Matemáticas Aplicadas a la Gestión

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

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.

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 function continuity, derivatives and integrals. -Interpret simple-function graphs. -Develop simple reasoning using these concepts in concrete applications. Content: a. Functional models. Real functions. Continuous functions. b. Derivative of a function. Applications c. 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: a. Two-variable functios. Partial derivatives. b. Extremes of a two-variable function. c. Constrained optimisation of functions. Graphical solution: level curves. d. Double integrals.
3. Matrices Aims of this unit: Upon completing this section, students should be able to: -Master matrix calculus language and fluidly use symbolic notations. -Know how to resolve problems that include matrices. -Understand and know how to apply square matrix diagonalisation processes. Content: a. Square matrix values and vectors. Matrix diagonalisation processes. b. Definition, classification and application of square matrices.

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 function continuity, derivatives and integrals.
-Interpret simple-function graphs.
-Develop simple reasoning using these concepts in concrete applications.

Content:
a. Functional models. Real functions. Continuous functions.
b. Derivative of a function. Applications
c. 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:
a. Two-variable functios. Partial derivatives.
b. Extremes of a two-variable function.
c. Constrained optimisation of functions. Graphical solution: level curves.
d. Double integrals.

3. Matrices

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

Content:
a. Square matrix values and vectors. Matrix diagonalisation processes.
b. Definition, classification and application of square matrices.

Methodology

Participatory sessions: In these participatory sessions, students will work in small groups (3 or 4 students). Faculty will distribute students into their groups to discuss exercises during the first class. These groups will remain the same throughout the course. There are 3 types of participatory sessions:
- Review preliminary concepts
- Introduce the topics
- Resolve more advanced problems.

In the last type of session, groups are required to turn in their solutions at the end of class. The session will end with a 10-minute test to assess what they have learned. These tests are part of students ongoing assessment for the course.

Description	%
Class participation	25
Peer evaluation	5
Learning tests	10
Subject block exams	60

Assessment criteria

Faculty will assess students' correct use of concepts and theoretical models and their mastery of mathematical notation achieved through problem-solving exercises that must be undertaken both through independent, out-of-class work as well as through group activities during the participatory classes.

Their ability to carry out reasoning and simple demonstrations will be assessed through discussion and problem-solving activities in the classroom during the participatory classes and different assessed learning activities.

25% - Class participation: dedication, involvement, effot and teamwork
5% - Peer evaluations
10% - Assessed learning activities
60% - Subject block exams.

Students who do not earn a minimum of 5 out of 10 on any of the 3 block exams can re-sit the content of that block or blocks during the final exam.

Students who pass all 3 block exams can sit the final exam to raise their marks if they so desire.

For students who have to retake the course but 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 on the different course components are required to obtain the final mark for the course.

Students that earn below a 5 out of 10 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 problems, exercises, tests 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
Renshaw, Geoff. Maths for economics. Oxford University Press. 3rd edition. 2012

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

Matemáticas Aplicadas a la Gestión (19BBA50000)

General information

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Workload distribution

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