Universidad de Jaén

Unit 1. Functions. The real line.

Real-valued functions of one real variable. Elementary functions. Limits and continuity of real-valued functions of one real variable. Modelization of economic phenomena using functions and the concept of limit.

Unit 2. Differentiability of real-valued functions of one real variable.

The concept of derivative, velocity or instantaneous rate change in phenomena modelized by functions. Geometrical interpretation of derivative. Differentiation rules. Relative extremes, convexity, concavity and inflection points. L'Hôpital Theorem.

Unit 3. Integration of functions.

Primitive, Indefinite integral and properties. Integration rules. Definite integral and properties. Aplications of the definite integral.

Unit 4. Matrices.

Data representation using matrices. Basic definitions and matrix operations. Matrix powers and iterative matrix models. Matrix rank. Determinants. Inverse matrix.

Unit 5. Linear systems of equations.

Vectors. Classification of  linear systems of equations. Parametric solution of a linear system. Gauss and Cramer methods to solve linear systems of equations. Vector subspaces. Bases, coordinates and dimension of vector subspaces.

Unit 6. Diagonalization of matrices.

Eigenvalues and eigenvectors, characteristic polynomial. Interpretation of eigenvectors and eigenvalues in matrix iterative processes. Role of dominant eigenvector and eigenvalue in asymptotic behaviour of matrix iterative processes.

Lectures (M1, M3, M4, M5): Theoretical contents and related practical examples will be developed in these sessions.

  Seminars (M6, M7, M8, M10, M12, M13): 15 one-hour long classroom sessions will be devoted for solving problems, with special emphasis on applications to economics. Additionally, 15 one-hour long computer lab sessions will be devoted for solving problems by using the software Mathematica.

Students with special educational needs should contact the Student Attention Service (Servicio de Atención y Ayudas al Estudiante) in order to receive the appropriate academic support

1. Detail:

* S1. ACTIVE ATTENDANCE: 0.5 points (5%): 0.5 points will be divided by the total number of hours attended. Learning results R12 and R13.

* S2. THEORETICAL CONCEPTS: 6.0 points (60%): Final written exam about the theoretical concepts and related exercises. Learning results R11 and R14.

* S3. CLASSROOM EXERCISES: 2 points (20%): Short classroom tests. Learning results R11 and R13.

*S4. COMPUTER LAB PRACTICES: 1.5 points (15%): Computer exam. Computer guidelines may be used in the exam. Learning results R11 and R13.

2. Marks from S1 and S3 will be maintained during the current academic year. Students who attend the final written exam (S2) and/or the computer exam (S4) will appear as 'SHOWN' in the grade list for the corresponding official exam call

3. The final continuous grade will be the sum of the marks obtained from S1, S2, S3, S4.

A final alternative grade given by the sum of the marks of the final written exam and the computer exam, weighted 80% and 20%, respectively, will be considered for each student at each official exam call.

The final student grade will be the maximum of the final continuous student grade and the final alternative student one at each official exam call.