Syllabus Information

5.1. Methodological overview

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The learning process designed for this subject is based on the following:

Strong interaction between the teacher/student. This interaction is brought into being through a division of work and responsibilities between the students and the teacher. Nevertheless, it must be taken into account that, to a certain degree, students can set their learning pace based on their own needs and availability, following the guidelines set by the teacher.

The current subject, Matemáticas III, is conceived as a stand-alone combination of contents, yet organized into three fundamental and complementary forms, which are: the theoretical concepts of each teaching unit, the solving of problems or resolution of questions, at the same time supported by other activities.

The organization of teaching will be carried out using the following steps:

Theory Classes:

Theoretical activities carried out mainly through exposition by the teacher, where the theoretical supports of the subject are displayed, highlighting the fundamental, structuring them in topics and or sections, interrelating them.

Practical Classes:

The teacher resolves practical problems or cases for demonstrative purposes. This type of teaching complements the theory shown in the lectures with practical aspects.

Individual Tutorials:

Those carried out giving individual, personalized attention with a teacher from the department. Said tutorials may be in person or online.

DEFENSE

The methodology of the course encourages students' continuous assessment focusing on the most practical aspects of differential equations. In order to achieve this goal, the theoretical concepts of the subject are presented with examples and case studies. Additionally, the notions discussed in class are reinforced weekly with tutorials and seminars. Also, the use of a mathematical software tool is promoted.

5.2. Learning tasks

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The programme offered to the student to help them achieve their target results is made up of the following activities…

Involves the active participation of the student, in a way that the results achieved in the learning process are developed, not taking away from those already set out, the activities are the following:

• Face-to-face generic activities:
  • Theory Classes: The theoretical concepts of the subject are explained and illustrative examples are developed as support to the theory when necessary.
  • Practical Classes: Problems and practical cases are carried out, complementary to the theoretical concepts studied.
• Generic non-class activities:
  • Study and understanding of the theory taught in the lectures.
  • Understanding and assimilation of the problems and practical cases solved in the practical classes.
  • Preparation of seminars, solutions to proposed problems, etc.
  • Preparation of the written tests for continuous assessment and final exams.

The subject has 6 ECTS credits, which represents 150 hours of student work in the subject during the trimester, in other words, 10 hours per week for 15 weeks of class.

DEFENSE

Theoretical lectures for the understanding of the basic knowledge, fostering a participatory approach.

Exercise and problem lectures, combining standard resolution of exercises on the blackboard with group work and discussion.

Computer lab sessions using a specific mathematical software. Classes are designed to allow students to practice and develop a wide range of practical and manipulative skills.

Personal attention both in small groups and individually.

Individual continuous work from the beginning of the academic year. Basic theoretical contents, worksheets, guides of computer lab sessions as well as any other complementary material are available on the Moodle platform.

5.3. Syllabus

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Matemáticas III program:

1. Ordinary Differential Equations: basic concepts, existence and uniqueness.
2. Analytic solvability.
3. Qualitative aspects: fixed points and linear stability.
4. Numerical methods: Euler, Runge–Kutta.
5. Higher orden ODE: Oscillators; resonance. Beam stability.
6. Higher order numerical methods (FDM y FEM).
7. Introduction to Partial Differential Equations: separation of variables; vibrations.
8. Laplace Transform.
9. Laplace Transform Applications.
10. Discrete time systems.
11. The Z Transform.
12. Z Transform Applications.
13. Fourier Series and Fourier Transform.
14. Applications of Fourier Series and Transforms.
15. Discrete Time Fourier Transform: FFT and Applications.

DEFENSE

The contents of this subject are organized as follows:

Chapter 1: Introduction to differential equations

Chapter 2: First-order ordinary differential equations

Chapter 3: Geometrical interpretation of first-order ordinary differential equations

Chapter 4: Higher-order ordinary differential equations

Chapter 5: System of ordinary differential equations

Chapter 6: Laplace transform

Chapter 7: Partial differential equations

Computer lab session 1: Symbolic computation and ordinary differential equations

Computer lab session 2: Numerical methods for ordinary differential equations

5.4. Course planning and calendar

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The dates of the final exams will be those that are officially published at http://www.eupla.es/secretaria/academica/examenes.html.

DEFENSE

The course is organized in 15 weeks of two-hour lectures twice a week approximately. The academic calendar, computer lab sessions, and the formal examination dates are published on the Moodle platform and the website of the Institution (http://cud.unizar.es) at the beginning of the academic year.

5.5. Bibliography and recommended resources

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Main resources

• Subject presentations (available in the subject's Moodle webpage)
• Problem sheets (available in the subject's Moodle webpage)
• Symbolic calculus tool Maxima http://andrejv.github.io/wxmaxima/.

Bibliography

• BB Matemáticas avanzadas para ingeniería / Glyn James … [et al.] ; traducción, Elena de Oteyza de Oteyza, Carlos Hernández Garciadiego ; revisión técnica, Juan Carlos del Valle, Juan Aguilar Pascual . - 2a ed. México [etc.] : Pearson Educación, 2002
• BB Zill, Dennis G.. Ecuaciones diferenciales con problemas de valores en la frontera / Dennis G. Zill, Michael R. Cullen . - 6ª ed. México D. F. : International Thomson, cop. 2006
• BC Ecuaciones diferenciales y problemas con valores en la frontera / R. Kent Nagle, Edward B. Saff, Arthur David Snider ; traducción, Óscar Alfredo Palmas Velazco ; revisión técnica, Ernesto Filio López … [et al.] . - 4ª ed. México [etc.] : Pearson Educación, 2005
• BC Folland, Gerald B.. Fourier analysis and its applications / Gerald B. Folland.. - 1º edición Pacific Grove, Calif : Wadsworth & Brooks/Cole Advanced Books & Software, c1992.
• BC Kress, Rainer. Numerical analysis / Rainer Kress New York : Springer, cop. 1998
• BC Quarteroni, Alfio. Cálculo científico con MATLAB y Octave / A. Quarteroni, F. Saleri Milano : Springer, cop. 2006
• BC Simmons, George F.. Ecuaciones diferenciales : con aplicaciones y notas históricas / George F. Simmons ; con un capítulo sobre métodos numéricos de John S. Robertson ; traducción Lorenzo Abellanas Rapun . - 2a ed. Madrid [etc.] : McGraw-Hill, D.L. 1998

You can also view an updated reference list through the webpage of the UNIZAR Library: http://psfunizar7.unizar.es/br13/eBuscar.php?tipo=a 

DEFENSE

5.5 Bibliography and recomended resources