Name: MATHEMATICS FOR BUSINESS II
Code: 510202005
Type: Compulsory
ECTS: 4.5
Length of subject: Per term
Semester and course: 2nd Year - First term
Speciality:
Language: English
Mode of study: On-site class
Lecturer data: COBACHO TORNEL, MARÍA BELÉN
Knowledge area: Métodos Cuantitativos para la Economía y Empresa
Department: Métodos Cuantitativos, Ciencias Jurídicas y Lenguas Modernas
Telephone: 968325402
Email: belen.cobacho@upct.es
Office hours and location: Tutorials will be carried out by request of the student sending an email to belen.cobacho@upct.es
Qualifications/Degrees:
Academic rank in UPCT: Profesora Titular de Universidad
Number of five-year periods: 5
Number of six-year periods: 1 de investigación
Curriculum Vitae: Full Profile
Responsible for the groups: G1, G2
Introducción a la optimización de funciones generales de varias variables aplicando técnicas del Cálculo Diferencial. Introducción a la Programación Lineal y formulación de problemas de optimización en general y de Programación Lineal en particular. Algoritmos de resolución de problemas de Programación Lineal e interpretación de las soluciones.
Teaching Unit 1. Optimization of multivariable functions
Topic 1. Introduction to the Optimization of Multivariable Functions
1.1. Basic Concepts in Optimization
1.2. Basic Concepts in Topology
Topic 2. Local optimization of multivariable functions
2.1 Local optimization of multivariable functions without constraints
2.2 Local optimization of multivariable functions with equality constraints
2.3 Local optimization of multivariable functions with strict inequality constraints
2.4 Local optimization of multivariable functions with non-strict inequality constraints
Topic 3. Global otimization of multivariable functions
3.1 Basic concepts of Topology
3.2 Global optimization of multivariable functions using the Weierstrass' Theorem
3.3 Global optimization of multivariable functions using concavity and convexity
Teaching Unit 2. Introduction to Linear Programming
Topic 4. Introduction to Linear Programming
4.1 Introduction to the formulation of Linear Programming problems
4.2 Basic concepts
4.3 Introduction to solving Linear Programming problems
Optimization of multivariable functions
Topic 1. Introduction to the Optimization of Multivariable Functions 1.1. Basic Concepts in Optimization 1.2. Basic Concepts in Topology Topic 2. Local optimization of multivariable functions 2.1 Local optimization of multivariable functions without constraints 2.2 Local optimization of multivariable functions with equality constraints 2.3 Local optimization of multivariable functions with strict inequality constraints 2.4 Local optimization of multivariable functions with non-strict inequality constraints Topic 3. Global otimization of multivariable functions 3.1 Basic concepts of Topology 3.2 Global optimization of multivariable functions using the Weierstrass' Theorem 3.3 Global optimization of multivariable functions using concavity and convexity
Introduction to Linear Programming
Topic 4. Introduction to Linear Programming 4.1 Introduction to the formulation of Linear Programming problems 4.2 Basic concepts 4.3 Introduction to solving Linear Programming problems
Promoting the continuous improvement of working and study conditions of the entire university community is one the basic principles and goals of the Universidad Politécnica de Cartagena. Such commitment to prevention and the responsibilities arising from it concern all realms of the university: governing bodies, management team, teaching and research staff, administrative and service staff and students. The UPCT Service of Occupational Hazards (Servicio de Prevención de Riesgos Laborales de la UPCT) has published a "Risk Prevention Manual for new students" (Manual de acogida al estudiante en materia de prevención de riesgos), which may be downloaded from the e-learning platform ("Aula Virtual"), with instructions and recommendations on how to act properly, from the point of view of prevention (safety, ergonomics, etc.), when developing any type of activity at the University. You will also find recommendations on how to proceed in an emergency or if an incident occurs. Particularly when carrying out training practices in laboratories, workshops or field work, you must follow all your teacher's instructions, because he/she is the person responsible for your safety and health during practice performance. Feel free to ask any questions you may have and do not put your safety or that of your classmates at risk.
Class in conventional classroom: theory, problems, case studies, seminars, etc
Lectures in which, in addition to the instructor's explanations, questions posed by students or identified by the instructor are addressed. These sessions are interspersed with practical examples and include questions for students to solve (whether graded or not). This approach encourages student interaction and contributes to the achievement of learning outcomes RA19 and RA35.
Practical activities (questions, exercises, problems) carried out in the classroom, along with similar activities assigned for students to complete independently (either individually or in groups), inside or outside the classroom (whether graded or not). Practical sessions allow students to apply the theoretical knowledge acquired, thereby supporting the achievement of learning outcomes RA19 and RA35.
27
100
Class in a computer classroom: practical classes / internships
Formulation and solving of problems using specific software in the computer classroom, along with interpretation of results. This activity contributes to the achievement of learning outcomes RA19 and RA35.
15
100
Assessment activities (continuous assessment system)
Through the completion of various assessable activities of a predominantly practical nature, the student's understanding of the subject and achievement of learning outcomes RA19 and RA35 will be progressively assessed.
3
100
Assessment activities (final assessment system)
The student's comprehension of the subject and attainment of learning outcomes RA19 and RA35 will be evaluated through a series of assessable activities, including a final examination.
2
100
Tutorials
Addressing questions related to theoretical and practical content, along with individualized monitoring of the student's progress toward learning outcomes RA19 and RA35.
2.5
80
Student work: study or individual or group work
Completion of practical exercises individually or in groups. Supports the achievement of learning outcomes RA19 and RA35.
Student's independent study of content related to lectures, practical sessions, and tutorials, etc. This includes exam preparation, library research, complementary readings, and solving problems and exercises. Supports the achievement of learning outcomes RA19 and RA35.
63
0
Spoken or written exams
The exam-based assessment will account for 80% of the overall grade. This part of the evaluation will be carried out through two midterm exams (written and completed individually), which will include practical and/or theoretical questions and exercises. Some exercises may require the use of specific software. In the case of multiple-choice questions (if included), incorrect answers will be penalized by a value equal to or greater than the probability of guessing the correct answer at random.
This assessment evaluates learning outcomes RA19 and RA35.
Students will have the option to retain the grade obtained in the exam component (as a whole, not individually for each midterm exam) throughout the academic year. They will not be required to take the equivalent exam activity in the final assessment system in order to pass the course. However, if a student takes all or part of the equivalent activity in the final assessment system, this will be considered as a waiver of the previously obtained grade for that component in the continuous assessment system for that specific exam session.
80 %
Presentation and defence of assignments
Completion of activities, exercises, or multiple-choice questionnaires (test-type questions) during class sessions. Some of these activities may be carried out in groups. Certain activities may require the use of specific software. In this assessment block, student attendance and participation, as well as other online or non-classroom activities, may also be taken into account. Evaluation activities that include multiple choice questions may apply a penalty for incorrect answers equal to or greater than the probability of guessing the correct answer at random.
This assessment evaluates learning outcomes RA19 and RA35.
Students will have the option to retain the grade obtained in this activity throughout the academic year and will not be required to take the corresponding activity in the final assessment system in order to pass the course. However, the completion (whether partially or fully) of the equivalent activity in the final assessment system will imply that the student waives the grade previously obtained for this component in the continuous assessment system for that specific exam session.
20 %
Spoken or written exams
Completion of activities, exercises, or multiple-choice questionnaires (test-type questions) during class sessions. Some of these activities may be carried out in groups. Certain activities may require the use of specific software. This assessment component may also take into account student attendance and participation, as well as other online or non-face-to-face activities. Evaluation activities that include multiple-choice questions may apply a penalty for incorrect answers equal to or greater than the probability of guessing the correct answer at random.
This component assesses learning outcomes RA19 and RA35.
Students will have the option to retain the grade obtained in this activity throughout the academic year and will not be required to complete the corresponding activity in the final assessment system in order to pass the course. However, partial or complete completion of the equivalent activity in the final assessment system will imply that the student waives the previously obtained grade for this component in the continuous assessment system for that particular exam session.
100 %
It makes it possible to verify that the teaching-learning process is progressing satisfactorily and to correct any deficiencies, generating useful information for both instructors and students. Formative assessment is not intended to assign a grade to the student, but rather to ensure that the objectives established in the learning process are being met. Activities will include the resolution of practical questions during class (not graded), as well as short control tests (not graded) based on questions posed throughout the lessons.
Author: Alegre Escolano, Pedro
Title: Ejercicios resueltos de matemáticas empresariales 2
Editorial: AC
Publication Date: 2005
ISBN: 8472880753
Author: Sydsaeter, Knut
Title: Essential mathematics for economic analysis
Editorial: Pearson Education
Publication Date: 2012
ISBN: 9780273760689
Author: Ríos Insua, Sixto
Title: Investigación operativa: Programación lineal y aplicaciones
Editorial: CEURA
Publication Date: 1996
ISBN: 8480042060
Author: Martín Martín, Quintín
Title: Investigación operativa problemas y ejercicios resueltos
Editorial: Prentice Hall
Publication Date: 2005
ISBN: 8420544663
Author: Hoy, Michael
Title: Mathematics for Economics
Editorial: the Mit Press
Publication Date: 2011
ISBN: 9780262516228
Author: Barbolla, Rosa
Title: Optimización cuestiones, ejercicios y aplicaciones a la economía
Editorial: Prentice Hall
Publication Date: 2001
ISBN: 8420529923
Author: Hillier, Frederick S.
Title: Introduction to operations research
Editorial: McGraw-Hill
Publication Date: 2005
ISBN: 007123828
Author: Camara Sánchez, Angeles
Title: Problemas resueltos de matemáticas para economía y empresa
Editorial: Thomson
Publication Date: 2008
ISBN: 9788497321709
Author: Salazar González, Juan José
Title: Programación matemática
Editorial: Díaz de Santos
Publication Date: 2001
ISBN: 8479785047
Author: Taha, Hamdy A.
Title: Operations research an introduction
Editorial: Prentice
Publication Date: 2011
ISBN: 0131391992
Modelos de Optimización en la Economía y la Empresa. Delgado, El Gibari et al. (2025). UMAEditorial. https://monografias.uma.es/index.php/mumaed/catalog/view/236/330/2597
Cañavate, R. Canal Youtube Introducción a WinQSB: http://es.youtube.com/robertocanavate
Cobacho, B. Canal Youtube Business Maths UPCT: https://www.youtube.com/user/BusinessMathsUPCT