Last update: 14-07-2015
340021 - FOMA-N1O43 - Fundamentals of Mathematics
Coordinating unit:
340 - EPSEVG - Vilanova i la Geltrú School of Engineering
Teaching unit:
743 - MA IV - Department of Applied Mathematics IV
Academic year:
2015
Degree:
BACHELOR'S DEGREE IN MECHANICAL ENGINEERING (Syllabus 2009). (Teaching unit Compulsory)
BACHELOR'S DEGREE IN INDUSTRIAL DESIGN AND PRODUCT DEVELOPMENT ENGINEERING
(Syllabus 2009). (Teaching unit Compulsory)
BACHELOR'S DEGREE IN ELECTRICAL ENGINEERING (Syllabus 2009). (Teaching unit Compulsory)
BACHELOR'S DEGREE IN INDUSTRIAL ELECTRONICS AND AUTOMATIC CONTROL ENGINEERING
(Syllabus 2009). (Teaching unit Compulsory)
ECTS credits:
6
Teaching languages:
Catalan, Spanish
Teaching staff
Coordinator:
M.Luisa Zaragozá
Degree competences to which the subject contributes
Specific:
1. CE1. Ability to solve arithmetic problems related to engineering. Aptitude to apply knowledge concerning: linear
algebra, geometry, differential geometry, differential and integral calculus, differential and partial equations, numerical
methods, numerical algorithms, statistics and optimization.
Transversal:
2. SELF-DIRECTED LEARNING - Level 1. Completing set tasks within established deadlines. Working with
recommended information sources according to the guidelines set by lecturers.
Learning objectives of the subject
Study load
Total learning time: 150h
Hours large group:
60h
40.00%
Hours medium group:
0h
0.00%
Hours small group:
0h
0.00%
Guided activities:
0h
0.00%
Self study:
90h
60.00%
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Universitat Politècnica de Catalunya
Last update: 14-07-2015
340021 - FOMA-N1O43 - Fundamentals of Mathematics
Content
1. Complex numbers
Learning time: 20h
Theory classes: 8h
Practical classes: 0h
Self study : 12h
Description:
How to operate with complex numbers and how to use them to decompose polynomials.
1
2
3
4
Complex numbers. Form Cartesian, polar and exponential.
Operations and properties. Euler formula.
Zeros of polynomials. Fundamental theorem of algebra.
Decomposition of polynomials in the real and complex.
2. Vector spaces.
Learning time: 26h
Theory classes: 10h
Practical classes: 0h
Self study : 16h
Description:
How to determine the dependence / independence of vectors and calculate dimensions and bases of a subspace.
1
2
3
4
Review of systems of linear equations. Methods Gauss and Cramer.
Vector spaces. Subspace.
Linear independence of vectors.
Dimension and basis of a vector space.
3 . Linear maps
Learning time: 30h
Theory classes: 12h
Practical classes: 0h
Self study : 18h
Description:
Linear maps, calculation kernel and image and its dimensions. His performance for solving systems. vectors and
eigenvalues.
1
2
3
4
5
Linear maps. Matrix associated with the linear map.
Image and kernel of a linear map. Rank Theorem.
Interpretation of a linear system in terms of a linear map.
Preimage of a vector.
Vectors and eigenvalues of a linear map. Characteristic polynomial.
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Universitat Politècnica de Catalunya
Last update: 14-07-2015
340021 - FOMA-N1O43 - Fundamentals of Mathematics
4. Diferential calculus
Learning time: 35h
Theory classes: 18h
Practical classes: 0h
Self study : 17h
Description:
Regarding the functions of a real variable: Study of continuity, differentiability study and calculation of the
tangent, the Taylor polynomial calculation, calculation of relative and absolute extreme.
1 Review of elementary functions.
Continuity 2. Bolzano.
3 Derivation. Geometric interpretation of the derivative. L'Hôpital rule.
4 Taylor polynomial. Waste. Application to the study of local functions.
5 Extreme absolute and relative.
5. Integration calculus
Learning time: 32h
Theory classes: 12h
Practical classes: 0h
Self study : 20h
Description:
Calculate change of variable primitives and parts. Calculation of integrals of rational functions. Rule Barrow.
1
2
3
4
Revision immediate calculation primitives. Change of variable and integration by parts.
Primitives rational functions.
Global defined as area. Barrow's rule.
Applications to the calculation of areas and volumes.
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Universitat Politècnica de Catalunya
Last update: 14-07-2015
340021 - FOMA-N1O43 - Fundamentals of Mathematics
Bibliography
Basic:
Anton, Howard. Introducción al álgebra lineal. 3a ed. México [etc.]: Limusa, 2003. ISBN 9681863178.
Estela Carbonell, M. Rosa. Fonaments de càlcul. 2a ed. Barcelona: Edicions UPC, 2005. ISBN 8483018357.
Kreyszig, Erwin. Matemáticas avanzadas para ingeniería. 3a ed. México, D.F. [etc.]: Limusa, 2006. ISBN 9789681853113.
Complementary:
Amer Ramon, Rafel. Curs d'àlgebra lineal [on line]. Terrassa: Universitat Politècnica de Catalunya. Escola Tècnica Superior
d'Enginyers Industrials de Terrassa, 2003 [Consultation: 21/03/2011]. Available on:
<http://ruth.upc.es/algebra/curs_algebra_lineal.pdf>.
Boadas Elvira, Joan. Funcions reals d'una variable real [on line]. Vilanova i la Geltrú: Escola Universitària Politècnica de
Vilanova i la Geltrú, Universitat Politècnica de Catalunya, 2001 [Consultation: 15/01/2015]. Available on:
<http://hdl.handle.net/2099.3/36440>. ISBN 8483016575.
Lay, David C. Álgebra lineal y sus aplicaciones. 3a ed. México [etc.]: Pearson Educación, 2007. ISBN 9789702609063.
Strang, Gilbert. Linear algebra and its applications. 4th ed. Australia [etc.]: Thomson, 2006. ISBN 9780534422004.
Stewart, James. Cálculo de una variable : trascendentes tempranas. 6a ed. México: International Thomson, 2008. ISBN
9789706866530.
Others resources:
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Universitat Politècnica de Catalunya