Mathematics 2
Module: Mètodes Quantitatius per a empresaris
Matter: 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.
Head instructor
Dra. Maria Dolors GIL - mdgil@uic.es
Office hours
By appointment. In order to make an appointment, please request one by writing to: mdgil@uic.es
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.
It is recommended that before enrolling in this module students have completed courses on linear algebra and differential calculus with one variable.
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.
After completing the course, students will have acquired the following:
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
Chapter 0 Presentation of the subject
Material
Ch.0 ppt presentation - English mathii-presentation.pdf
Ch.0 ppt presentation - Catalan matesii-presentacio.pdf
Chapter 1 Functions of several variables
Material
Ch.1 Glossary - English glossarychapter1-mathii.pdf
Ch.1 Glossary - Catalan glossaritema1-matesii.pdf
Ch.1 ppt presentation - English mathii-chapter1.pdf
Ch.1 ppt presentation - Catalan matesii-tema1.pdf
Chapter 2 Limits and continuity of scalar functions
Material
Ch.2 Glossary - English glossarychapter2-mathii.pdf
Ch.2 Glossary - Catalan glossaritema2-matesii.pdf
Ch.2 ppt presentation - English mathii-chapter2.pdf
Ch.2 ppt presentation - Catalan matesii-tema2.pdf
Chapter 3 Differentiation of functions of several variables
Material
Ch.3 Glossary - English glossarychapter3-mathii.pdf
Ch.3 Glossary - Catalan glossaritema3-matesii.pdf
Ch.3 ppt presentation - English mathii-chapter3.pdf
Ch.3 ppt presentation - Catalan matesii-tema3.pdf
Chapter 4 Applications of the derivatives: Optimisation
Material
Ch.4 Glossary - English glossarychapter4-mathii.pdf
Ch.4 Glossary - Catalan glossaritema4-matesii.pdf
Ch.4 ppt presentation - English mathii-chapter4.pdf
Ch.4 ppt presentation - Catalan matesii-tema4.pdf
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 |
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.