Taking into account the different modes for students to access the Degree in Business Administration and Management, and since in this degree, mathematics have a basic and instrumental function, the first goal of the course is to unify the knowledge that the students have acquired in their previous education. The second goal of the course is to offer students

basic tools of differential calculus and linear algebra, in order to ensure that they master the fundamentals and can use them in other subjects.

SPECIFIC COMPETENCES

* An ability to manage basic concepts and techniques of differential calculus and linear algebra.

* An ability to justify the procedures and the formulation of logical arguments properly using deductive reasoning.

* An ability to formalise quantifiable phenomena related to economic and business science through mathematical models.



TRANSVERSAL COMPETENCES

* Develop learning skills to acquire a high degree of autonomy in order to undertake studies later, as well as to improve their own self-training in a context of continuous changes and innovations.

* Know how to search, identify, analyse and synthesize information from various sources, with critical capacity to assess the situation and foreseeable evolution of a company, make reasoned judgments and take decisions.

* Capacity for written and oral communication.

* Ability to work in a team, with responsibility and respect, initiative and leadership.



KEYWORDS

Calculus: Single-variable real functions. Differential calculus. Integral calculus.

Linear algebra: Matrices and determinants. Vector space. Linear Equation Systems. Matrix diagonalization.



LEARNING OUTCOMES

* Application of basic concepts and techniques of differential calculus and linear algebra to practical assumptions related to economic and business science.

* Being able to employ deductive reasoning to justify procedures and formulate logical arguments.

* Mathematical formalisation of quantifiable economic phenomena in practical cases.

Part I: SINGLE-VARIABLE CALCULUS



Unit 1. SINGLE-VARIABLE FUNCTIONS

1.1 Concept of function. Definition domain. Graphic representation.

1.2 Reverse function.

1.3 Most frequent functions.

1.4 Conical.

1.5 Piecewise-defined functions. Absolute value function.

1.6 Composite function.

1.7 Definition domain calculation.



Unit 2. LIMITS, CONTINUITY AND DERIVATIVES

2.1 Limit of functions. Lateral limits.

2.2 Limit properties. Indeterminations.

2.3 Bounded function.

2.4 Continuity of a function.

2.5 Derivative function. Geometric meaning.

2.6 Derivative of the composite function (chain rule).

2.7 General derivative rule. Differentiation rules.

2.8 Derivative of the inverse function.

2.9 Successive derivatives.

2.10 Lateral derivatives. Differentiability of a function.

2.11 Continuity and differentiability

2.12 Implicit functions. Differentiation of the implicit function.

2.13 Application of differentiation in economics. Elasticity.



Unit 3. APPLICATIONS OF CONTINUITY AND DIFFERENTIABILITY

3.1 Properties of continuous functions.

3.2 Properties of continuous and differentiable functions.

3.3 Resolving indeterminate forms: L'Hôpital’s Rule.

3.4 The differential of a function.

3.5 Polynomial Approximation of Functions: Taylor's formula. Differential and linear approximation.



Unit 4. INTEGRATION

4.1 Primitive of a function. Indefinite integral.

4.2 Immediate integration.

4.3 Integration by parts.

4.4 Integration by change of variable.

4.5 Applications of the indefinite integral.

4.6 Definite integral. Geometric interpretation.

4.7 Mean Value theorem. Average value of a function in a range.

4.8 Fundamental theorem of calculus. Integral function.

4.9 Barrow Rule.

4.10 Application of the definite integral to the areas.

4.11 Improper Integral.



Part II: LINEAR ALGEBRA



Unit 5.- MATRICES AND VECTORS. VECTORIAL SPACE

5.1 Matrices. Operations with matrices.

5.2 Types of matrices.

5.3 Vectors. Operations with vectors. Linear combination of vectors.

5.4 Vector space.

5.5 Euclidean vector space.



Unit 6.- DETERMINANTS AND INVERSE MATRICES

6.1 Determinant of a square matrix.

6.2 Calculation of determinants of order 2 and 3: Sarrus rule.

6.3 Calculation of determinants of order higher than 3: Method of the attachments.

6.4 Properties of the determinants.

6.5 Creating zeros in a determinant.

6.6 Reverse matrix. Invertible and singular matrices.

6.7 Properties of the inverse matrix.

6.8 Calculation of the inverse matrix.



Topic 7.- THEORY OF RANK AND SYSTEMS OF LINEAR EQUATIONS

7.1 Linear independence of vectors.

7.2 Rank of a matrix. Properties

7.3 Calculation of the range.

7.4 Systems of linear equations. Matrix and vector expression.

7.5 Compatible and incompatible systems: Rouché-Frobenius theorem.

7.6 Homogeneous systems.

7.7 Non-matrix systems resolution methods.

7.8 Matrix methods for solving linear systems.

7.9 Systems of linear equations with economic significance.



Unit 8.- DIAGONALIZATION OF MATRICES

8.1 Definition.

8.2 Eigenvalues and eigenvectors of a square matrix: Diagonalizable matrix condition.

8.3 Applications of diagonalization

Lectures (75%); practical classes (25%).

Practical classes are resolution of exercises workshops.



In the event that the health situation does not allow face-to-face teaching, it will be taught remotely using the tools that the University makes available to us. In this case, the corresponding adaptation of this teaching guide would be published in egela.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • Written test to be taken (%): 75
  • Individual works (%): 25

GUIDANCE ON CONTINUOUS EVALUATION

Final written test: up to 7.5 points of the mark.

Individual evaluation of the resolution of exercises workshops: up to 2.5 points of the mark.



WAIVER

Students may waive continuous evaluation during the first 10 weeks of the term. This waiver must be submitted in writing to the course teaching staff.

The students that waive continuous evaluation will get their total mark by means of the final written test.



In the event that the health situation does not allow conducting the tests in person, another alternative procedure will be activated. In this case, the corresponding adaptation of this teaching guide would be published in egela.

The same criteria as in the ordinary evaluation.

However, those students who have been subject to continuous evaluation may waive it and choose to get their total mark by means of a final written test.

Available in the virtual learning classroom and at the reprographic service of the Faculty.

Basic bibliography

* SYDSAETER, K. HAMMOND, P. y CARVAJAL, A. (2012): Matemáticas para el Análisis Económico. Editorial Pearson. Madrid (2ª edición).

* JACQUES, I. (2018): "Mathematics for economics and Business". Editorial Pearson. Harlow UK, (9th edition).

In-depth bibliography

* CABALLERO, R. y otros (1993): "Matemáticas aplicadas a la Economía y a la Empresa. 380 ejercicios resueltos y comentados". Editorial Pirámide. Madrid.
* HOFFMAN, L. y BRADLEY, G. (2004): "Cálculo aplicado para Administración, Economía y Ciencias Sociales". Editorial McGraw-Hill. Bogotá (8ª edición).
* STEWART, J. (2006): "Cálculo (conceptos y contextos)". Editorial Thomson. México D.F. (5ª edición).

Web addresses

https://www.wolframalpha.com/
http://reshmat.ru/linear_programming_online.html