other areas outside physics, giving rise to the general theory of dynamical systems.

This course aims to give the student basic background knowledge on dynamics and the computational techniques used to solve dynamical systems. A Computer Algebra System (CAS) is used, in order to allow the student to solve practical problems in mechanics and dynamical systems, rather than spending their time learning abstract analytical techniques. The knowledge on dynamics and computer modeling of physical systems acquired will be very important in other courses of their curriculum: computer graphics and visualization, games theory, simulation and scientific computing.

Learning outcomes and competences

In order to pass this course students must prove to be able to:

  • Solve simple equations of motion analytically, using the separation of variables method.
  • Identify the forces and torques acting on a mechanical system and write down the equations of motion.
  • Analyze a dynamical system and identify its state variables, evolution equations and type of system.
  • Find the equilibrium points of a dynamical system and explain their features.
  • Solve the evolution equations of a system numerically and interpret the obtained solutions.

Working method


Pre-requirements (prior knowledge) and co-requirements (common knowledge)

High-school physics. Introductory College Calculus. Linear Algebra.


  1. Kinematics. Solution of simple motion equations using the method of separation of variables.

  2. Vector kinematics. Identification of the degrees of freedom of a mechanical system and resolution of systems of equations of motion.

  3. Curvilinear motion. Tangent and normal vectors. Centripetal acceleration. Trajectory curvature. Kinematics of rigid bodies.

  4. Vector Mechanics. Newton's laws. Types of forces found in mechanical systems.

  5. Rigid body dynamics. Addition of forces. Torque. Moment of inertia. Equations for the plane motion of rigid bodies.

  6. Work and energy. Relations between work and energy. Conservative and dissipative forces.

  7. Dynamical systems. Phase space. Stable and unstable equilibrium. Phase portraits. Conservative systems.

  8. Lagrangian mechanics. Generalized coordinates, velocities and forces. Lagrange equations. Lagrange multipliers.

  9. Linear systems. Harmonic oscillators. Classification of the equilibrium points. Eigenvalues and eigenvectors. Stability analysis.

  10. Non linear systems. Pendulums. Linear approximations. Jacobian matrix. Phase spaces with many dimensions.

  11. Limit cycles and two-species systems. Van der Pol oscillator. Predator-prey systems. Evolution and coexistence of two species.

  12. Chaotic systems. Asymptotic behavior, strange attractors and chaotic systems.

Mandatory literature

Jaime E. Villate; Dinâmica e Sistemas Dinâmicos, edição do autor, 2012. ISBN: 978-972-99396-1-7 (Available in http://def.fe.up.pt)

Complementary Bibliography

S. Targ ; trad. de Albano Pinheiro e Melo; Curso teórico-prático de mecânica
Steven H. Strogatz; Nonlinear dynamics and chaos. ISBN: 0-7382-0453-6
Lawrence Perko; Differential equations and dynamical systems. ISBN: 0-387-95116-4

Teaching methods and learning activities

This is a practical course, with an active teaching methodology using computer tools for e-learning, computer algebra system (CAS) and simulations. The practical sessions are conducted in the Physics Studio of the Department of Engineering Physics (room B233). During those sessions students work in groups of two at one of the computers in the room, which has access to the support material including some practical activities or simulations, lecture notes, multiple-choice questions and proposed problems. Students should answer the multiple-choice questions among and solve some of the problems in the chapter for that week. The remaining problems in the chapter are left as homework.

The lectures are used to make experimental demonstrations and simulations, as well as giving further explanations for the textbook material (http://def.fe.up.pt/en) and the computer algebra system used. The support for this course, including lecture notes, teaching materials, quizzes results, and communication among students and teachers, is done using the e-learning server (http://def.fe.up.pt/eic0010) which has public access, except for the sections related to evaluation.




Physical sciences > Physics > Classical mechanics
Physical sciences > Mathematics > Chaos theory
Physical sciences > Mathematics > Computational mathematics
Physical sciences > Mathematics > Mathematical analysis > Differential equations

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation Weight (%)
Exame 60,00
Participação presencial 0,00
Teste 40,00
Total: 100,00

Amount of time allocated to each course unit

Designation Time (hours)
Estudo autónomo 110,00
Frequência das aulas 52,00
Total: 162,00

Eligibility for exams


To be evaluated, students must fulfill the minimum attendance requirement which consists of not exceeding the maximum 25% of unattended classes. This minimum attendance requirement is waive for students registered as working-students and students who have attended the course in one of the two previous years.

Distributed component of the evaluation

The distributed component of the evaluation (40% of the final grade) is the mean of the 2 quizzes. A minimum of 5 is required in this component of the evaluation in order to be admitted to any of the exams. Working-students are not required to do the quizzes and their final grade will be the grade obtained in the exam. Students who have obtained a grade for the distributed component in previous years might decide to attend the course again and do the quizzes; in that case, their grade for the distributed component will be the highest between the one obtained this year and that previously obtained.


There will be two quizzes, on April 10th and June 5th, from 8:30 to 10:00 a.m. Quiz grades will have two decimal digits and their mean will be rounded to one decimal digit. Only the students that are attending the course and who do not have more than 3 unjustified absences can attend the quizes. Working students and students who have already taken the course who would like to attend the quizes must also attend the course.

Quiz absences

An unjustified absence in a quiz results on a grade of 0. Absences properly justified, within the specified time limit, give the student the right to do the missing quiz at a later date.

Calculation formula of final grade

If D denotes the grade for the distributed component and E the exam grade, the final grade is calculated with the following equation:

     Maximum ( E; 0.4*D + 0.6*E )

Namely, if the grade of the distributed component is higher than the exam grade, the distributed component will have a weight of 40% and the exam 60%. But if the exam grade is higher, the distributed component will be ignored and the final grade will be the exam grade. There is no minimum grade required in the exam and the exam grade will have one decimal digit. The final grade will be rounded to an integer (9.5 is rounded to 10 but 9.4999 is rounded to 9).

Examinations or Special Assignments


Special assessment (TE, DA, ...)

Students who are not required to attend classes and obtain a grade for the distributed component do not need to make any additional tests or assignments before the exam. The final grade will be equal to the exam grade rounded to an integer.

Classification improvement

As stipulated in the 10th item of the evaluation rules, students may attempt to improve their exam grade, only once, during either the normal or makeup exam scheduled for the course immediately after the exam where they obtained the former grade. If that next exam is in the following year it will not be necessary to attend the course again. Students who have not passed the course but have obtained a grade for the distributed component in previous years, can attempt to improve that grade by attending the course again and taking the quizzes.


It is recommended a period of off-class independent work of at least 3 hours per week, in order to keep off with the subjects introduced every week. Independently of their attendance status, it is expected from all enrolled students to preview at home the chapter of the textbook which will be covered in the following practical session. It is also recommended to periodically check the announcements and forum messages posted in the e-learning server.

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