Educational guide

IDENTIFYING DATA

2024_25

Subject

ENGINEERING MATHEMATICS

Code

00708012

Study programme

0708 - GRADO EN INGENIERÍA MECÁNICA

Descriptors

Credit.

Type

Year

Period

Basic Training

Second

First

Language

Castellano

Prerequisites

Department

MATEMATICAS

Coordinador

GARCÍA FERNÁNDEZ , ROSA MARTA

E-mail

rmgarf@unileon.es
rsans@unileon.es

Lecturers

GARCÍA FERNÁNDEZ , ROSA MARTA

SANTAMARÍA SÁNCHEZ , RAFAEL

Web

http://

General description

Tribunales de Revisión

Tribunal titular
Cargo	Departamento	Profesor
Presidente	MATEMATICAS	FRANCISCO IRIBARREN , ARACELI DE
Secretario	MATEMATICAS	SAEZ SCHWEDT , ANDRES
Vocal	MATEMATICAS	CASTRO GARCIA , NOEMI DE

Tribunal suplente
Cargo	Departamento	Profesor
Presidente	MATEMATICAS	SUSPERREGUI LESACA , JULIAN JOSE
Secretario	MATEMATICAS	ARIAS MOSQUERA , DANIEL
Vocal	MATEMATICAS	ARANA SUAREZ , MARIA VICTORIA

Competencias

Code
A18145
B5634
B5635
B5643
B5644
B5645
C1	CMECES1 That students have demonstrated possession and understanding of knowledge in an area of study that is based on general secondary education, and is usually found at a level that, although supported by advanced textbooks, also includes some aspects that involve knowledge from the cutting edge of their field of study
C4	CMECES4 That students can transmit information, ideas, problems and solutions to both a specialised and non-specialised audience
C5	CMECES5 That students have developed those learning skills necessary to undertake further studies with a high degree of autonomy

Learning aims

	Competences
Solving mathematical models in engineering.	A18145	B5635 B5643 B5644	C1
Addresses engineering problems using techniques of differential equations and differential geometry.	A18145	B5634 B5643	C4 C5
Translating information, ideas, problems, and solutions from the field of engineering into mathematical language allows for precise analysis and modeling		B5635 B5644	C1 C5
Learning new methods and theories is essential for adapting to new situations.		B5645	C4 C5
Addresses engineering problems using techniques of differential equations and differential geometry.	A18145		C5
Learning new methods and theories to adapt to new situations.	A18145	B5634	C5

Contents

Topic	Sub-topic
Block I: DIFFERENTIAL EQUATIONS	Topic 1: FIRST ORDER DIFFERENTIAL EQUATIONS Introduction to techniques for solving linear and nonlinear first-order differential equations. Topic 2: HIGHER-ORDER DIFFERENTIAL EQUATIONS AND SYSTEMS OF FIRST-ORDER DIFFERENTIAL EQUATIONS Introduction to solution techniques for systems of differential equations based on Linear Algebra and their application to solving higher-order differential equations.
Block II: PARTIAL DIFFERENTIAL EQUATIONS	Topic 3: INTRODUCTION TO TWO-DIMENSIONAL FIRST-ORDER PARTIAL DIFFERENTIAL EQUATIONS.
Block III: DIFFERENTIAL GEOMETRY	Topic 4: DIFFERENTIAL CURVES AND SURFACES IN THE PLANE AND SPACE Differential curves in the plane and space. Parametrized surfaces. First and second fundamental forms. Distinguishable curves on surfaces. Integration of scalar and vector functions over curves and surfaces. Parametrized surfaces. First and second fundamental forms. Distinguished curves on surfaces.
Block iV: INTEGRATION	Topic 5: LINE AND SURFACE INTEGRALS Green's, Stokes', and Gauss's Divergence Theorems.

Planning

Methodologies :: Tests
	Class hours	Hours outside the classroom	Total hours
Problem solving, classroom exercises	25	37.5	62.5

Tutorship of group	0.5	0.5	1

Lecture	26	52	78

Extended-answer tests	4	0	4
	4.5	0	4.5

(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies

Methodologies ::

	Description
Problem solving, classroom exercises	Problem-solving/exercise resolution in the regular classroom, promoting student participation to the extent possible.
Tutorship of group	Small group activity to monitor the progress of the teaching/learning process.
Lecture	Development of theoretical content and models of problems and exercises.

Personalized attention

Lecture

Problem solving, classroom exercises

Tutorship of group

Description

Individually by prior appointment via email or in person. Tutorial sessions can be arranged at any time, taking into account the professor's and student's class schedules. Tutorials will take place in Room 317 of the School of Industrial, Computer, and Aerospace Engineering.

Assessment

	Description	Qualification
Extended-answer tests		60%
	Completion and presentation of assignments: In Class, exercises will be proposed for students to submit to complete continuous assessment. Additionally, positive and participatory attitudes of students during the course will be valued.	40%

Other comments and second call
<div>Evaluation will be of a summative type. To pass the subject, it is necessary to obtain a score of 50%. The first test will cover the content developed throughout the course up to the date of its administration. Subsequent tests will cover content developed since the administration of the previous test. The last test will be held at the end of the semester. Additionally, throughout the course, students will be assigned tasks and exercises to complete and submit on specified dates. Students who do not pass the subject in the first sitting may choose to do so in the second sitting, which will consist of a single test covering all subject content.</div><div><br /></div><div>The use of electronic devices enabling communication, such as mobile phones, tablets, and transmitters, is expressly prohibited. In the event of non-compliance with the above, as established by the GUIDELINES FOR ACTION IN CASES OF PLAGIARISM, COPYING, OR FRAUD IN EXAMS OR EVALUATION TESTS, approved by the University's Governing Council, the exam will be withdrawn (photography or screenshot in computer-based tests), the student will be expelled from the classroom, and they will receive a failing grade.</div>

Sources of information

Access to Recommended Bibliography in the Catalog ULE

Basic	Zill, D. G., Wright, W, S., Advanced Engineering Mathematics, Jones and Bartlett Publishers, 2011 Marsden, J. E., Tromba, A.J., Cálculo vectorial , Pearson, 2018 Boyce, W. E., DiPrima, R. C., Elementary Differential Equations and Boundary Value Problems, John Wiley &amp; Sons, John Wiley &amp; Sons, 2017

Complementary	Zill, D. G., Ecuaciones Diferenciales con aplicaciones de modelado, Thomson, 1997 Agarwal, R. P., O'Reagan, D., An introduction to ordinary differential equations, Springer, 2008 Klingenberg, W. , Curso de geometría diferencial, Alhambra, 1978 Toponogov, V. A., Differential geometry of curves and surfaces. A concise guide , Birkhäuser, 2006 Simmons, G. F., Ecuaciones Diferenciales con aplicaciones y notas históricas, McGraw-Hill, 1999 Novo S., Obaya R., Rojo J., Ecuaciones y sistemas diferenciales, Editorial AC, 1992 López de la Rica, A., de la Villa Cuenca A., Geometría Diferencial, CLAGSA, 1991 Do Carmo, M. P., Geometria diferencial de curvas y superficies, Alianza, 1995 Galindo, F., Sanz, J., Tristán, L. A., Guía práctica de Cálculo en varias variables, Thomson, 2005 Campbell, S. L., Haberman, R., Introducción a las ecuaciones diferenciales con problemas de valor de frontera, McGraw-Hill, 1998 Varona, J. L., Métodos clásicos de resolución de ecuaciones diferenciales ordinarias, Servicio de Publicaciones, Universidad de La Rioja, 1996 J. San Martín, V. Tomeo, I. Uña, Métodos Matemáticos, Paraninfo , 2015 Gadella, M., Nieto, L. M., Métodos Matemáticos avanzados en Ciencias e Ingeniería, Secretariado de Publicaciones de la Universidad de Valladolid, 2000 Walter, W., Ordinary differential equations, Springer, 1998 Jost, J., Partial Differential Equations, Springer, 2007 Stephenson, G., Partial Differential Equations for scientists and engineers, Word Scientific, 1996

Recommendations

Subjects that it is recommended to have taken before

LINEAR ALGEBRA AND GEOMETRY / 00708001

DIFFERENTIAL AND INTEGRAL CALCULUS / 00708002

NUMERICAL AND STATISTICAL METHODS / 00708006


Other comments
The student who does not participate in any of the assessment tests will receive a score of zero in said test, a grade that will be taken into account for the final grade calculation. In this regard, once the date of a partial written test is set, it will be unchangeable, and the student who does not attend will receive a zero grade in it.