29910 - Mathematics III

Syllabus Information

2017/18
Subject:
29910 - Mathematics III
Faculty / School:
110 - Escuela de Ingeniería y Arquitectura
Degree:
435 - Bachelor's Degree in Chemical Engineering
ECTS:
6.0
Year:
1
Semester:
435-First semester o Second semester
107-Second semester
Subject Type:
Basic Education
Module:
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5.1. Methodological overview

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

• Exposition of contents and results on the subject together with problem solving and practical exercises in the classroom, encouraging student participation.
• Student daily work on classroom's activities.
• Application of the methods, concepts and results presented in the classroom to the resolution of problems and exercises by the students, both individually and in groups.
• Development of lab sessions in small groups using computer resources available at the School.
• Development of optional additional activities throughout the semester to provide incentives for continued and autonomous student work.
• Personal attention to the students during the office hours established by the teacher.

The following activities are offered to the students to help them to achieve the expected results:

1) Classroom expositions.

3 hours a week will be devoted to theoretical and problem classes. Theoretical results will be complemented with problem solving and practical exercises to make the development of the subject as clear as possible.

A collection of problems and exercises will be available to the students. Some of them will be solved in the classroom, and others will be given as recommended material for the student.

2) Lab.

A 2 hours lab session every other week will take place using computer resources available at the School. The student will get a guide to be developed  in each session.

3) Supervised work.

Students may perform some work directed or supervised by the teacher. The teacher will inform  the students about its evaluation date.

5.3. Syllabus

The contents of the course can be divided into two sections: Ordinary Differential Equations (ODE's) and Partial Differential Equations (PDE's).

Section 1: Ordinary Differential Equations:

• First-order equations: Geometric aspects. Existence and uniqueness of solutions. Basic methods of integration.
• Higher-order linear equations:  homogeneous and nonhomogeneous.  Equations with constant coefficients. Undetermined coefficients method. Variation of parameters. Reduction of order. Cauchy-Euler equation.
• Linear systems: homogeneous and nonhomogeneous systems. First-order systems with constant coefficients. Variation of parameters. Stability of first-order systems.
• Numerical solutions of ordinary differential equations: Runge-Kutta methods.

Section 2: Partial Differential Equations:

• Fourier series.
• Separation of  variables.
• Boundary-value problems for second-order linear equations: heat equation, wave equation and Laplace's equation.

5.4. Course planning and calendar

`Schedule of classes and works' evaluation`
`Classes and practical sessions in the laboratory are held according to the schedule and times established by the Engineering School, available on its website.`
`Each teacher will inform about the office hours.`
`Other activities will be planned and announced well in advance.`

5.5. Bibliography and recommended resources

 BB Edwards, Charles Henry, Jr.. Ecuaciones diferenciales elementales con aplicaciones / C.H. Edwards,jr., David E. Penney ; traducción Habacuc Pérez Castillo ; revisión técnica Francisco Javier Sánchez Bernabé . - [1a. ed. en español, reimp.] México [etc.] : Prentice-Hall Hispanoamericana, 1991 BB Zill, D.G., Cullen, M.R.. Matemáticas avanzadas para Ingeniería, vol. 1: Ecuaciones diferenciales / D.G. Zill, M.R. Cullen. 3ª edición. McGraw-Hill Interamericana, México 2006. BC Boyce, William E.. Ecuaciones diferenciales y problemas con valores en la frontera / William E. Boyce, Richard C. DiPrima . - 4ª ed., [reimp.] México [etc.] : Limusa Wiley, cop. 2007 BC Burden, R.L., Faires, J.D., Reynolds, A.C.. Análisis numérico / R.L. Burden, J.D. Faires, A.C. Reynolds, Grupo Editorial Iberoamericano, México 2004 BC Kreyszig, Erwin. Matemáticas avanzadas para ingeniería / Erwin Kreyszig . - 3a. ed. México : Limusa, cop. 2000 BC Marcellán, Francisco. Ecuaciones diferenciales : problemas lineales y aplicaciones / Francisco Marcellán, Luis Casasus, Alejandro Zarzo . [1a ed. en español] Madrid [etc.] : McGraw-Hill, D.L. 1990 BC Métodos numéricos para la Física y la Ingeniería / Luis Vázquez Martínez ... [et al.] . Madrid [etc.] : McGraw Hill, cop. 2009 BC Nagle, R. Kent. Ecuaciones diferenciales y problemas con valores en la frontera / R. Kent Nagle, Edward B. Saff, Arthur David Snider ; traducción, Óscar Palmas Velazco ; revisión técnica, Juan Carlos del Valle Sotelo . - 3ª ed. México [etc.] : Pearson Educación, 2001 BC Quarteroni, Alfio. Cálculo científico con MATLAB y Octave / A. Quarteroni, F. Saleri Milano : Springer, cop. 2006 BC Simmons, George Finlay. 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. 1993