Mathematics Applied to Economic Analysis

General information

Type:	OPT	Curs:	2	Period:	S semester
ECTS Credits:	7 ECTS

Teaching Staff:

Group	Teacher	Department	Language
Year 2	Jordi Montserrat Adell	Operaciones, Innovación y Data Sciences	ENG

Prerequisites

Ability to work in English..

Previous Knowledge

Basic knowledge of functions of one variable and solving linear equations (simultaneous or not).

Workload distribution

50% In-class activities
50% Individual study

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, as well as differential equations, to apply them over the course of their academic and professional career.
- Use mathematical reasoning and demonstrate basic propositions.
- Demonstrate rigorous deductive processes.

CONTENT

1. Study of functions of one variable 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 function of two variables 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. Partial and directional derivatives. 3. Extremes of a two-variable function. 4. Constrained optimisation of functions.
3. Differential equations Aims of this unit: Upon completing this section, students should be able to: -Understand the concept of differential equations. -Know how to solve problems and develop reasoning including differential equations. Content: 1. Definition of differential equations. 2. Resolution of differential equations.
4. 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. Eigenvalues and eigenvectors. 4. Diagonalisation

1. Study of functions of one variable

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 function of two variables

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. Partial and directional derivatives.
3. Extremes of a two-variable function.
4. Constrained optimisation of functions.

3. Differential equations

Aims of this unit:
Upon completing this section, students should be able to:
-Understand the concept of differential equations.
-Know how to solve problems and develop reasoning including differential equations.

Content:
1. Definition of differential equations.
2. Resolution of differential equations.

4. 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. Eigenvalues and eigenvectors.
4. Diagonalisation

Relation between Activities and Contents

	1	2	3	4
Class participation
Tests
Exam Units 1&2
Exam Units 3&4

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	10
Tests	25
Exam Units 1&2	40
Exam Units 3&4	25

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% - Class participation
25% - Tests
40% - Exam Units 1&2
25% - Exam Units 3&4

For the overall average to be computed, students' marks for the different course components are required.

Students that earn below a 5 on the final average will have to resit on an extraordinary exam on all units of the course, with a weight of 65%. The rest will be the continuous evaluation with the same weights than in the ordinary sitting (10% class participation and 25% tests).

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).

According to ESADE internal regulations for the Law School students must attend at least 80% of the sessions to seat in the first attempt exam, minimum attendance to have the right to do the resit exam is 50%.

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
Year 2	Jordi Montserrat Adell	Operaciones, Innovación y Data Sciences

Timetable Year 2

From 2022/9/6 to 2022/11/25:
Each Tuesday from 14:00 to 16:30. (Except: 2022/11/1)
Each Friday from 15:00 to 17:30. (Except: 2022/11/4)

From 2022/12/9 to 2022/12/12:
Each Monday from 14:15 to 18:45.
Each Friday from 9:00 to 10:30.

Friday 2023/2/10 from 9:15 to 12:30.

Mathematics Applied to Economic Analysis (2225.YR.013003.3)