Educational guide

IDENTIFYING DATA

2024_25

Subject

DIFFERENTIAL AND INGTEGRAL CALCULUS

Code

00709001

Study programme

0709 - GRADO EN INGENIERÍA INFORMÁTICA

Descriptors

Credit.

Type

Year

Period

Basic Training

First

Language

Castellano

Prerequisites

Department

MATEMATICAS

Coordinador

CASTRO GARCIA, NOEMI DE

E-mail

ncasg@unileon.es
mfgonr@unileon.es

Lecturers

GONZÁLEZ RODRÍGUEZ , MANUEL FERNANDO

CASTRO GARCIA, NOEMI DE

Web

http://

General description

Tribunales de Revisión

Tribunal titular
Cargo	Departamento	Profesor
Presidente	MATEMATICAS	GOMEZ PEREZ , JAVIER
Secretario	MATEMATICAS	ARIAS MOSQUERA , DANIEL
Vocal	MATEMATICAS	VEGA CASIELLES , SUSANA

Tribunal suplente
Cargo	Departamento	Profesor
Presidente	MATEMATICAS	SUSPERREGUI LESACA , JULIAN JOSE
Secretario		SUAREZ CORONA , ADRIANA
Vocal		QUIROS CARRETERO , ALICIA

Competencias

Code
A18096
B5623
B5624
B5625
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
That students can convey information, ideas, problems, and solutions to both specialized and non-specialized audiences.			C4
That students have developed the learning skills necessary to undertake further studies with a high degree of autonomy.			C5
That students have demonstrated possession and understanding of knowledge in a field of study that builds on the foundation of general secondary education, typically found at a level that, while supported by advanced textbooks, also includes some aspects that entail knowledge from the forefront of their field of study.			C1
Ability to solve mathematical problems that may arise in engineering. Aptitude to apply knowledge of differential and integral calculus.	A18096
Ability to communicate orally and/or in writing, information, ideas, problems, and solutions using mathematical language		B5625
Capacity for critical reasoning and self-criticism.		B5624
Solving mathematical problems that may arise in engineering.	A18096	B5623

Contents

Topic	Sub-topic
BLOCK I: Sequences and Series of Real Numbers.	1: Real Numbers and Sequences 1.1. Real Numbers. 1.2. Sequences of Real Numbers. Limit of a sequence and convergence criteria. 2: Series of Real Numbers 2.1. Definition and properties of a serie of real numbers. 2.2. Convergence and sum of a series. 2.3. Series of positive real numbers: Convergence criteria. 2.4. Sum of some types of series. 2.5. Alternating series. Series of positive and negative terms.
BLOCK II: Differential Calculus in One Variable.	3. REAL FUNCTIONS OF A REAL VARIABLE 3.1. Limit of a real function of a real variable. 3.2. Continuity of a function at a point. 4. DIFFERENTIABILITY IN FUNCTIONS OF ONE VARIABLE 4.1. Derivative of a function. Calculation of derivatives. 4.2. Continuity and differentiability in real functions of one variable. 4.3. Successive derivatives. Implicit differentiation. Differential of a function. 4.4. Applications of the derivative.
BLOCK III: Differential Calculus in Several Variables.	5. LIMIT AND CONTINUITY OF A REAL FUNCTION OF SEVERAL REAL VARIABLES 5.1. Scalar and vector functions. 5.2. Limit of a function of several variables. 5.3. Continuity of functions of several variables. 6: DIFFERENTIABILITY, DIFFERENTIATION, AND OPTIMIZATION IN FUNCTIONS OF SEVERAL VARIABLES 6.1. Partial derivatives of a function of several variables. 6.2. Directional derivative of a function of several variables. 6.3. Differentiability of a function of several variables. 6.4. Optimization in functions of several variables.
BLOCK IV: Integral Calculus.	7: INTEGRAL OF A REAL FUNCTION OF A REAL VARIABLE 7.1. Definite integral. Definition and properties. 7.2. Calculation of primitives. 7.3. Improper integrals. 7.4. Applications of the definite integral. 8. MULTIPLE INTEGRALS 8.1. Double integral. 8.2. Change of variable in the double integral. 8.3. Applications of the double integral.

Planning

Methodologies :: Tests
	Class hours	Hours outside the classroom	Total hours
Problem solving, classroom exercises	35.5	41	76.5

Practicals using information and communication technologies (ICTs) in computer rooms	2	7.5	9.5
Personal tuition	1	0	1

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	Practical classes in which exercises and problems will be solved. These exercises may be worked on by the student beforehand or proposed in the classroom by the teacher.
Practicals using information and communication technologies (ICTs) in computer rooms	Analysis of useful computer tools in solving the mathematical problems and exercises proposed in the subject. These can be carried out in a computer lab or a regular classroom.
Personal tuition	Face-to-Face Tutoring: Individual or group tutoring sessions will be held in the classroom to address any doubts that may arise related to the understanding of concepts or the completion and resolution of assignments proposed by the teacher. Virtual Tutoring: Students communicate with the teacher through the Moodle forum or email to raise and resolve doubts about the course, not the content.
Lecture	Theoretical classes, in which the teacher presents the contents through lectures. Blackboard, projector, or other materials available on the web may be used.

Personalized attention

Practicals using information and communication technologies (ICTs) in computer rooms

Lecture

Problem solving, classroom exercises

Description

In addition to group tutoring, where doubts arising in the preparation of written tests can be addressed, students may request individual tutoring by prior appointment arranged via email.

Assessment

	Description	Qualification
Practicals using information and communication technologies (ICTs) in computer rooms	Deliverables in which students will solve a proposed collection of problems using computer tools.	10%-20%
Extended-answer tests	A minimum of two written tests of development.	80%-90%

Other comments and second call
At the beginning of the course, the teacher will specify all aspects of assessment that will be applied in the subject and are not included in the teaching guide, such as the minimum score required in tests, or the final weights of the different evaluation instruments. Assessment will be continuous, summative type and passing grade is achieved by obtaining at least 5 points out of a maximum of 10. It will be carried out through: First Call: At least two partial exams or assessment controls. These partial exams, together, will account for at least 80% of the final grade. Additionally, the corresponding grade of the practices through ICT will be added. During the development of the tests, handling any material except that indicated by the teacher will not be allowed. The possession and use of mobile and/or electronic devices during the tests are strictly prohibited. The mere possession of such devices as well as notes, books, folders, or various unauthorized materials during the evaluation tests will result in immediate withdrawal from the exam, expulsion from it, and a failing grade, with the incident reported to the Academic Authority of the Center to carry out the actions provided for in the Guidelines for Action in Cases of Plagiarism, Copying, or Fraud in Exams or Evaluation Tests, approved by the Permanent Commission of the Governing Council on January 29, 2015". Extraordinary Call: Those students who have failed the first opportunity (January) will have the right to a second opportunity (February). In this one, the approved partial exams during continuous evaluation will be taken into account, as well as the grade of the practices. December Call: Those students who are entitled to use this call will have a single exam, of an eminently practical nature related to the entire subject. The grade obtained in this test will not be added to any other obtained previously. In any case, the proposed evaluation is subject to the technical, material, and human resources available, as well as to the achievement of the planning of face-to-face classes.

Sources of information

Access to Recommended Bibliography in the Catalog ULE

Basic	BRADLEY, G.L. y SMITH, K., Cálculo de varias variables. , Prentice Hall. , 1998. LARSON, R. Y HOSTETLER, R., 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. , 1994. BURGOS, J. de,, Cálculo infinitesimal de varias variable. , McGraw-Hill , 1995. James Stewart, Cálculo. Conceptos y contextos., Thomson Learning, 1999 Zill, D.G. , Cálculo. Trascendentes tempranas, McGraw-Hill, 2011 GALINDO SOTO, F. SANZ GIL, J. y TRISTAN VEGA, L. A.,, Guía práctica de cálculo infinitesimal en una variable., Thomson., 2003. GALINDO SOTO, F. SANZ GIL, J. y TRISTAN VEGA, L. A.,, Guía práctica de cálculo infinitesimal en varias variables., Thomson. , 2005. Franco, J.R., Introducción al cálculo: Problemas y ejercicios resueltos, Prentice Hall, 2003 UÑA JUAREZ, I. y otros. , Problemas resueltos de Cálculo en varias variables. , Thomson. , 2007.

Complementary	PISKUNOV, N. , Cálculo Diferencial e Integral. , Montaner y Simón. , 1970. COQUILLAT, F. , Cálculo Integral. Metodología y problemas. , Tebar Flores. , 1997. SMITH, R. y MINTON, R. , Cálculo Vol. 1. , McGraw-Hill. , 2003. TEBAR FLORES, E. , Problemas de cálculo infinitesimal. , Tebar Flores. , 2005.

Recommendations


Other comments
It is recommended that the student master the Mathematics curriculum of the Science and Technology Bachelor's degree. Otherwise, the completion of the Instrumental Mathematics Crash Course is proposed.