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Academic Year/course: 2017/18

423 - Bachelor's Degree in Civil Engineering

28700 - Mathematics applied to engineering I


Syllabus Information

Academic Year:
2017/18
Subject:
28700 - Mathematics applied to engineering I
Faculty / School:
175 - Escuela Universitaria Politécnica de La Almunia
Degree:
423 - Bachelor's Degree in Civil Engineering
ECTS:
6.0
Year:
1
Semester:
First semester
Subject Type:
Basic Education
Module:
---

5.1. Methodological overview

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

Strong interaction between the teacher and the 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 "Matemática Aplicada a la Ingeniería I" is conceived as a stand-alone combination of contents, yet organized into two fundamental and complementary forms, which are: the theoretical concepts of each teaching unit and 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 solves 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.

Regarding to the slides, proposed exercise photocopies, laboratory session guides and other materials used in class, all of them are going to be available on the Moodle platforma of this subject.

 

 Material Format
Topic theory notes Paper/repositry
Topic problems
Topic theory notes Digital/Moodle, E-mail
Topic presentations
Topic problems
Related links
Educational software Open source Maxima and Octave

5.2. Learning tasks

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 semester, in other words, 10 hours per week for 15 weeks of class.

A summary of a weekly timetable guide can be seen in the following table. These figures are obtained from the subject file in the Accreditation Report of the degree, taking into account the level of experimentation considered for the said subject is moderate.

 

Activity Weekly school hour
Lectures 6
Other activities 3

 

Nevertheless, the previous table can be shown into greater detail, taking into account the following overall distribution:

  • 52 hours of lectures, with 50% theoretical demonstration and 50% solving type problems.
  • 8 hours of written assessment tests, one hour per test.
  • 90 hours of personal study, divided up over the 15 weeks of the 1st semester.

There is a tutorial calendar timetable set by the teacher that can be requested by the students who want a tutorial.

5.3. Syllabus

Introduction to the open-source software Maxima and revision of real functions of real variables

Limits and Continuity of functions
  • Limits, indeterminate forms, equivalence functions
  • Continuity and discontinuity of functions
  • Classical theorems
  • Bisection method

The derivative

  • The derivative, the tangent (straight) line, properties and rules
  • The chain rule
  • Implicit differentiation, inverse function and parametric functions
  • Newton's Method
  • Classical theorems: Rolle, Mean value and L'Hôpital
  • Taylor polynomials and approximations
  • Interpolation and numerical differentiation
  • Monotonic function, increasing and decreasing functions, concavity and convexity of functions

Integration

  • Riemmann Integral and its basic properties
  • Antiderivatives and indefinite integration
  • Fundamental theorems of Calculus
  • Improper integrals
  • Geometric applications
  • Numerical integration

System of linear equations

  • Groups, rings and fields
  • System of linear equations: elementary operations
  • Gaussian elimination and rank of a matrix
  • Theorems of characterization (Rouché-Frobenius)
  • Determinants
  • Numerical Gaussian elimination, condition number
  • Decompositions: LU, QR and Cholesky
  • Iterative methods

Vector spaces with inner products

  • Linearly independent sets, dimension and basis
  • Subspaces of vector spaces
  • Inner product
  • Length, angles and orhtogonality
  • Orthogonal subspaces and sets
  • Orthogonal projection and optimal approximation

Diagonalization

  • Eigenvalues and eigenvectors
  • Spectral decomposition and polynomials of matrices
  • Normal matrices
  • Numerical methods for approximating eigenvalues
  • Compatible matrices
  • Singular value decomposition (SVD)

5.4. Course planning and calendar

The dates of the final exams will be those that are officially published at Distribución de exámenes.

The written assessment tests will be related to the following topics:

  • Test 1: Limits and continuity.
  • Test 2: The derivative.
  • Test 3: Infinitesimal calculus.
  • Test 4: System of linear equations.
  • Test 5: Vector spaces.
  • Test 6: Linear Algebra.

 

Week Topic Contents Test Weight Themes
1 1 Maxima - functions  First test  5%  Limits - Continuity
2 2 Limits - Continuity
3 3 The derivative   Second test   5% The derivative
4 Taylor
5 Interpolation
6 4 Integration  First written exam   40%   Infinitesimal calculus
7 Applications
8 Numerical integration
9 5 System of linear equations Third test   5%   Linear systems
10 Determinants
11 Numerical Linear Algebra
12 6 Vector spaces  Fourth test  5%  Vector spaces
13 Optimal approximation
14 7 Diagonalization Second written exam   40%  Linear Algebra
15 Singular value decomposition

5.5. Bibliography and recommended resources

Bibliography

 

Updated bibliography on this subject is available in Spanish and can be consult on the webpage of the library at: http://psfunizar7.unizar.es/br13/eBuscar.php?tipo=a

 

 

BB Burgos Roman, Juan de. Algebra lineal y geometría cartesiana / Juan de Burgos Román . - 2ª ed. Madrid : McGrawHill, D.L. 1999
BB Burgos Román, Juan de. Cálculo infinitesimal de una variable / Juan de Burgos Román Madrid[etc.] : McGraw-Hill, D.L.1997
BB Chapra, Steven C.. Métodos numéricos para ingenieros / Steven C. Chapra, Raymond P. Canale ; revisión técnica José Job Flores Godoy , Enrique Muñoz Díaz . - 7ª ed. México D. F. : McGraw-Hill/Interamericana, cop. 2015
BB Larson, Ron. Precálculo / Ron Larson, Robert Hostetler ; [traducción del inglés por, Javier León Cárdenas] . - 7ª ed. Barcelona [etc.] : Reverté, cop. 2008
BC Apostol, Tom M.. Calculus. Vol.1, Cálculo con funciones de una variable, con una introducción al álgebra lineal / Tom M. Apostol. - 2ª ed. reimp. Barcelona [etc.] : Reverté, cop. 2002
BC Apostol, Tom M.. Calculus. Vol.2, Cálculo con funciones de varias variables y álgebra lineal, con aplicaciones a las ecuaciones diferenciales y a las probabilidades / Tom M. Apostol. - 2ª ed., 7ª reimp. Barcelona, [etc.] : Reverté, D.L. 2002
BC Coquillat Blasco, Fernando. Cálculo integral : metodología y problemas / Fernando Coquillat . - Nueva ed. amp. Madrid : Tebar Flores, D.L. 1997
BC Demidovich, B.P.. 5.000 problemas de análisis matemático / B.P. Demidóvich ; traducido del ruso por Emiliano Aparicio Bernardo Madrid : Paraninfo, 1976
BC Fuertes García, Jesús. Problemas de cálculo infinitesimal / Jesús Fuertes García , Jesús Martínez Hernando . - [1a. ed. en español] Madrid [etc.] : McGraw-Hill, D.L.1997
BC Galindo Soto, Félix. Guía práctica de cálculo infinitesimal en una variable real / Félix Galindo Soto, Javier Sanz Gil, Luis A. Tristán Vega . - 1ª ed. Madrid [etc.] : Thomson, D. L. 2003
BC García Castro, Fernando. Cálculo infinitesimal-I / Fernando García Castro, Andrés Gutiérrez Gómez . - [5a. ed.] Madrid : Pirámide, D.L. 1992
BC García Castro, Fernando. Cálculo infinitesimal-II / Fernando García Castro, Andrés Gutiérrez Gómez Madrid : Pirámide, 1990-1992
BC Larson, Ron. Cálculo 1 : De una variable / Ron Larson, Bruce H. Edwards ; revisión técnica, Marlene Aguilar Abalo ... [et al.] ; [traducción: Joel Ibarra Escutia ... (et al.)]. - 9ª ed. México [etc.] : McGraw Hill, cop. 2010
BC Larson, Ron. Cálculo 2 : De varias variables / Ron Larson, Bruce H. Edwards ; revisión técnica, Marlene Aguilar Abalo ... [et al.] ; [traducción: Joel Ibarra Escutia ... (et al.)]. - 9ª ed. México [etc.] : McGraw Hill, cop. 2010
BC Rojo, Jesús. Algebra lineal / Jesús Rojo . - 2ª ed. Madrid [etc.] : McGraw-Hill Interamericana, D. L. 2007
BC Stewart, James. Precálculo : matemáticas para el cálculo / James Stewart , Lothar Redlin, Saleem Watson ; revisión técnica Héctor Vidaurri, Alejandro Alfaro . - 5ª ed. México D. F. : Thomson, cop. 2007