Course code: 176104 | Subject title: MATHEMATICS | ||||
Credits: 6 | Type of subject: Basic | Year: 1 | Period: 1º S | ||
Department: Mathematics | |||||
Lecturers: | |||||
INDURAIN ERASO, ESTEBAN [Mentoring ] | DE MIGUEL VELASCO, JUAN R. (Resp) [Mentoring ] |
Differential calculus: a study of the functions of one and several variables, properties, operations, graphical representations, continuity, differentiability, asymptotic behavior. Homogeneous functions. Optimization, extreme of functions of one and several variables, unconstrained optimization, optimization with equality constraints. Integral calculus: indefinite and definite integral. Calculation of primitives. Applications to the calculation of areas and other applications. Matrices, determinants, operations and applications: Matrix calculus. Discussion and solving of systems of linear equations. Applications to Economics and Business Models.
- CG01: A capacity for analysis and synthesis.
- CG02: A capacity for organisation and planning.
- CG03: Oral and written communication in their mother tongue.
- CG04: Oral and written communication in a foreign language.
- CG05: Computer skills relevant to the field of study.
- CG06: The ability to search for and analyse information from different sources.
- CG07: The capacity to solve problems.
- CG08: The capacity to make decisions.
- CG09: The capacity to work as part of a team.
- CG14: Critical and self-critical skills.
- CG16: The capacity to work in high-pressure environments.
- CG17: A capacity for self-reliant learning.
CE02: To identify sources of economic information relevant to their particular enterprise and their contents.
CE03: To discern information and data relevant to their particular enterprise which a non-professional would be unable to recognise.
CE04: To analyse business management problems, applying professional criteria based on the use of technical instruments.
Learning Outcomes | Contents | Training activities | Evaluation |
R15 - R17 | Basic elements of linear algebra and differential and integral calculus | Theoretical sessions. Practical sessions. Preparation of assignments, individually or in groups. Individualized tutoring or in small groups. Personal study. | Tests of control. Working in groups. Final exam. |
R16 - R18 | Mathematical optimization | Theoretical sessions. Practical sessions. Preparation of assignments, individually or in groups. Individualized tutoring or in small groups. Personal study. | Tests of control. Working in groups. Final exam. |
The methodology used throughout this subject matter aims to give a positive answer to the following challenges (among others):
To do so, the lecturer will develop the scheduled activities in the following way:
Learning outcomes | Evaluation | Weight (%) | Recoverable nature |
R15 R16 R17 R18 | Continuous assessment: active participation in the course, tests of control and working in groups, individually or in small groups | 40 | No |
R15 R16 R17 R18 | Regular assessment (individual): in which the students should solve problems or case studies | 60 It is compulsory to get at least 4 points (up to 10) in order to pass this subject matter | Yes |
1. MATRIX CALCULUS (LINEAR ALGEBRA)
1.1. Matrices
1.2. Transpose of a matrix
1.3. Addition of matrices.
1.4. Product of a matrix by a scalar number.
1.5. Product of matrices.
1.6. Inverse matrices.
1.7. Elementary transformations of a matrix.
1.8. Successive powers of a matrix.
1.9. Determinants
1.10. Determinants and inverse matrices.
1.11. Rank of a matrix.
1.12. Systems of linear equations.
2. DIFFERENTIAL CALCULUS
2.1. The real line and the n-dimensional space.
2.2. Real functions.
2.3. Limits.
2.4. Continuity.
2.5. Derivatives (functions of a single real variable).
2.6. Partial derivatives (functions of several real variables).
2.7. Optimization (functions of a single real variable).
2.8. Concave and convex functions.
2.9. Optimization without constraints (functions of two real variables).
2.10. Optimization with constraints.
3. INTEGRAL CALCULUS
3.1. Primitive integral of a real function.
3.2. Definite integral.
4: APPENDICES
4.1. Homogeneous functions.
4.2 Optimization theory (functions of several real variables).
Access the bibliography that your professor has requested from the Library.
By means of the tool "MiAulario", the students will have access to schemes, lists of exercises, links to complementary material, etc., related to the subject matter.
We do not recommend any particular textbook on this subject. There are many possible books on Differential Calculus, Integral Calculus, Linear Algebra and related items, even from a point of view of Economics or reportedly addressed to students of Economics and/or Business Administration, that can be found in any "average-size" universitary library.
Perhaps the reference "Mathematical models in the Social, Management ald Life Sciences", by D.N. Burghes and A. D. Wood (Ellis Horwood. Chichester, UK. 1984) is an excellent reference to find "case-studies" related to the main concepts to be developed throughout the semester in this subject matter.
For the sake of completeness, we include below a list (not exhaustive, and by no means the only possible one) of texts in Spanish that can be used in the preparation of some lectures.
LIST (texts in Spanish) FOLLOWS: