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Matemáticas Aplicadas a la Gestión (18BBA50000)

General information

Type:

BAS

Curs:

1

Period:

S semester

ECTS Credits:

6 ECTS

Teaching Staff:

Group Teacher Department Language
Sec: A Núria Agell Jané Operaciones, Innovación y Data Sciences CAT
Sec: A Xari Rovira Llobera Operaciones, Innovación y Data Sciences CAT

Group Teacher Department Language
Sec: B Xari Rovira Llobera Operaciones, Innovación y Data Sciences ESP

Group Teacher Department Language
Sec: C Xari Rovira Llobera Operaciones, Innovación y Data Sciences CAT

Prerequisites

Basic knowledge of variable functions and resolving systems of linear equations.

Workload distribution

Lectures: 30 hours
Participatory sessions: 30 hours
Independent study: 90 hours

COURSE CONTRIBUTION TO PROGRAM

Mathematics is an essential tool for quantitative information analysis, the creation and interpretation of models to explain the economic and financial reality of the business environment and for the development of structured reasoning processes.

Course Learning Objectives

After completing this course, students should be able to:

- Recognise and use mathematical language fluently in specific situations.
- Understand, relate and use the concepts and theoretical models of basic matrix algebra and one and two-variable calculus to apply them over the course of their academic and professional career.
- Use mathematical reasoning and demonstrate basic propositions.
- Demonstrate rigorous deductive processes.

Competences

1. Knowledge acquisition, comprehension and structuring
5. Ability for continuous learning/Ability to learn continually
2. Application of knowledge to achieve results
4. Conveying information and/or knowledge

CONTENT

1. Study of one-variable functions

Aims of this unit:
Upon completing this section, students should be able to:
-Use one-variable calculus language.
-Understand, use and apply the concepts of limits, continuity and function derivatives.
-Interpret simple-function graphs.
-Develop simple reasoning using these concepts in concrete applications.

Content:
1. Introduction. Functional models
2. Real functions
3. Limits of functions. Continuous functions
4. Derivative of a function. Applications
5. Taylor polynomial. Optimisation of functions
6. Single integrals

2. Study of two-variable functions

Aims of this unit:
Upon completing this section, students should be able to:
-Use two-variable calculus language.
-Understand, use and apply concepts related to two-variable functions.
-Represent and interpret level curves and use them in specific applications.
-Represent enclosed areas in the plane and resolve some double integrals.

Content:
1. Level curves: Representing two-variable functions.
2. Partial and directional derivatives.
3. Extremes of a two-variable function.
4. Constrained optimisation of functions. Graphical solution.
5. Double integrals.

3. Matrices

Aims of this unit:
Upon completing this section, students should be able to:
-Master matrix calculus language and use symbolic notations.
-Know how to resolve problems and develop simple reasoning including matrices.
-Understand and know how to apply square matrix diagonalisation processes.

Content:
1. Definition and types of matrices and operations
2. Linear combination and dependency. Matrix range
3. Square matrix eigenvalues and eigenvectors.
4. Square matrix diagonalisation
5. Definition, classification and application of square matrices.

Methodology

Lectures and participatory sessions:

Lectures: Faculty will combine theoretical explanations with exercises. Lecture classes will include tests. Students' marks on these will be taken into account to determine their overall marks for the subject.

Participatory sessions: Some of these classes will focus on preliminary concepts, while others will be dedicated to resolve more advanced problems as defined by faculty. These exercises are to be completed in groups and handed in at the end of class. Students will work in small groups of 3 or 4 each in all participatory sessions. These groups will be created on the first day of class and will remain the same throughout the course.

ASSESSMENT

ASSESSMENT BREAKDOWN

Description %
Class participation 20
Tests 10
Mid-term exam 25
Final exam 45

Assessment criteria

The correct use of concepts and theoretical models, and mastery of mathematical notation achieved through the completion of exercises that must be undertaken both through independent, out-of-class study as well as through group-work activities during the participatory classes.
The ability to carry out reasoning and simple demonstrations will be assessed through discussion and problem-solving activities in the classroom during the participatory classes. This will also be assessed through tests and the mid and final exams.

Students' final marks will be based on the following activities and their respective percentages:
20% - Class participation
10% - Tests
25% - Mid-term exam
45% - Final exam on the material not included in the mid-term exam.

For students who do not earn a minimum of 5 out of 10 on the mid-term exam, the final exam will include all the course content and will be worth 70% of students' final marks.

For students who earn at least a 5 out of 10 on the mid-term exam, they have to earn a minimum of 4 out of 10 on the final exam in order to pass the class.

For students that have to retake the course and can only sit the final exam, 100% of the mark for the course will be the mark they obtain on the final exam which covers all the course material. For the remaining students, students' marks for the different course components are required to obtain the final mark for the course.

Students that earn below a 5 on the final exam will have to re-sit the latter in July.

For students to be able to assess their own learning and progress, they will receive feedback from faculty throughout the course. This feedback will be given in different ways depending on the evaluation activity (corrected tests and exams and feedback in the participatory sessions).

Bibliography

Any basic mathematical text applied to social sciences and economics can be useful to enhance the learning process in this course. Below are a few such texts students can consult:
Sydsaeter, K. and Hammond, P. Essential Mathematics for Economic Analysis. Ed Pearson, Fourth Edition 2012
Pemberton, M. and Rau, N. Mathematics for Economists: An Introductory Textbook. Ed Manchester University Press, Third Edition 2013
Hoffmann, L.; Bradley, G and Rosen, K. Applied Calculus for Business, Economics and the Social and Life Sciences. Ed McGraw-Hill, 2004

Timetable and sections

Group Teacher Department
Sec: A Núria Agell Jané Operaciones, Innovación y Data Sciences
Sec: A Xari Rovira Llobera Operaciones, Innovación y Data Sciences

Timetable Sec: A

Group Teacher Department
Sec: B Xari Rovira Llobera Operaciones, Innovación y Data Sciences

Timetable Sec: B

Group Teacher Department
Sec: C Xari Rovira Llobera Operaciones, Innovación y Data Sciences

Timetable Sec: C