Educational guide
IDENTIFYING DATA							2023_24
Subject	CALCULUS I					Code	00809002
Study programme	0808 - GRADO EN INGENIERIA MINERA
Descriptors	Credit.	Type	Year	Period
	6	Basic Training	First	First
Language	Castellano
Prerequisites
Department	MATEMATICAS
Coordinador	CASTRO GARCIA, NOEMI DE				E-mail	ncasg@unileon.es jgomp@unileon.es
Lecturers	GÓMEZ PÉREZ , JAVIER CASTRO GARCIA, NOEMI DE
Web	http://
General description	Differential and integral calculus with applications and some numerical methods. Introduction to multivariate calculus.
Tribunales de Revisión	Tribunal titular Cargo Departamento Profesor Presidente QUIROS CARRETERO , ALICIA Secretario MATEMATICAS ARIAS MOSQUERA , DANIEL Vocal MATEMATICAS SANTAMARIA SANCHEZ , RAFAEL Tribunal suplente Cargo Departamento Profesor Presidente MATEMATICAS GARCIA FERNANDEZ , ROSA MARTA Secretario MATEMATICAS ARANA SUAREZ , MARIA VICTORIA Vocal MATEMATICAS TROBAJO DE LAS MATAS , MARIA TERESA

Competencias

Code
A16279
A16287
A16288
A16289
A16290
A16291
B5121
B5122
B5125
B5131
B5132
B5134
B5135
B5141
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
	A16279
	A16287
	A16288
	A16290
	A16291
		B5125
		B5141
		B5132
		B5121	C1
		B5122	C4
		B5134	C5
		B5131
		B5135
	A16279 A16287 A16288 A16289 A16290 A16291

Contents

Topic	Sub-topic
Differential calculus	1. PRELIMINARIES. Complex numbers, functions and graphs. 2. DIFFERENTIAL CALCULUS WITH ONE VARIABLE.Derivatives, properties and fundamenta theorems. Taylor polynomial and applications. 3. DIFFERENTIAL CALCULUS WITH SEVERAL VARIABLES. Partial and directional derivatives. Differentiability. Gradient. Optimization.
Integral calculus	4. INTEGRAL CALCULUS. Riemann integral. Integration methods. Introduction to differential equations. Improper integrals. 5. APPLICATIONS INTEGRAL CALCULUS. Areas and arclength computation. Introduction to the computation of volumes and surfaces.
Introduction to numerical methods	6. SEQUENCES AND SERIES. Sequences. Series. Applications to numerical methods of solving non-linear equations.

Planning

Methodologies  ::  Tests
	Class hours	Hours outside the classroom	Total hours
Problem solving, classroom exercises	36	41	77
Personal tuition	1	0	1
Practicals using information and communication technologies (ICTs) in computer rooms	2	7	9
Lecture	16	40	56
Extended-answer tests	7	0	7
(*)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	Lectures where problems and theoretical questions about the contents of the course are discussed.
Personal tuition
Practicals using information and communication technologies (ICTs) in computer rooms
Lecture	The contents of the course are presented.

Personalized attention

Problem solving, classroom exercises Lecture

Description Students can have personalized attention by making an appointment by email for office hours.

Assessment

	Description	Qualification
Practicals using information and communication technologies (ICTs) in computer rooms		10%-20%
Extended-answer tests		80%-90%
Others	Attendance	10%
Other comments and second call
<p>The grade wil be computed attending to two types of assessment: summative and continuous. In order to pass the course, it is necessary to obtain a grade of at least 50%. The final grade will be computed only if the student has a grade of at least 40% in every assignment and test.  </p><p>The sumative part will be assessed with at least a test, accounting for 70% of the total grade, which might contain both theoretical and practical questions. </p><p>As for the continuous assessment, the students will need to attend lectures. This part will account for 10% of the total grade. Moreover, the student should attend the classes in the lab, where they will need to take a test to use specific software to solve some of these questions. This will account for 20% of the grade.</p><p>The grade of the second call will be the grade obtained in a theoretical-practical test. If the grade in the practical test is at leat 40%, it could also be taken into account.</p><p>The use of any electronic device (cell phones, tablets, etc) allowing the student to have communication with other people will be forbidden while doing the tests, as well as any material not explicitly allowed by the professor. </p><p> If a student breaks this rule, he will fail the exam and the Academic Authority of the Center will be informed so that they can follow the procedure approved by the Governing Council of the University on January 29th, 2015.</p>

Sources of information

Access to Recommended Bibliography in the Catalog ULE

Basic	Burgos, J. de, Cálculo infinitesimal de varias variables, McGraw-Hill, 1995 Bradley, G. L. y Smith, K. , Cálculo de varias variables. , Prentice Hall. , 1998. Larson, R.E. y Hostetler, R.P., Cálculo (Volumen I y II). , McGraw-Hill, 2008 Bradley, G. L. y Smith, K. , Cálculo de una variable. , Prentice Hall., 1998. García, A. y otros, Cálculo I y Cálculo II., CLAGSA. , 1993. Burgos, J. de, Cálculo infinitesimal de una variable, McGraw-Hill, 1996 Stewart, James, Cálculo. Conceptos y contextos., Thomson Learning, 1999 Zill, D.G. , Cálculo. Trascendentes tempranas, McGraw-Hill, 2011 Galindo Soto, F., Sanz Gil, J. y Tristán Vega, L. A., Guía práctica de cálculo infinitesimal en una variable., Thomson., 2003. Galindo Soto, F., Sanz Gil, J. y Tristán Vega, L. A., Guía práctica de cálculo infinitesimal en varias variables., Thomson. , 2005. Galindo, F., Gómez, J., Sanz, J., Tristán, L.A., Guía Práctica de Variable Compleja y Aplicaciones, Universidad de Valladoilid-Universidad de León, 2019 Franco, J.R., Introducción al cálculo: Problemas y ejercicios resueltos, Prentice Hall, 2003 Uña Juárez, I. y otros. , Problemas resueltos de Cálculo en varias variables. , Thomson. , 2007.
Complementary	P. Cembranos y J. Mendoza, Cálculo Integral, ANAYA (Base universitaria), P. Cembranos y J. Mendoza, Límites y Derivadas, ANAYA (Base universitaria),

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