Business Mathematics I

With this program it is introducing the student to the basics of matrix Algebra and differential calculus of one and several variables, in order to provide it with the necessary instruments for the development of those subjects that have a quantitative.

I LINEAR ALGEBRA


Theme I: VECTOR SPACES

1. The vector space Rn.
2. Dependence on linear independence.
3. Basis and dimension.

Theme II: MATRICES AND LINEAR APPLICATIONS

1. Review of the algebra of matrices: basic definitions.
2. Matrix operations. Range and inverse of a matrix.
3. Definition of linear application.
4. Matrix associated to a linear application.


Theme III: DETERMINANTS.

1. Fundamental concepts. Properties.
2. Inverse matrix . Calculation.

Theme IV: SYSTEMS OF LINEAR EQUATIONS.

1. Introduction.
2. Cramer system.
3. Homogeneous systems.
4. General case.



II. CALCULATING DIFFERENTIAL


Theme V: EUCLIDEAN SPACE n-DIMENSIONAL

1. Domestic product, standard and Euclidean distance.
2. Topological notions in Rn and R.
3. Sequences of real numbers. Limits.


Theme VI: REAL FUNCTIONS OF A REAL VARIABLE : LIMITS AND CONTINUITY.

1. Real functions of a real variable.
2. Concept of limit of a function.
3. Operations with limits and calculation of limits.
4. Continuity of a function.
5. Specific theorems of real functions of real variable.

Theme VII: REAL FUNCTIONS OF A REAL VARIABLE DIFFERENTIABLE.

1. Derived from a function at a point. Geometric interpretation of the derivative.
2. Calculation of derivatives. Rules of derivation.
3. Concept of the differential of a function at a point.
4. Concerning derivable functions theorems: Rolle, Value Means, L' Hôpital's Rule.
5. Successive derivatives. Functions of class n (Cn) Taylor Formula.
6. Study of the curve of a function: growth, decrease, ends, concavity, convexity and turning points.

Basic and additional bibliography:
- Alegre Escolano, P. e outros (1995), Matemáticas empresariales. Ed. AC
- Arya, Larner; Matemáticas Aplicadas a la Administración y a la Economía. Ed. Prentice-Hall.
- Caballero, R.. e outros (1993). Métodos matemáticos para la Economía. Ed. McGraw-Hill.
- Camacho, E. e outros (2005). Fundamentos de Cálculo para Economía y Empresa. Ed. Delta.
- Chiang, A.C. (1987). Métodos fundamentales de Economía matemática. Ed. McGraw-Hill.
- Jarne, G.; Perz-Grasa, I.; Minguillón, E.(1997): Matemáticas para la Economía. Álgebra Lineal y Cálculo Diferencial. Editorial McGraw-Hill.
- López Cachero, M. (1994). Curso básico de matemáticas para la economía y dirección de empresas II. Ejercicios. Ed. Pirámide.
- Pallas,J; Miranda, F; Ramos, A.; De Miguel, J.C.(2003): Manual de Álgebra Lineal. Tórculo Edicións.
- Sydsaeter, K. e Hammond, P. (1998), Matemáticas para el análisis económico. Ed. Prentice-Hall.

In the following books will have a good and extensive selection of solved problems of linear algebra and differential calculus

-Arvesú, Marcellán, Sánchez; Problemas resueltos de Álgebra Lineal. Ed. Thomson.

-García, Ruiz, Saiz; Álgebra. Teoría y Ejercicios. Ed. Paraninfo.

- Calvo, Escribano, Fernández y otros; Problemas resueltos de Matemáticas aplicadas a la Economía y la Empresa. Ed, AC.

-Basics of mathematics to the economy: A virtual and open text. http://eco-mat.ccee.uma.es/libro/libro.htm

Basic and general:
CB1 - That students have demonstrated to possess and understand knowledge in an area of study that part of the base of the
general secondary education, and is often found at a level that, although it is supported by advanced textbooks, includes also
some aspects that involve knowledge from the forefront of their field of study
CB2 - Students know how to apply their knowledge to their work or vocation in a professional manner and possess the competencies that are often shown through the preparation and defense of arguments and the resolution of problems within their field of study
CB3- Students to have the ability to gather and interpret relevant data (typically within their field of study) to issue judgements that include a reflection on issues of such social, scientific or ethical
CB4 - Students can pass information , ideas, problems and solutions to an audience both specialized and not-specialized
CB5 - Students have developed those learning skills needed to undertake further studies in with a high degree of autonomy
CG5 - Own general knowledge and learning skills necessary to continue studying and to undertake studies specialized in different areas of the company and other related areas , with a high degree of autonomy.

Cross:
CT1 - - Analysis and synthesis
CT6 - - Resolution of problems.
CT9 -- Autonomy in learning

Specific:
C1 - Fundamentals of linear algebra, differential and integral calculus, mathematical optimization and financial operations
Math
D8 - Derive relevant information impossible to recognize by non-professional data
D9 - Usually using communications and information technology in all of their professional performance
D10 - Professional criteria based on the management of technical instruments applied to the analysis of problems

The subject consists of 6 ECTS:
The theoretical sessions will be expository and in a large group. The practical sessions, in small groups, will be interactive and will be mainly devoted to solving exercises that help to understand and apply the concepts and results previously explained in the theoretical classes.

These activities will be complemented with the personal work that the student must dedicate to each one of them: search for bibliographic material, reading it and autonomous work that will be guided by the teacher during the hours assigned to tutoring.

Students (new enrollment and repeaters) without waiver of class attendance: the qualification of this subject will be obtained by adding the mark obtained in the continuous assessment and the mark obtained in a compulsory final test. The mark obtained in the continuous evaluation will be in accordance with the level of attendance and active participation in the classes and the completion of the exercises and work that may be indicated in the case.
The partial distributions of the overall score of the subject will be:

Both 1st and 2nd opportunities

Continuous Evaluation -------> 30%
Final Test ----------------> 70%

Competences CB1, CB2, CB3, CB4, CB5, CG5, CT1, CT6, CT9, C1, D8, D9, D10 will be assessed through class work and the compulsory final test.


Students (new enrollment and repeaters) with exemption from class attendance: in this particular case, 100% of the score can be obtained in the final compulsory test. Therefore, for students in this situation, this test will have a maximum score of 10 points.

In cases of fraudulent completion of exercises or tests, the provisions of the "Normativa de avaliación do rendemento académico dos estudantes e de revisión de cualificacións" shall apply.

In addition to assistance to presenciais activities, consider that you need at least 6 hours weekly of personal work to assimilate the contents seen in the class and do exercises; Although this will largely depend on the capabilities and knowledge of each student.

As advice of a general nature for learning and overcoming of this matter:

-Is very important to overcome the material that the student attends class and study continuously, as well as performing the relevant practices.

- Prior knowledge in many cases are essential to be able to follow classes. That is why it is important that before a class the student has reviewed by your account concepts that worked in the former. In addition, it is also important to promptly solve the exercises proposed.

- Convenient is that every day understand as explained in the own classroom or completing with time review is needed, and with the help that can receive both teacher and peer. It should be taken into account that ask questions that the student can arise during explanations, work and the proposed exercises done, and talk with professors and colleagues of any issues that may arise during class form in the classroom part both of the objectives of the course as well as evaluation.

- Must learn to differentiate between what is proper study and memorization of what is assimilation and understanding of explained. To master the concepts and definitions, it is not enough to learn them by heart but that we need to deepen its meaning by performing the corresponding personal work.

- The topics that make up the different blocks are closely related among them and it is required that the learning is progressive, which means the understanding of previous concepts in order to study the new.

- This matter, and particularly those new concepts that involve more difficulty, should be considered with pen and paper. We consider fundamental, for ideal assimilation of the material and the development of intuition, know write correctly in the mathematical language and represent geometrically, to the extent possible, all those concepts and situations that are formulated during the course. Geometrically view any new concept will be a big help for their understanding and improves the ability of logical reasoning.

Classes are taught in Castilian.

The course material will be available to students on the virtual campus.