2020/2021

Degree | Type | Year | Semester |
---|---|---|---|

2501572 Business Administration and Management | FB | 1 | 1 |

2501573 Economics | FB | 1 | 1 |

The proposed teaching and assessment methodology that appear in the guide may be subject to changes as a result of the restrictions to face-to-face class attendance imposed by the health authorities.

- Name:
- Maria del Mar Gómez Pujalte
- Email:
- MariaDelMar.Gomez@uab.cat

- Principal working language:
- catalan (cat)
- Some groups entirely in English:
- Yes
- Some groups entirely in Catalan:
- Yes
- Some groups entirely in Spanish:
- Yes

- Vladimir Zaiats Protchenko
- Sergio Baena Mirabete
- Laia Egea Cortes
- Pol Orobitg Bernades

The objective of the Mathematics I course is to bring all the students to a certain level of mathematics that will allow them to acquire and consolidate theknowledge and skills necessary to understand and correctly manipulate basic mathematical concepts and carry out the analysis of a real variable. In addition, the student must be capable of applying such knowledge to simple models and problems as they pertain to an economics and business context. The skills and knowledge acquired in Mathematics I, together with Mathematics II, will afford the student the necessary tools to study more advanced subjects.

For this reason, the objectives that are intended to be achieved are the following:

1. To familiarise the student with the formulation and mathematical reasoning.

2. To introduce the role of mathematical models in economics and business.

3. To identify and know how to manipulate the main families of functions.

4. To work with derivatives and solve function limits of one variable.

5. To understand and know how to determine the basic properties that exhibit the functions of one variable.

6. To represent functions of one variable graphically.

7. To solve optimisation problems with one variable.

8. To determine and calculate primitives using the basic integration techniques.

- Apply mathematical instruments to synthesise complex economic-business situations.
- Capacity for oral and written communication in Catalan, Spanish and English, which enables synthesis and oral and written presentation of the work carried out.
- Demonstrate an understanding of mathematical language and some methods of demonstration.
- Organise the work in terms of good time management, organisation and planning.
- Use of the available information technology and adaptation to new technological environments.

- Demonstrate an understanding of mathematical language and some methods of demonstration.

- A capacity of oral and written communication in Catalan, Spanish and English, which allows them to summarise and present the work conducted both orally and in writing.
- Analyse and draw functions.
- Analytically consider and solve optimisation problems in the context of the economy.
- Be able to work with inequalities and sequences.
- Calculate and study the extrema of functions.
- Calculate the functional integrals of a variable.
- Deduce the properties of a function based on its graph.
- Organise work, in terms of good time management and organisation and planning.
- Solve problems that involve considering integrals in problems in the context of the economy (consumer and producer surplus, etc.).
- Use available information technology and be able to adapt to new technological settings.
- Work intuitively, geometrically and formally with the notions of limits, derivatives and integrals.

PART I. INTRODUCTION

Topic 1. **BASIC CONCEPTS**

1.1. Basics: variables, constants, parameters, equations and identities

1.2. Sets. Basic operations and properties between sets

1.3. The real number: concept and absolute value

1.4. The real line: distance, inequalities, inequalities and intervals

Topic 2. **BASICS OF ALGEBRA AND BASIC OPERATIONS**

2.1. Growth rates

2.2. The use of logarithms. Applications to the economy

2.3. Calculation with fractions, powers and roots

2.4. Simplification of mathematical expressions

PART II. STUDY AND REPRESENTATION OF FUNCTIONS

Topic 3. **FUNCTIONS**

3.1. Real functions of one variable; domain and image

3.2. Type of functions and properties

3.3. Operations with functions

Topic 4. **CONTINUITY**

4.1. Limits and indeterminations

4.2. Study of the continuity of a function. Discontinuity classification

Topic 5. **DIFFERENTIATION**

5.1. The concept of derivative. Economic and geometric interpretation

5.2. The derived function. Differentiation rules

Topic 6. **STUDY AND REPRESENTATION OF FUNCTIONS**

6.1. Differentiable functions

6.2. Basic study of functions; cutting points and symmetries

6.4. Monotony of functions. Increase, decrease and local

stationary points

6.5. Curvature of functions. Concavity, convexity, maximum, minimum and points of inflection

6.6. Asymptotes

6.7. Graphical representation of functions

PART III. OPTIMISATION WITH ONE INDEPENDENT VARIABLE

Topic 7. **OPTIMISATION WITH ONE VARIABLE**

7.1. Optimisation issues. Local stationary points and optimum solutions

7.2. Optimisation at closed intervals. The Weierstrass theorem

PART IV. PRINCIPLES OF INTEGRATION

Topic 8. **INTRODUCTION TO INTEGRATION**

8.1. The concept of integral

8.2. Primitives and the calculation of integrals

8.3. Defined Integrals

Topic 9. **PRIMITIVE CALCULUM METHODS**

9.1. Integration by parts

9.2. Integration by substitution

Teaching will be offered on campus or in an on-campus and remote hybrid format depending on the number of students per group and the size of the rooms at 50% capacity.

To achieve the objectives previously outlined, the following types of activities will be used:

**1. Theoretical lectures where teachers** **will present the main concepts**

The objective of this activity is to present the fundamental notions of the subject, and to facilitate their learning through the analysis of examples, which will emphasise both intuitive aspects and applications and explanations in the field of Economics.

**2. Practical classes where the resolution of the problems will be discussed**

This activity has the purpose to answer doubts that students may have encountered during the resolution of the problems and to correct possible errors committed. The presentation of solutions by students will be prioritised, either orally as a first step in their discussion, or in written form.

**3. Problem solving by students**

Each topic will have a list of associated problems, which the students will have to solve independently. This activity has a dual objective of allowing the student to demonstrate that he/she has assimilated the theoretical concepts and work tools presented in class and that he/she has acquired the necessary skills to solve exercises and problems.

**4. Attending office hours**

The student will have access to some tutorials with the teacher that presents the course, in order to address doubts that may have arisen during the study of the subject and in the resolution of the problems. Due to the use of mathematical symbols that this activity implies, the tutorials will be developed in person.

The proposed teaching methodology may undergo some modifications according to the restrictions imposed by the health authorities onon-campus courses.

Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|

Type: Directed | |||

Problem sets resolution | 13 | 0.52 | 2, 5, 6, 1, 7, 4, 8, 3, 9, 11, 10 |

Theory lectures | 33 | 1.32 | 2, 5, 6, 7, 4, 3, 9, 11 |

Type: Supervised | |||

Follow-up of homework | 3 | 0.12 | 2, 5, 6, 1, 7, 4, 8, 3, 9, 11, 10 |

Tutorships | 3.5 | 0.14 | 2, 5, 6, 1, 7, 4, 8, 3, 9, 11, 10 |

Type: Autonomous | |||

Study | 94 | 3.76 | 2, 5, 6, 1, 7, 4, 8, 3, 9, 11, 10 |

The evaluation of the course will be carried out in a continuous way, through partial assessments and a final exam. The type of activities and their relative weight in the final note is the following:

- Final exam: 50% of the final mark (it will include the totality of the syllabus)

- Mid-term exam: 30% of the final mark

- Continuous assessment activities: a total of 20% of the final mark

The final grade will be the weighted average of all the activities. The minimum mark for any activity is not set.

If, once applied the above mentioned percentage the mark achieved is 5 or higher, the course is considered as passed and this will not be subject to a new evaluation. In case of a grade less than 3.5, the student will have to sit it again in the following year. For those students who have obtained a grade that is equal to or greater than 3.5 and less than 5 there will be a re-take exam. The teachers of the subject will decide the modality of this re-take exam. This re-take exam is scheduled in the last week of the semester. The re-take exam grade will be qualitative and will only have two possible options: PASS or NO PASS. If the student obtains a PASS grade, it is considered that they have passed the subject with a maximum numerical grade equal to 5. If the student obtains a NO PASS score, they do not have passed the subject and the final grade will be equal to the one obtained before the re-take exam.

A student is considered to be "Not Evaluated" in the subject as long as he/she has not participated in any of the assessment activities. Therefore, it is considered that a student who carries out some components of the continuous assessment modality can no longer opt for a "Not Evaluated".

Students attending the subject for the second, third or fourth time have the option to follow the continuous modality or to sit directly and only the final exam, which will count 100% of the final grade.

The choice of this last option must accordingly be notified to their teacher during the first weeks of the semester, prior to any of the continuous evaluation activities. Submission of any of such activities shall be understood as to implicitly waiving this option.

Both the mid-term and the final exams will be common to all the bachelor grades of the Faculty and they will be carried out on the same day and at the same time (the mid-term will take place either in the morning or in the afternoon, according to the group the student was previously assigned to).

Students must be examined in the classroom assigned to the group where they are enrolled. Doing the exam in the classroom assigned to another group may entail invalidation of the examand it will be classed as ‘Not-attended’.

**Calendar of evaluation activities**

The dates of the evaluation activities (midterm exams, exercises in the classroom, assignments, ...) will be announced well in advance during the semester.

The date of the final exam is scheduled in the assessment calendar of the Faculty.

*"The dates of evaluation activities cannot be modified, unless there is an exceptional and duly justified reason why an evaluation activity cannot be carried out. In this case, the degree coordinator will contact both the teaching staff and the affected student, and a new date will be scheduled within the same academic period to make up for the missed evaluation activity."* *Section 1 of Article 115. Calendar of evaluation activities (Academic Regulations UAB)**.* Students of the Faculty of Economics and Business, who in accordance with the previous paragraph need to change an evaluation activity date must process the request by filling out an **Application for exams' reschedule** https://eformularis.uab.cat/group/deganat_feie/application-for-exams-reschedule

**Grade revision process**

After all grading activities have ended, students will be informed of the date and way in which the course grades will be published. Students will also be informed of the procedure, place, date and time of grade revision following University regulations.

**Retake Process**

*"To be eligible to participate in the retake process, it is required for students to have been previously been evaluated for at least two thirds of the total evaluation activities of the subject." Section 3 of Article 112 ter. The recovery (UAB Academic Regulations).* Additionally, it is required that the student to have achieved

The date of the retake exam will be posted in the calendar of evaluation activities of the Faculty. Students who take this exam and pass, will get a grade of 5 for the subject. If the student does not pass the retake, the grade will remain unchanged, and hence, student will fail the course.

**Irregularities in evaluation activities**

In spite of other disciplinary measures deemed appropriate, and in accordance with current academic regulations, *"in the case that the student makes any irregularity that could lead to a significant variation in the grade of an evaluation activity, it will be graded with a 0, regardless of the disciplinary process that can be instructed. In case of various irregularities occur in the evaluation of the same subject, the final grade of this subject will be 0"*. *Section 10 of Article 116. Results of the evaluation. (UAB Academic Regulations).*

The proposed evaluation activities may undergo some changes according to the restrictions imposed by the health authorities on on-campus courses.

Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|

Activities to be delivered | 20% | 0.5 | 0.02 | 2, 5, 6, 7, 4, 8, 3, 9, 11, 10 |

Final exam | 50% | 2 | 0.08 | 2, 5, 6, 1, 7, 4, 3, 9, 11 |

Mid-term exam | 30% | 1 | 0.04 | 2, 5, 6, 1, 7, 4, 3, 9, 11 |

**Main textbooks:**

- Sydsaeter, K. and P.J. Hammond,
*Mathematics for Economic Analysis*. London, Prentice Hall (1995). - Sydsaeter, K. and P.J. Hammond,
*Essential Mathematics for Economic Analysis*. Fourth edition. Pearson Education (2012).

**Complementary textbooks:**

- Alejandre, F., F. Llerena, i C. Villela,
*Problemes de matemàtiques per a econòmiques i empresarials,*Editorial Media (1995). - Chiang, A.C., Fundamental Methods of Mathematical Economics, McGraw-Hill. (2005).
- Hoffmann, L.D., G.L. Bradley, G., and K.H. Rosen, 2005, Applied Calculus for Business, Economics, and the Social and Life Sciences, McGraw-Hill (2005).
- Alegre, P., L. Jorba, F.J. Orti, G. Rodriguez, J.B. Saez, T. Sancho i A. Terceño,
*Ejercicios Resueltos de Matemáticas Empresariales II*. Editorial Alfacentauro, Madrid (2000).