Contactar Esade

Matemáticas (BBA50000)

General information

Type:

BAS

Curs:

1

Period:

S semester

ECTS Credits:

6 ECTS

Teaching Staff:

Group Teacher Department Language
Sec: A Xari Rovira Llobera Operaciones, Innovación y Data Sciences CAT
Sec: A Núria Agell Jané 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 the functions of a variable and system resolution.

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.

In addition, this course aims to help students to develop their resilience (the ability to overcome adverse situations), a priority developmental tool for the programme.

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:
-Introduction. Functional models
-Real functions
-Limits of functions. Continuous functions
-Derivative of a function. Applications
-Taylor Polynomial. Optimisation of functions
-Single integrals

Activities:
-Six 1.5-hour lecture classes
-Six 1.5-hour participatory classes

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:
-Level curves: Representing two-variable functions.
-Partial and directional derivatives.
-Extremes of a two-variable function.
-Constrained optimisation of functions. Graphical solution.
-Double integrals.

Activities:
-Six 1.5-hour lecture classes
-Six 1.5- hour participatory classes

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:
-Definition and types of matrices and operations
-Linear combination and dependency. Matrix range
-Square matrix eigenvalues and eigenvectors.
-Square matrix diagonalisation

Activities:
-Four 1.5-hour lecture classes
-Four 1.5-hour participatory classes

4. Quadratic forms

Aims of this unit:
After completing this section, students should be able to:
-Master the language of matrix calculus and the use of symbolic notation
-Recognise the concepts and applications of quadratic forms
-Classify quadratic forms
-Master the concepts of scalar product, norm and distance in Rn (Euclidean space)
Content:
-Definition and classification of quadratic forms
-Sign of a quadratic form
-Scalar product, norm and distance

Activities:
-Three 1.5-hour lecture classes
-Three 1.5-hour participatory classes

Methodology

Lectures and participatory sessions:

Lectures: Faculty will combine theoretical explanations with exercises. In some lecture sessions, faculty will dedicate approximately 15 minutes to give students a pop quiz.

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 %
Completion of exercises and class participation 10
Tests 10
Mid-term exam 20
Final exam 60

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:
10% - Exercises and class participation
10% - Tests
20% - Mid-term exam; students who receive a mark under 5 (out of 10) on this exam will have to retake this material as part of the final exam.
60% - Final exam on the remaining material not included in the mid-term exam.

For students to pass this course, they need to earn a minimum mean mark of 4 between the final and mid-term exams (or after resitting the latter).

For students who must 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 four course components are required to obtain the final mark for the course.

If the mark on the final exam is below a 5, the mark they obtain in the re-sit will represent 100% of the mark for the class.

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

Short bibliography:

The course website details reference texts to be used for this course.

Timetable and sections

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

Horari Sec: A

From 2015/9/14 to 2015/10/5:
Monday and Thursday from 9:30 to 11:00. (Except: 2015/9/24 and 2015/10/1)
Monday and Thursday from 8:00 to 9:30. (Except: 2015/9/24 and 2015/10/1)

From 2015/10/1 to 2015/10/22:
Monday and Thursday from 9:30 to 11:00. (Except: 2015/10/5 and 2015/10/12)
Monday and Thursday from 8:00 to 9:30. (Except: 2015/10/5 and 2015/10/12)

From 2015/11/2 to 2015/12/3:
Monday and Thursday from 9:30 to 11:00.
Monday and Thursday from 8:00 to 9:30.

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

Horari Sec: B

From 2015/9/14 to 2015/10/5:
Each Monday from 17:00 to 18:30.
Each Thursday from 15:30 to 17:00. (Except: 2015/9/24 and 2015/10/1)
Each Thursday from 14:00 to 15:30. (Except: 2015/9/24 and 2015/10/1)
Each Monday from 18:30 to 20:00.

From 2015/10/1 to 2015/10/22:
Each Monday from 17:00 to 18:30. (Except: 2015/10/5 and 2015/10/12)
Each Thursday from 15:30 to 17:00.
Each Thursday from 14:00 to 15:30.
Each Monday from 18:30 to 20:00. (Except: 2015/10/5 and 2015/10/12)

From 2015/11/2 to 2015/12/3:
Each Monday from 17:00 to 18:30.
Each Thursday from 15:30 to 17:00.
Each Monday from 18:30 to 20:00.
Each Thursday from 14:00 to 15:30.

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

Horari Sec: C

From 2015/9/14 to 2015/10/5:
Monday and Thursday from 12:30 to 14:00. (Except: 2015/9/24 and 2015/10/1)
Monday and Thursday from 11:00 to 12:30. (Except: 2015/9/24 and 2015/10/1)

From 2015/10/1 to 2015/10/22:
Monday and Thursday from 12:30 to 14:00. (Except: 2015/10/5 and 2015/10/12)
Monday and Thursday from 11:00 to 12:30. (Except: 2015/10/5 and 2015/10/12)

From 2015/11/2 to 2015/12/3:
Monday and Thursday from 12:30 to 14:00.
Monday and Thursday from 11:00 to 12:30.