Universitat Internacional de Catalunya
Business Mathematics-2
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.
Teaching staff
By appointment. In order to make an appointment, please request one by writing to: mdgil@uic.es
Introduction
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.
Competences/Learning outcomes of the degree programme
- 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 of the subject
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
- Ch.1 Glossary - English
- Ch.1 Glossary - Catalan
- Ch.1 ppt Presentation - English
- Ch.1 ppt Presentation - Catalan
- Ch.2 Glossary - English
- Ch.2 Glossary - Catalan
- Ch.2 ppt Presentation - English
- Ch.2 ppt Presentation - Catalan
- Ch.3 Glossary - English
- Ch.3 Glossary - Catalan
- Ch.3 ppt Presentation - English
- Ch.3 ppt Presentation - Catalan
- Ch.4 Glossary - English
- Ch.4 Glossary - Catalan
- Ch.4 ppt Presentation - English
- Ch.4 ppt Presentation - Catalan
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 |
17 |
|
solving problems in classroom |
18 |
|
lecture |
19 |
|
lecture |
20 |
|
lecture |
32 |
|
individual study |
50 |
|
individual study |
51 |
|
solving problems in classroom |
56 |
|
individual study |
64 |
|
in-class practical work (solving problems/videos/text comments/essays) |
65 |
|
in-class practical work (solving problems/videos/text comments/essays) |
54 |
| TRAINING ACTIVITY | COMPETENCES |
|---|---|
| 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
Given that the maximum number of justified absences is two, if this number is exceeded the student will get a zero in the continuous evaluation. No unjustified absences are allowed towards the continuous evaluation.
In case of not being able to take the mid-course examination for one of the reasons stipulated by the faculty, this will not be repeated another day, but the final examination will have a weight of 85% of the overall grade.
The behaviour in the classroom will have a very significant weight in the continuous evaluation. In this sense, repeated inappropriate behavior due to interruptions, distractions, or use of electronic devices in the classroom, will result in a zero in the continuous evaluation.
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.