Universidad de Jaén

Chapter 1: Functions. The real line. Real functions of one variable. Main functions in Analysis and Economy. Limits and continuity. Economic modelling by means of functions and limits.

Chapter 2. Differentiation of functions. The derivative, pointwise rate of change in economic modelling, geometric interpretation. Computations of derivatives. Derivative and shape preserving properties of a function. L'Hôpital’s theorem.

Chapter 3. Integration of functions. Primitive of a function, indefinite integral and its properties. Computation of primitives. Definite integral and its properties. Applications of the definite integral.

Chapter 4. Matrices. Data representation by means of matrices. Basic definitions and matrix operations. Matrix power and matrix iterative models. Rank of a matrix. Determinant. Inverse matrix.

Chapter 5. Systems of linear equations. Vectors. Classification of systems of linear equations. Parametric expression of the solution of a linear system. Cramer's Rule and Gauss Elimination. Linear subspace. Basis, coordinates and dimensión for linear subspaces.

Chapter 6. Matrix diagonalization. Diagonalization process: eigenvalues, eigenvectors and characteristic polynomial. Interpretation of eigenvalues and eigenvectors and tendence in iterative matrix models. Tendency study in matrix models.

Classes of theory for all the group (big group): The theoretical aspects of the subjects will be exposed along with general practical examples.

Problems classes in small groups: 15 hours will be devoted to the resolution of problems and exercises with applications in Economy.

Computer classes in small groups: 15 hours will be carried out in the computer laboratory with the aid of the software Wolfram Research 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

Items considered to compute the mark:

(S1) (1 point = 10% of the total mark) Attendance and/or participation: The attendance to the theory, problems and computer classes will be considered taking into account the active participation of the students, in the terms that the professor will determine, to give the following points:

• Theory/problems: 0.5 points (5%).
• Computer practices: 0.5 point (5%): in proportion to the number of computer sessions attended.

(S2) (8 points = 80% of the total mark) Basic concepts of the subject.

• Theory/problems, 7 points (70%): Written exam at the end of the quarter .
• Computer practices, 1 point (10%): Exam in the computer classroom at the end of the quarter .

(S3) (1 point = 10% of the total mark) Works, exercises or short exams proposed by the professor along the quarter.

The following criteria will also be applied:

• The points obtained in (S1) and (S3) will be maintained for all the official exam calls of the course.
• The mark obtained in the exam of computer practices, item (S2)-2, will be maintained for all the official exam calls of the course. Only the last mark obtained in an official practices exam will be considered no matter if the student had better marks in previous calls.
• The final mark of those students that did not attend the theory exam, item (S2)-1, will be “No Presentado† , no matter if they participate in any of the rest of activities of the course.
• The final mark will be sum of the points obtained in (S1), (S2) and (S3) provided that in the theory exam, (S2)-1, the student obtains more than 3 points (out of 10).