Guías Docentes Electrónicas
1. General information
Course:
CALCULUS AND NUMERICAL METHODS
Code:
42300
Type:
BASIC
ECTS credits:
6
Degree:
346 - DEGREE IN COMPUTER SCIENCE AND ENGINEERING
Academic year:
2019-20
Center:
604 - SCHOOL OF COMPUTER SCIENCE AND ENGINEERING (AB)
Group(s):
10  11  12  13  14 
Year:
1
Duration:
First semester
Main language:
Spanish
Second language:
English
Use of additional languages:
English (group I, bilingual option)
English Friendly:
N
Web site:
https://campusvirtual.uclm.es/
Bilingual:
Y
Lecturer: HERMENEGILDA MACIA SOLER - Group(s): 10  11 
Building/Office
Department
Phone number
Email
Office hours
ESII / 1.B.6
MATEMÁTICAS
2474
hermenegilda.macia@uclm.es
Se anunciará en la plataforma virtual

Lecturer: GUILLERMO MANJABACAS TENDERO - Group(s): 11  12  13 
Building/Office
Department
Phone number
Email
Office hours
Infante Don Juan Manuel. Despacho 1.B.4
MATEMÁTICAS
2172
guillermo.manjabacas@uclm.es
Will be available on www.esiiab.uclm.es/tutorias.php

2. Pre-Requisites

In order to achieve the learning objectives of the subject it is necessary to have a good command of some contents supposed to be studied in a course similar to the second course of Spanish Bachillerato or even previously, such as, basic notions of geometry and trigonometry, elementary calculations (fractions, powers, logarithms), elementary functions and a sound knowledge of differential and integral calculus.

The ESII offers a special course (Seminario de refuerzo de Cálculo) given simultaneously with the subject to help students who may need it.

There are, of course, some online resources that may be helpful as well as some books of Bachillerato level.

3. Justification in the curriculum, relation to other subjects and to the profession

A computer science engineer needs some mathematical tools to comprehend the proper technics useful for his professional life. Our subject provides some of them.

Another important point is that mathematics helps students to develop the abstraction capacity, the scientific rigour and the analysis and synthesis skills that are helpful for future engineers.

In this subject we include some mathematical background useful for other subjects, such as Fundamentos Físicos de la Informática (Physics for Computer Science), Estadística (Statistics) and Metodología de la programación (Programming methodology).


4. Degree competences achieved in this course
Course competences
Code Description
BA1 Ability to solve mathematical problems which can occur in engineering. Skills to apply knowledge about: lineal algebra; integral and differential calculus; numerical methods, numerical algorithms, statistics, and optimization.
BA3 Ability to understand basic concepts about discrete mathematics, logic, algorithms, computational complexity, and their applications to solve engineering problems.
INS5 Argumentative skills to logically justify and explain decisions and opinions.
PER2 Ability to work in multidisciplinary teams.
PER5 Acknowledgement of human diversity, equal rights, and cultural variety.
UCLM2 Ability to use Information and Communication Technologies.
UCLM3 Accurate speaking and writing skills.
5. Objectives or Learning Outcomes
Course learning outcomes
Description
Understanding of the use of induction definition method (recursion) and its particular importance in computer programming.
Implementation and analysis of several numerical methods.
Utilization of programs for symbolic and numerical calculus.
Enunciation and resolution of optimization problems.
Use of fundamental concepts of derivatives and integrals.
Resolution of fundamental concepts of derivative and integral.
Additional outcomes
Not established.
6. Units / Contents
  • Unit 1: Numbers, sequences and series
    • Unit 1.1: Numbers. Different sets of numbers and their properties. Principle of mathematical induction.
    • Unit 1.2: Sequences of real numbers.
    • Unit 1.3: Series. An introduction.
  • Unit 2: Differential calculus.
    • Unit 2.1: Basic concepts: functions, limits and continuity.
    • Unit 2.2: Differentiation. Basic properties.
    • Unit 2.3: Applications of the derivative. Maximum and minimum points. Increasing and decreasing functions. Rolle and the mean value theorems. L'Hôpital's rule. Convexity and concavity.
    • Unit 2.4: Approximation by polynomial functions. Taylor's polynomial and Lagrange's remainder theorem.
    • Unit 2.5: Approximating the solution of an equation: bisection, Newton and fix point methods.
    • Unit 2.6: Polynomial interpolation.
  • Unit 3: Integral calculus.
    • Unit 3.1: Riemann integral. Definite integral and its properties. Fundamental theorem of calculus.
    • Unit 3.2: Indefinite integrals. Applications of integrals.
    • Unit 3.3: Improper integrals. Convergence. Different types of improper integrals.
    • Unit 3.4: Approximating a definite integral: trapezoid and Simpson rules.
7. Activities, Units/Modules and Methodology
Training Activity Methodology Related Competences (only degrees before RD 822/2021) ECTS Hours As Com R Description *
Class Attendance (theory) [ON-SITE] Combination of methods BA1 BA3 INS5 PER5 1.28 32 N N N
Problem solving and/or case studies [ON-SITE] Workshops and Seminars BA1 BA3 INS5 PER2 UCLM3 0.24 6 N N N
Computer room practice [ON-SITE] Practical or hands-on activities BA1 BA3 INS5 UCLM2 0.48 12 N N N
Project or Topic Presentations [ON-SITE] Practical or hands-on activities BA1 BA3 INS5 UCLM2 UCLM3 0.08 2 Y Y N A presentation about one laboratory session (groups of 3-4 students). It is compulsory to attend office hours before the presentation in order to check your work.
Writing of reports or projects [OFF-SITE] Problem solving and exercises BA1 BA3 INS5 UCLM2 UCLM3 0.6 15 Y N N A collection of problems must be submitted during the course. Evaluation through self and peer assessment could be used.
Writing of reports or projects [OFF-SITE] Combination of methods BA1 BA3 INS5 UCLM3 0.12 3 Y Y N A report about the contents of the oral presentation has to be handed in.
Study and Exam Preparation [OFF-SITE] Combination of methods BA1 BA3 INS5 2.8 70 N N N
Final test [ON-SITE] Assessment tests BA1 BA3 INS5 UCLM3 0.2 5 Y Y Y There will be three exams (one per unit). It is compulsory to reach a minimum mark of 4 out of 10 in each exam to pass the course. In the regular/extraordinay exam session you can retake the parts in case you have not reached the minimum mark previously.
On-line Activities [OFF-SITE] Self-study BA1 BA3 INS5 0.08 2 Y N N There will be online tests about the theoretical part of the course.
Progress test [ON-SITE] Assessment tests BA1 BA3 INS5 0.04 1 Y N N There will be online tests about the computer work.
Individual tutoring sessions [ON-SITE] Other Methodologies BA1 BA3 INS5 UCLM3 0.08 2 Y Y N Before the oral presentation, it is compulsory to attend office hours in order to check your work.
Total: 6 150
Total credits of in-class work: 2.4 Total class time hours: 60
Total credits of out of class work: 3.6 Total hours of out of class work: 90

As: Assessable training activity
Com: Training activity of compulsory overcoming
R: Rescheduling training activity

8. Evaluation criteria and Grading System
  Grading System  
Evaluation System Face-to-Face Self-Study Student Description
Assessment of problem solving and/or case studies 20.00% 0.00% [INF] Individual activity.
Oral presentations assessment 10.00% 0.00% [PRES] Group activity.
Assessment of activities done in the computer labs 15.00% 0.00% [LAB] Online tests (10%, individual activity) and the report about the laboratory session (5%, group activity).
Test 55.00% 0.00% [ESC] Individual activity. There exams, one per unit (unit 1: 20%, unit 2: 20% and unit 3: 15%). A mininum mark of 4 in each part is compulsory to pass the course.
Total: 100.00% 0.00%  

Evaluation criteria for the final exam:
A minimum average mark of 5 out of 10 including all the activities and a minimum mark of 4 out of 10 in each partial test is compulsory to pass the course. Below this minimum, the student will have to take the corresponding parts in the extra exam session. After this, if the student has not reached the minimum mark of 4 in each partial test or has not passed the final exam, the final grade will be less than or equal to 4 even if the average mark (when considered all the activities) is greater than or equal to 5.
Specifications for the resit/retake exam:
Students with marks below 4 out of 10 in the partial tests can take the corresponding parts or take an overall exam corresponding to the contents of the three partial tests instead. Anyway, this part represents a 55% in the final mark, and the other 45% (lab practices, oral presentation and others) are those obtained during the course. A minimum mark of 4 out of 10 in each partial test together with an average mark of 5 out of 10 including all the activities are compulsory to pass the course.
Specifications for the second resit / retake exam:
Students must take an examination about all the contents of the course: theory, problems and laboratory sessions. In addition, students must do an oral presentation together with a written report about one laboratory session.
9. Assignments, course calendar and important dates
Not related to the syllabus/contents
Hours hours
Project or Topic Presentations [PRESENCIAL][Practical or hands-on activities] 2
Writing of reports or projects [AUTÓNOMA][Combination of methods] 3
Individual tutoring sessions [PRESENCIAL][Other Methodologies] 2

Unit 1 (de 3): Numbers, sequences and series
Activities Hours
Class Attendance (theory) [PRESENCIAL][Combination of methods] 14
Problem solving and/or case studies [PRESENCIAL][Workshops and Seminars] 2
Computer room practice [PRESENCIAL][Practical or hands-on activities] 2
Writing of reports or projects [AUTÓNOMA][Problem solving and exercises] 5
Study and Exam Preparation [AUTÓNOMA][Combination of methods] 22
Final test [PRESENCIAL][Assessment tests] 2
On-line Activities [AUTÓNOMA][Self-study] .75
Progress test [PRESENCIAL][Assessment tests] .25
Teaching period: Weeks 1-5

Unit 2 (de 3): Differential calculus.
Activities Hours
Class Attendance (theory) [PRESENCIAL][Combination of methods] 7
Problem solving and/or case studies [PRESENCIAL][Workshops and Seminars] 2
Computer room practice [PRESENCIAL][Practical or hands-on activities] 8
Writing of reports or projects [AUTÓNOMA][Problem solving and exercises] 5
Study and Exam Preparation [AUTÓNOMA][Combination of methods] 24
Final test [PRESENCIAL][Assessment tests] 2
On-line Activities [AUTÓNOMA][Self-study] 1
Progress test [PRESENCIAL][Assessment tests] .5
Teaching period: Weeks 6-10

Unit 3 (de 3): Integral calculus.
Activities Hours
Class Attendance (theory) [PRESENCIAL][Combination of methods] 11
Problem solving and/or case studies [PRESENCIAL][Workshops and Seminars] 2
Computer room practice [PRESENCIAL][Practical or hands-on activities] 2
Writing of reports or projects [AUTÓNOMA][Problem solving and exercises] 5
Study and Exam Preparation [AUTÓNOMA][Combination of methods] 24
Final test [PRESENCIAL][Assessment tests] 1
On-line Activities [AUTÓNOMA][Self-study] .25
Progress test [PRESENCIAL][Assessment tests] .25
Teaching period: Weeks 11-15

Global activity
Activities hours
General comments about the planning: This course schedule is APPROXIMATE. It could vary throughout the academic course due to teaching needs, bank holidays, etc. A weekly schedule will be properly detailed and updated on the online platform (Virtual Campus). Note that all the lectures, practice sessions, exams and related activities performed in the bilingual groups will be entirely taught and assessed in English. Classes will be scheduled in 3 sessions of one hour and a half per week. The assessment activities could be performed in the afternoon, in case of necessity.
10. Bibliography and Sources
Author(s) Title Book/Journal Citv Publishing house ISBN Year Description Link Catálogo biblioteca
 
García, A. et al Cálculo I : teoría y problemas de análisis matemático en una CLAGSA 978-84-921847-2-9 2007 Ficha de la biblioteca
Manjabacas, G. et al Ejercicios de Cálculo II : cálculo diferencial e integral en Popular Libros 84-932789-8-X 2004 Ficha de la biblioteca
Manjabacas, G. et al Ejercicios de cálculo I Popular Libros 84-932789-0-4 2002 Ficha de la biblioteca
Apostol, Tom M. Calculus Reverté 84-291-5001-3 (o.c) 1997 Ficha de la biblioteca
Burden, R.L. & Faires, J.D. Análisis numérico Thomson Learning 970-686-134-3 2003 Ficha de la biblioteca
García, N. et al Una invitación al análisis numérico con MATLAB Popular Libros 84-932789-9-8 2005 Ficha de la biblioteca
Mathews, John H. Métodos numéricos con MATLAB Pearson/Prentice Hall 978-84-8322-181-5 2007 Ficha de la biblioteca



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