Physics I

Code:

EIC0010

Acronym:

FISI1

Keywords
Classification	Keyword
OFICIAL	Physics

Instance: 2011/2012 - 2S

Active?	Yes
Web Page:	http://def.fe.up.pt/eic0010
Responsible unit:	Department of Engineering Physics
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	204	Syllabus since 2009/2010	1	-	6	56	162

Teaching language

Suitable for English-speaking students

Objectives

1- BACKGROUND
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.

2- SPECIFIC AIMS
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 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. A working knowledge of dynamics and computer modeling of physical systems will be very important in other courses of their curriculum: computer graphics and visualization, games theory, simulation and scientific computing.

3- PREVIOUS KNOWLEDGE
High-school physics. Introductory College Calculus. Linear Algebra.

4- LEARNING OUTCOMES
To pass this course a student should 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.

Program

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

2. Systems with many degrees of freedom. Identification of the degrees of freedom of a mechanical system and resolution of systems of equations of motion.

3. Dynamics. Newton laws and their applications. Types of forces found in mechanical systems.

4. Work and energy. Resolution of the equations of motion using the concepts of work and energy.

5. Curvilinear motion. Tangent and normal vectors. Centripetal acceleration. Trajectory curvature.

6. Rigid bodies motion. Addition of forces. Torque. Moment of inertia. Equations for the plane motion of rigid bodies.

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

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

9. Non linear systems. Pendulums. Linear approximations. Jacobian matrix.

10. Numerical methods for dynamical systems. Euler method. Fourth-order Runge-Kutta method.

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. Bifurcations. Examples of chaotic systems.

Mandatory literature

Jaime E. Villate; Física 1. Dinâmica, edição do autor, 2012. ISBN: 978-972-99396-1-7

Teaching methods and learning activities

This is a practical course, with an active teaching methodology based on computing tools for e-learning, programming, computer algebra and simulation.

The recitation sessions are conducted in the Physics Studio of the Department of Engineering Physics (room B233). During those sessions students will work in groups at one of the terminals in the room, which has access to the support material including experiments, simulations, lecture notes, multiple-choice questions and proposed problems. Students should answer the multiple-choice questions among the group and some of the problems. The remaining problems in the chapter are left as homework.

The master lectures are used to explain the subject matter of the textbook, trying not to repeat (when possible) the same explanations given in the book, and to demonstrate the experiments, simulations and software 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 at http://def.fe.up.pt/eic0010, which has public access, except for the sections related to evaluation.

Six quizzes will be given during the practical sessions, without any previous announcement, to be solved within 20 minutes. Most of the quizzes consist of 8 multiple-choice questions, but they can also consist of one problem or handing in one of the problems solved in the class. The questions and problems used in the quizzes are similar to those found in the textbook. In every practical session students must be prepared to be tested on the subject of that session and the previous one.

The final exam consists of a first part with two problems and a second part with 15 multiple-choice questions.

During the quizzes and the exams students are allowed to use an equations sheet and a calculator or some computer program to make calculations. The equation sheet to be used could be the one given in the course's Webpage or a custom one made by the student, with no more than one A4 page.

Software

Maxima
Moodle

keywords

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

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	48,00
Participation in the activities of the e-learning site	Trabalho escrito	24,00
Final exam	Exame	4,00
	Total:	-	0,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
Exam preparation	Estudo autónomo	20
Independent study	Estudo autónomo	66
	Total:	86,00

Eligibility for exams

It will be attributed a "Frequency" grade equal to the average of the best five grades obtained in the 6 quizzes. The quizzes are graded with one decimal digit but the frequency grade is rounded to an integer between 0 and 20 (in accordance with evaluation directives).

A student will only be admitted to the final exam if:
1- The number of absences in the practical sessions was less than 25% (article 4th, number 1, FEUP evaluation rules).
2- The "Frequency" grade obtained was at least 6.

As established by Article 4th, number 3, of FEUP Evaluation Rules, these requirements are waived for students enrolled as working-student or military, and for students who already obtained the minimum Frequency Grade in the previous academic year (student union members and athletes do hav to attend the classes).

Students who do not qualify for frequency waiving and do not obtain the minimum frequency grade cannot be admitted to any of the exams.

Calculation formula of final grade

Being F the Frequency Grade and E the exam grade, the final grade is computed with the equation:

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

Namely, the frequency grade has a weight of 40% and the exam 60%, but the frequency grade should never decrease the grade of the exam; if it did, the final grade would be equal to that of the exam.

The exam grade will have one decimal grade and the frequency grade will be an integer. The final grade will be rounded to an integer (as required by the evaluation rules; 9.5 is rounded to 10, but 9.4999 is rounded to 9).

Examinations or Special Assignments

None.

Special assessment (TE, DA, ...)

The special exams (completion of the degree program and students with a Special Status) have the same format as the regular exams. Students with Military status or Working-Student status who do not have a frequency grade, will not have to make any additional assignments.

Classification improvement

As stipulated by FEUP's Evaluation Rules, the students who have already approved the course can try to improve their grade, during the additional exams of the semester when they approved the course, or in any of the exams of the following academic year. In that case, it is necessary to register for the exam within the stipulated dates. Please consult the Secretary about those dates and the registration requirements. The new grade will be calculated using the same formula explained in section "Final Grade".

Observations

Students are advised to spend at least 3 hours per week for independent study and homework. It is expected that all enrolled students, whether they attend the classes or not, study each week the material on the corresponding chapter of the textbook; during each practical session the students should have previously read the material on the textbook, in order to be able to solve the problems and pose questions to the teacher.
The course Webpage in the e-learning server should be accessed regularly.