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 to: - Extend the concepts of one variable functions to several variables. - Understand the basic tools of calculus with several variables. - Apply all the above concepts to economic problems. We classify the competences in two groups: specific competences and generic competences or skills. Regarding the specific competences, the student will be able to: - Understand the fundamental concepts involved in the calculus of functions of several variables: differentiability, chain rule, implicit differentiation. - Describe the qualitative properties of the functions of several variables, such as growth, concavity and convexity. - Approximate a function of several variables using the Taylor polynomial. 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. K5: Know quantitative and qualitative research techniques, and be able to discern which are the most appropriate to apply in the field of economics. K7: Understand the economic variables that regulate the economy and govern the behaviour of 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. 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 S12: Model and quantitatively interpret specific economic issues C4: Solve economic models of interest from both theoretical and numerical perspectives.

The course is an introduction to the calculus of functions of several variables. The topics studied are the following ones: Functions of several variables: Continuity. Calculus of several variables: partial derivatives. Differentiable functions. Convexity. Implicit differentiation.

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.