Identifying Data 2016/17
Subject (*) Ecuacións Diferenciais Code 770G01011
Study programme
Grao en Enxeñaría Electrónica Industrial e Automática
Descriptors Cycle Period Year Type Credits
Graduate 1st four-month period
 Second FB 6
Language
Spanish
Galician
Teaching method Face-to-face
Prerequisites
Department Matemáticas
Coordinador
Cao Rial, María Teresa
 E-mail
teresa.cao@udc.es
Lecturers
Cao Rial, María Teresa
Suarez Taboada, Maria
 E-mail
teresa.cao@udc.es
maria.suarez3@udc.es
Web http://moodle.udc.es
General description As ecuacións diferenciais e os seus métodos de resolución son ferramentas básicas para a descrición e o estudo dos modelos matemáticos máis simples que gobernan unha gran variedade de fenómenos físicos: no ámbito da mecánica de fluídos, do electromagnetismo, da termodinámica ou da resistencia de materias. Nesta materia farase unha introducción ao estudo das ecuacións diferenciais (tanto de primeira orde coma de orde superior) e estudaranse distintos métodos de resolución tanto analíticos como numéricos. Ademais, describiranse as nocións máis básicas das ecuacións en derivadas parciais e o cálculo en variable complexa.

Study programme competencies
Code Study programme competences

Learning aims
Learning outcomes Study programme competences
To be able to write the mathematical models goberning simple physical phenomena in terms of differential equations. A6
 B1
B2
B4
 C1
To undestand the basic characteristics of differential equations: clasify them and their solving particularities. A6
 B1
B2
B4
 C1
To know and be able to aply the several analitic methods for solving ordinary differential equations (either first order or higher order). A6
 B1
B2
B4
 C1
To understand and be able to aply Laplace transform to solve systems of ordinary differential equations and initial value problems. A6
 B1
B4
 C1
To understand and be able to aply Fourier and Z-tranform to solve linear ordinary differential equations. A6
 B1
B2
B4
 C1
To understand and be able to aply simple numerical methods to approximate the solution of differential equations. A6
 B1
B2
B3
B4
 C1
To understand basic notions of partial differential equations and complex analysis and its relation with the mathematical models goberning physical phenomena in two and three dimensional spaces. A6
 B1
B2
B3
B4
 C1
To be able to use the course literature and the IT tools available to find the information required to solve a particular problem. B3
B4
B6
 C3
C6

Contents
Topic Sub-topic
Introduction to ordinary differential equations (ODE) Motivación
Terminoloxía básica: orde, tipo e linearidade
Solución xeral e solución particular
Existencia e unicidade de solución para un problema de valor inicial de primeira orde
Algunhas EDOs que gobernan fenómenos físicos na Enxeñaría
First Order ODE Ecuacións en variables separadas
Ecuacións exactas. Factor integrante
Ecuacións lineais
Aplicacións das EDOs de primeira orde
Introduction to the numerical resolution of ODE Motivación. Xeneralidades
Resolución numérica dun problema de valor inicial de primeira orde
Métodos de Euler e Runge-Kutta
Higher order ODE Ecuacións lineais de segunda orde
Ecuacións lineais homoxéneas con coeficientes constantes
Solución xeral
Ecuacións lineais non homoxéneas con coeficientes constantes
Ecuacións lineais de orde superior. Aplicacións.
Laplace Transform Definición da transformada de Laplace
Cálculo e propiedades da transformada de Laplace
Transformada inversa de Laplace
Aplicación á resolución de sistemas lineais de ecuacións diferenciais Aplicacións na Enxeñaría Eléctrica
ODE linear systems Sistemas de ecuacións diferenciais lineais de primeira orde
Estructura dos conxuntos de solucións
Wronskiano dun conxunto de funcións
Resolución de sistemas homoxéneos con coeficientes constantes
Fourier series and Z-transform Definición das series de Fourier e transformada Z
Cálculo e propiedades das series de Fourier e transformada Z
Transformada Z inversa
Aplicacións á resolución de EDOs de orde superior
Introduction to partial differential equations (PDE) Definición de EDP: orde e solución dunha EDP
EDPs de segunda orde lineais
Introducción ás ecuacións clásicas: ecuacións do calor e de ondas
Método de separación de variables

Planning
Methodologies / tests Competencies Ordinary class hours Student’s personal work hours Total hours
Guest lecture / keynote speech B2 B3 B4 C1 21 42 63
Laboratory practice A6 B1 B3 B4 B6 C3 9 9 18
Mixed objective/subjective test A6 B1 B2 C1 C6 4 0 4
Seminar A6 B1 B2 B3 B7 C1 21 42 63
 
Personalized attention 2 0 2
 
(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies
Methodologies Description
Guest lecture / keynote speech
Presentation of the subject contents. The aim of the sessions is to provide the student with the basic knowledge to allow him to explore the subject as autonomously as possible. Examples of applications are developed and related activities are proposed.
Laboratory practice Interactive practice where computer programs are used to solve problems commented in the lectures.
Mixed objective/subjective test Written test may consist of an explanation of any content of the course, the answer of test questions, the resolution of theoretical and practical issues and developing solutions to issues involving deep knowledge of the subject. They are useful to determine the degree of knowledge that students get at classes and with their personal study.
Seminar Sessions where we move from theory to practice. Specific problems of the subject developed in the lectures are solved and student's questions will be answered.

Personalized attention
Methodologies
Seminar
Laboratory practice
Description
a) The diversity of students and their training makes advisable to provide personalized guidance, which could be carried out in the framework of a tutorial action
b) In computer practice, teachers will help students in the development of the problems identified in the practical sessions, both in the management of the computer program Matlab / Octave and the understanding of the theoretical and practical aspects of differential equations
c) During the seminars, teachers will make a more detailed monitoring of students in the learning process by solving theoretical questions, problem solving and applications to simple problems in the field of Electronic Engineering.

Assessment
Methodologies Competencies Description Qualification
Seminar A6 B1 B2 B3 B7 C1 Active participation and work done in the problem solving sessions (individually or in very small groups) 20
Mixed objective/subjective test A6 B1 B2 C1 C6
Written test including the resolution of problems and short questions (related to theoretical and practical subjects) 		75
Laboratory practice A6 B1 B3 B4 B6 C3 Solving practical problems and illustration of theoretical aspects with the help of the computer program Matlab/Octave 5
 
Assessment comments

The final grade of this subjet consists of
three parts:

  • the
    grade obtained in laboratory practice, based on deliverables related to lab
    tasks: NP (between 0 and 0.5)
  • the
    grade obtained in the assorted objective test: NE (between 0 and 7.5) from
    which 0.5 points come from the final lab test and 7 points from the January
    final test.
  • the grade
    obtained in the problem solving classes: NS (between 0 and 2), from which 1
    point comes from deliverables related to class tasks, and 1 point from the
    partial test.


The final grade will be the sum of
NP+NE+NS as long as the following two conditions are met:

  • unjustified
    absence to problem solving classes do not exceed 20% and
  • the
    grade obtained in the assorted objective test NE is greater than 2.65.


Otherwise, the final grade will be the one
obtained in the objective test NE (7.5 at most).



The grades NP and NS are retained for the
present course until the second opportunity exam in July.



Should a student prefer
to be graded just with the January final test, he/she needs to explicitly ask for it during the first
weeks of the semester, and in any case before any continuous evaluation test or
deliverable is handed. As soon as any part of NS is graded, it will no longer
be possible to desist from continuous evaluation. 



Part-time students with academic
dispensation are graded through:

  • the
    grade obtained with a lab practice report: NP (between 0 and 0.5)
  • the
    grade obtained with the assorted objective test: (between 0 and 7.5) from which
    0.5 points come from the final lab test and 7 points from the January final
    test.
  • The grade of an essay applied to a real
    Engeneering problem: NS (between 0 and 2).


The final grade will be the sum of
NP+NE+NS

Sources of information
Basic S. L. Ross (1992). Ecuaciones Diferenciales. Reverté
P. Quintela (2001). Ecuaciones Diferenciales. Tórculo
G. F. Simmons (1991). Ecuaciones Diferenciales. Mcgraw-Hill
W. R. Derrick, S. I. Grossman (1984). Ecuaciones Diferenciales con aplicaciones. Fondo Educativo Interamericano
D. G. Zill (2002). Ecuaciones diferenciales con aplicaciones de modelado. Thomson learning
R. K. Nagle, E. B. Saff (2005). Ecuaciones diferenciales y problemas con valores en la frontera. Pearson Education
M. Braun (1990). Ecuaciones Diferenciales y sus Aplicaciones. Ed. Iberoaméricana
C. H. Edwards, D. E. Penney (2008). Elementary Differential Equations. Prentice-Hall
W. E. Boyce, R. C. DiPrima (2005). Elementary Differential Equations and Boundary Value Problems. John Wiley & Sons
R. K. Nagle, E. B. Saff (1992). Fundamentos de ecuaciones diferenciales. Addison-Wesley
J. Gonzalez Montiel (1988). Problemas de ecuaciones diferenciales. Publ. Univ. Politécnica de Madrid
M. R. Spiegel (2001). Transformadas de Laplace. Mcgraw-Hill

Complementary S. Rosloniec (2008). Fundamental Numerical Methods for Electrical Engineering. Springer (Capítulos 6-8)
T. B. A. Senior (1986). Mathematical Methods in Electrical Engineering. Cambridge University Press (Capítulos 2,4)


Recommendations
Subjects that it is recommended to have taken before
Cálculo/770G01001
Física I/770G01003
Alxebra/770G01006

Subjects that are recommended to be taken simultaneously

Subjects that continue the syllabus

Other comments
  • Estudo diario dos contidos tratados nas sesións expositivas, complementados co curso virtual e a bibliografía recomendada
  • Resolución tanto dos exercicios propostos nas sesións presenciais como doutros atopados na bibliografía recomendada
  • Revisar periodicamente as prácticas de ordenador, para o que se dispón das aulas de Informática de libre acceso no centro
  • Uso das horas de titoría do profesorado para resolver todo tipo de dúbidas sobre os contidos da materia.
    		•


    (*)The teaching guide is the document in which the URV publishes the information about all its courses. It is a public document and cannot be modified. Only in exceptional cases can it be revised by the competent agent or duly revised so that it is in line with current legislation.