Mathematics 1
Module: Mètodes Quantitatius per a empresaris
Matter: Mathematics
Main language of instruction: Spanish
Other languages of instruction: Catalan, English
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
During the 18th and 19th centuries the study of economics took a spectacular turn, as economic reasoning began to be formalised and developed, incorporating increasingly complex theories with multiple variables involved.
Agustin Cournot was the first to use the language of mathematics to study demand curves and resolve optimisation problems. By using the language of mathematics has models on the behaviour of economic variables have been created.
Students of economics require a solid base in mathematics in order to have the linguistic means required to understand these theories.
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In order to enrol in this module, it is recommended that students be able to solve equation systems, calculate derivatives and solve second- and third-degree equations.
The objective of this course is to master infinitesimal calculus with functions of one variable, since these concepts are used as a basic tool in the mathematical description of economic phenomena.
The main problem in economics lies in optimising the always limited resources; therefore special attention should be paid to optimisation problems that can be formulated using functions of one variable, showing that a greater understanding of mathematical analysis can lead to a natural solution for such problems.
By the end of the course, students will have acquired the following learning outcomes:
Chapter 1: Real Function of One Variable
1.1. Definition of Real Function of One Variable. Domain
1.2. Functional Limits
1.3. Continuity. Types of Discontinuities
1.4. Definition of a Derivative. Tangent Line. Calculation of Derivatives
1.5. Elasticity of a Function
1.6. Applications of Derivatives: Increasing and Decreasing Functions, Extreme Values, Curvature and L'Hôpital's Rule
1.7. Economic Applications
Chapter 2: Integration
2.1. Calculation of Primitives. The Indefinite Integral
2.2. The definite integral. Barrow’s Rule
2.3. Applying the Definite integral to the Calculation of Areas
2.4. Improper Integral
2.5. First Order Differential Equations
2.6. Economic Applications
Chapter 3: Linear Algebra
3.1. Systems of Linear Equations
3.2. Definition of a Vector Space
3.3. Linear Combination
3.4. Linear Independence
3.5. Spanning Set
3.6. Basis of a Vector Space
3.7. Definition of a Vector Subspace
3.8. Scalar Product, Norm, Angle and Distance
3.9. Quadratic Forms
3.10. Economic Applications
Chapter 4: Numerical Sequences and Series
4.1. Sequences of Real Numbers
4.2. Properties of Sequences
4.3. Finite and Infinite Series
4.4. Convergence Criteria
4.5. Economic Applications
Chapter 0 Presentation of the subject
Material
Ch.0 ppt presentation - English mathi-presentation.pdf
Ch.0 ppt presentation - Catalan matesi-presentacio.pdf
Chapter 1 Real function of one variable
Material
Ch.1 Glossary - English glossarychapter1-mathi.pdf
Ch.1 Glossary - Catalan glossaritema1-matesi.pdf
Ch.1 ppt presentation - English mathi-chapter1.pdf
Ch.1 ppt presentation - Catalan matesi-tema1.pdf
Chapter 2 Integration
Material
Ch.2 Glossary - English glossarychapter2-mathi.pdf
Ch.2 Glossary - Catalan glossaritema2-matesi.pdf
Ch.2 ppt presentation - English mathi-chapter2.pdf
Ch.2 ppt presentation - Catalan matesi-tema2.pdf
Chapter 3 Linear algebra
Material
Ch.3 Glossary - English glossarychapter3-mathi.pdf
Ch.3 Glossary - Catalan glossaritema3-matesi.pdf
Ch.3 ppt presentation - English mathi-chapter3.pdf
Ch.3 ppt presentation - Catalan matesi-tema3.pdf
Chapter 4 Numerical sequences and series
Material
Ch.4 Glossary - English glossarychapter4-mathi.pdf
Ch.4 Glossary - Catalan glossaritema4-matesi.pdf
Ch.4 ppt presentation - English mathi-chapter4.pdf
Ch.4 ppt presentation - Catalan matesi-tema4.pdf
Theoretical aim:
The theory of the module is presented in detail, yet avoiding excessive formalisation that could override the true purpose of the course: to apply mathematical language to economics. For this reason, abstract mathematical concepts are illustrated using applications and practical exercises in connection with economics.
Practical aim:
The concepts should be consolidated by solving the problems given to the students throughout each chapter. These problems will be solved and discussed in class. It would also be useful for students to solve other problems from the recommended books in the bibliography.
TRAINING ACTIVITY |
COMPETENCES |
lecture |
17 |
lecture |
18 |
lecture |
19 |
in-class practical work (solving problems/videos/text comments/essays) |
20 |
in-class practical work (solving problems/videos/text comments/essays) |
32 |
lecture |
50 |
in-class practical work (solving problems/videos/text comments/essays) |
51 |
report presentations & discussions |
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 |
The module will be evaluated on the basis of three elements: continuous evaluation, mid-course examination and final examination, 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 for the module will be the same as for the first sitting.
E: exam date | R: revision date | 1: first session | 2: second session: