This subject provides the quantitative instruments that are needed to pose and analyze economic problems with the aid of a formal model. In working toward the above goal the student will acquire the following competences and skills. Regarding the contents of the course, the student will be able of: - Understand basic concepts of matrices and algebra of matrices. - Analyze dynamic economic models. - Pose and solve differential and difference equations and systems, and styudy in detail the qualitative behavior of the solutions. - Apply all the above concepts to economic problems. Pertaining the general competences or skills, in the class the student will develop: - The ability to address economic problems by means of abstract models. - The ability to solve the above formal models. - The ability to interpret and classify the different solutions and apply the appropriate conclusions to social contexts. - The ability to use the basic tools that are need in the modern analysis of economic problems. Through out the course, the student should maintain: - An inquisitive attitude when developing logical reasoning, being able to tell apart a proof from an example. - An entrepreneurial and imaginative attitude towards the cases studied. - A critical attitude towards the formal results and their applicability in social contexts.

K3: Acquire knowledge of the theories and techniques specific to Economics, employing appropriate terminology and the scientific method. K4: To understand the functioning of the economy as the efficient allocation of scarce resources, including the importance of equity. K5: Know quantitative and qualitative research techniques, and be able to discern which are the most appropriate to apply in the field of economics. K6: Comprehend the economic and social impact of various public policies on different agents and in diverse socioeconomic contexts. K7: Understand the economic variables that regulate the economy and govern the behaviour of agents. K8: Understanding economic institutions K9: Identify the economic, political, and social framework for the activities of various economic, political, or social agents. K10: Understand the fundamental elements of the economic environment from the perspective of different theories and various economic agents. S3: Apply the knowledge acquired in the degree program to rigorously, accurately, and scientifically identify socioeconomic processes and propose potential solutions. S4: Manage and develop autonomous learning within the field of Economics. S5: Formulate, debate, and defend critical and ethical arguments related to Economics. S6: Identify, collect, interpret and manage relevant information on economic issues, using the appropriate concepts and methodologies of analysis. S7: Design economic and social programs to address the needs of economic agents. S8: Formally representing economic decision-making processes S9: Derive relevant economic information from the data, and be able to process it to answer the questions of interest S10: Prepare advisory reports for economic agents relevant to decision-making. S12: Model and quantitatively interpret specific economic issues C2: Communicate effectively to different audiences knowledge, methodologies, ideas and solutions in the field of study. C3: Independently develop and defend a problem within the disciplinary scope of the degree, proposing well-founded solutions through the application of the knowledge, skills, tools, and strategies acquired or developed throughout the degree program. C4: Solve economic models of interest from both theoretical and numerical perspectives. C5: Use appropriate statistical and econometric tools to address and solve economic problems.

The course has two parts: (I) Matrix algebra and matrix diagonalization and (II) Differential and difference equations and systems. (I) Matrix algebra and matrix diagonalization: After a brief review of the elementary operations with matrices, some fundamental concepts for obtaining the canonical form of a matrix are given. (II) Differential and difference equations and systems: definition and illustration of these concepts with examples coming mainly from economics. The main tools of resolution are given, and special emphasis on the analysis of the qualitative behavior of the solutions is done. The techniques are applied to some classical economic models.

The course lectures will be based on combining theoretical explanations with several practical exercises. The students should attempt to solve the exercises by themselves, before they are addressed in class. Student participation is considered very important in order to acquire the skills needed to pose and solve economic models.