Educational guide
IDENTIFYING DATA							2020_21
Subject	CALCULUS					Code	00809010
Study programme	0808 - GRADO EN INGENIERIA MINERA
Descriptors	Credit.	Type	Year	Period
	6	Compulsory	First	Second
Language	Otros
Prerequisites
Department	MATEMATICAS
Coordinador	CARRIEGOS VIEIRA , MIGUEL				E-mail	mcarv@unileon.es mttrom@unileon.es
Lecturers	CARRIEGOS VIEIRA , MIGUEL TROBAJO DE LAS MATAS , MARÍA TERESA
Web	http://matematicas.unileon.es
General description	Mathematical methods in mechanical engineering: Vector calculus, differential equations and differentoial geometry
Tribunales de Revisión	Tribunal titular Cargo Departamento Profesor Presidente MATEMATICAS GOMEZ PEREZ , JAVIER Secretario MATEMATICAS MAZCUñAN NAVARRO , EVA MARIA Vocal MATEMATICAS PISABARRO MANTECA , MARIA JESUS Tribunal suplente Cargo Departamento Profesor Presidente MATEMATICAS GARCIA FERNANDEZ , ROSA MARTA Secretario MATEMATICAS LOPEZ CABECEIRA , MONTSERRAT Vocal MATEMATICAS RODRIGUEZ SANCHEZ , CRISTINA

Competencias

Code
A16337
A16338
A16339
A16340
A16341
A16342
A16343
B5121
B5122
B5125
B5131
B5132
B5134
B5135
B5141
B5142
C1
C4
C5

Learning aims

	Competences
			C1
			C4
			C5
		B5121
		B5122
		B5125
		B5131
		B5132
		B5134
		B5135
		B5141
		B5142
	A16337
	A16338
	A16339
	A16340
	A16341
	A16342
	A16343

Contents

Topic	Sub-topic
I. Geometry	1.- Conics 2.- Quadric surfaces 3.- Vectorial functions: Parametric curves 4.- Curvature 5.- Surfaces in 3D space 6.- First Fundamental Form
II. Vector Calculus	7.- Differential Operators 8.- Path integrals 9.- Multiple integral 10.- Green's Theorem 11.- Surface integral 12.- Stokes' Theorem 13.- Gauss Divergence Theorem
III. Differential Equations	14.- Ordinary differential equations. 15.- A first look at mathematical models 16.- First order equations 17.- Exact equations. Separable equations. 18.- First order linear equations 19.- Higher order differential equations 20.- Linear homogeneous equations of higher order 21.- Non-homogeneous linear equations. Variation of parameters 22.- Mass-spring linear models 23.- Differential models for linear circuits.
IV. Systems of Linear Differential Equations	24.- Homogeneous systems of linear equations 25.- Non-homogeneous systems 26.- Qualitative behavior of non-linear systems 27.- 2D Phase portraits

Planning

Methodologies  ::  Tests
	Class hours	Hours outside the classroom	Total hours
Problem solving, classroom exercises	30	15	45
Personal tuition	1	9	10
Lecture	30	15	45
Extended-answer tests	6	44	50
(*)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 in the classroom
Personal tuition
Lecture	As usual

Personalized attention

Description Please contact previously by mail (miguel.carriegos@unileon.es). Engineering School. Building II (Tecnológico). Room 374. T-F 10:00-11:30

Assessment

	Description	Qualification
Extended-answer tests	At least an ordinary evaluation	95%
Others	Some students can be requested to an oral examination.	up to 50%
Other comments and second call
<p>Students qualify after obtaining at least 50% global.</p><div><br /></div><div>Second call (University agenda): Students can qualify at second call in the same way than first.</div>

ADDENDUM

Contingency plan due to COVID-19 emergency conditions that prevents from presence based teaching

COVID-19 Teaching Guide Addendum Access Link

Sources of information

Access to Recommended Bibliography in the Catalog ULE

Basic	J. Marsden, A. Tromba, Cálculo Vectorial, Addison-Wesley, 1998 D. Zill, W. Wright, Ecuaciones Diferenciales, Cengage, 2013 E. Kreyszig, Matemáticas Avanzadas para la Ingeniería, Wiley, 10ª Edición
Complementary	L. Turyn, Advanced Engineering Mathematics, CRC Press, 2014 J. Marsden, A. Weinstein, Calculus II, Springer, 1985 J. Marsden, A. Weinstein, Calculus III, Springer, 1985 S. Novo, R. Obaya, J. Rojo, Ecuaciones y sistemas diferenciales, AC, M.P. DoCarmo, Geometría diferencial de curvas y superficies, Alianza, Arnol'd, VI., Lectures on partial differential equations, Springer, 2004 A. Sharma, The Book of Vector Calculus, Discovery Publishing House, 2006 Hinchey, FA., Vectores y tensores, Limusa, 1976

Recommendations

Subjects that it is recommended to have taken before

ALGEBRA / 00809001 CALCULUS I / 00809002