Universitat Internacional de Catalunya

Mathematics 2

Mathematics 2
3
7795
1
Second semester
OB
Mètodes Quantitatius per a empresaris
Mathematics
Main language of instruction: Catalan

Other languages of instruction: English, Spanish

If the student is enrolled for the English track then classes for that subject will be taught in the same language and also in Spanish.
If the student is enrolled for the English track then classes for that subject will be taught in the same language.

Teaching staff


By appointment. In order to make an appointment, please request one by writing to: mdgil@uic.es

Introduction

In the event that the health authorities announce a new period of confinement due to the evolution of the health crisis caused by COVID-19, the teaching staff will promptly communicate how this may effect the teaching methodologies and activities as well as the assessment.


Today’s techniques for solving optimisation problems are essential in business and various fields of research.

In Mathematics 2 we will discuss optimisation problems with functions of more than one variable, and study the mathematical techniques required for solving these problems.

 

 

Pre-course requirements

It is recommended that before enrolling in this module students have completed courses on linear algebra and differential calculus with one variable.

Objectives

The main objectives of this course are to acquire a good command of the functions of several variables, especially their derivatives, and to know how to plan and solve problems of maximums and minimums with more than one variable.

Competencies

  • 17 - To be familiar with the mathematical models used to describe financial phenomena.
  • 18 - To provide mathematical models for financial phenomena.
  • 19 - To analyse quantitative financial variables and take them into account when making decisions.
  • 20 - To make decisions on resource optimisation using mathematical tools.
  • 31 - To develop the ability to identify and interpret numerical data.
  • 32 - To acquire problem solving skills based on quantitative and qualitative information.
  • 36 - To interpret quantitative and qualitative data and apply mathematical and statistical tools to business processes.
  • 40 - To be able to choose statistical methods appropriate to the object of analysis.
  • 41 - To be able to descriptively summarise information.
  • 42 - To be able to empirically analyse financial phenomena.
  • 43 - To acquire skills for using statistical software.
  • 44 - To be able to select appropriate econometric methods.
  • 45 - To be able to work with academic papers.
  • 50 - To acquire the ability to relate concepts, analyse and synthesise.
  • 51 - To develop decision making skills.
  • 52 - To develop interpersonal skills and the ability to work as part of a team.
  • 53 - To acquire the skills necessary to learn autonomously.
  • 54 - To be able to express one’s ideas and formulate arguments in a logical and coherent way, both verbally and in writing.
  • 56 - To be able to create arguments which are conducive to critical and self-critical thinking.
  • 64 - To be able to plan and organise one's work.
  • 65 - To acquire the ability to put knowledge into practice.
  • 66 - To be able to retrieve and manage information.

Learning outcomes

After completing the course, students will have acquired the following:

  • A good command of functions of several variables.
  • Ability to formulate and solve optimisation problems.
  • Ability to analyse and synthesise information obtained in the course.
  • Ability to decide and select an appropriate mathematical method to solve a certain economic optimisation problem.

Syllabus

Chapter 1: Functions of Several Variables

1.1. Definition of scalar functions

1.2. Domains of scalar functions

1.3. Graphical representation of functions of two variables. Level curves

1.4. Examples of functions in economics and business

Chapter 2: Limits and Continuity of Scalar Functions

2.1. Limit of a function at a point

2.2. Calculation of limits: repeated limits and directional limits

2.3. Definition of a continuous function

Chapter 3: Differentiation of Functions of Several Variables

3.1. Derivative by a vector

3.2. First order partial derivatives. Gradient vector

3.3. Second order partial derivatives. Hessian matrix

3.4. Directional derivatives

3.5. Tangent planes

3.6. Elasticity

3.7. Differentiation of composite functions: chain rule

Chapter 4: Applications of Derivatives: Optimisation

4.1. Relative extrema

4.2. Constrained extrema and Lagrange multipliers method

4.3. Economic interpretation of Lagrange multipliers

Teaching and learning activities

In person



Theoretical aim:

The theory behind each of the topics in the course programme is shown in detail, yet avoiding excessive formality that could mask the true purpose of the course, which is to apply mathematical language to economics. For this reason, abstract mathematical concepts are illustrated using applications and practical problems in economic terms.

Practical aim:

The concepts should be consolidated by solving the problems given to the students throughout each chapter. These problems will be resolved and discussed in class. It would also be useful for students to solve further problems from the recommended books in the bibliography.

TRAINING ACTIVITY

COMPETENCES

individual study
report presentations & discussions
solving problems in classroom

17

solving problems in classroom

18

lecture
in-class practical work (solving problems/videos/text comments/essays)
individual study
solving problems in classroom
tutorials

19

lecture
in-class practical work (solving problems/videos/text comments/essays)
individual study
solving problems in classroom
tutorials

20

lecture
individual study
solving problems in classroom
tutorials

32

individual study
solving problems in classroom

50

individual study
solving problems in classroom

51

solving problems in classroom

56

individual study

64

in-class practical work (solving problems/videos/text comments/essays)
solving problems in classroom

65

in-class practical work (solving problems/videos/text comments/essays)

54

 

TRAINING ACTIVITYCOMPETENCES
individual study
report presentations & discussions
solving problems at classroom
17
solving problems at classroom
18
magister class
classroom practice (solving problems/videos/text comments/essays)
individual study
solving problems at classroom
tutorials
19
magister class
classroom practice (solving problems/videos/text comments/essays)
individual study
solving problems at classroom
tutorials
20
magister class
individual study
solving problems at classroom
tutorials
32
individual study
solving problems at classroom
50
individual study
solving problems at classroom
51
solving problems at classroom
56
individual study
64
classroom practice (solving problems/videos/text comments/essays)
solving problems at classroom
65
classroom practice (solving problems/videos/text comments/essays)
54

Evaluation systems and criteria

In person



The module will be evaluated on the basis of three elements: continuous evaluation, mid-course examination and final examination, and as follows:

Continuous evaluation

15%

15%

Mid-course examination

15%*

30%*

Final examination

70%*

55%*

* This percentage will be determined by the mark obtained in the mid-course examination

Second sitting

For students taking the second-sitting examination, evaluation will take place as follows:

Continuous evaluation

15%*

Final examination

85%

* The continuous evaluation mark will be the same as for the first sitting.

Bibliography and resources

  • Adillon, R.; Álvarez, M.; Gil, D.; Jorba, L.: Mathematics for Economics and Business. Publicacions i Edicions de la UB. Economy UB.
  • Sydsaeter, K.; Hadmmond, P.J.: Mathematics for Economic Analysis. Prentice Hall.
  • Guzman, L.; et al.: Fundamentos matemáticos para la Administración y Dirección de empresas. Centro de estudios Ramon Areces.
  • Alegre, P.; et al.: Ejercicios resueltos de matemáticas empresariales 2. A.C.
  • Cámara, A.; et al.: Problemas resueltos para Economía y Empresa. A.C.

Teaching and learning material