27302 -- Mathematics I

Curso:

1

Semestre:

1

Créditos:

6.0

Universidad de Zaragoza

Learning outcomes that define this course

1

- To have gained a certain ability in using mathematical language, both in comprehension and writing.
- To be able to distinguish whether the relations between variables in a problem are linear or non-linear, and to be able to represent the different cases by means of a suitable mathematical tool.
- To be able to use matrix notation to represent a problem of an economic nature with linear relations between variables and to be able to apply matrix algebra to solve the problem.
- To be able to study a system of linear equations making use of the Rouché-Frobenius theorem.
- To know how to solve a consistent system of linear equations by the most suitable method and be able to interpret the solutions in accordance with the underlying context.
- To be able to identify a diagonalisable square matrix.
- To know how to diagonalise a square matrix when this is possible.
- To be able to apply matrix diagonalisation to an economic context, such as the study of a dynamical process in the long run.
- To be able to identify a quadratic form and determine its sign by the most suitable method.
- To be able to distinguish the endogenous and exogenous variables of an economic system and to know how to use functions to represent the relations between these variables.
- To understand the concepts of continuous and differentiable function applied to an economic context.
- To be skilled in calculating partial derivatives and in their interpretation in Economics.
- To be able to identify a differentiable function and to know the implications of differentiability.
- To be able to identify the chained dependency between different variables and to know how to calculate the variation in the final variables with respect to any of the initial ones.
- To be able to distinguish whether a function is written in explicit or implicit form and to know how to obtain the partial derivatives in both cases.
- To be able to identify a homogeneous function and its implications, in particular, in the scenario of production functions.
- To know which mathematical tool allows the recovery of a total magnitude from the corresponding marginal magnitude.
- To understand the concepts of primitive function and indefinite integral.
- To identify whether the indefinite integral of a function can be obtained by basic integration and to be able to work it out by using the table of basic integrals.
- To be able to choose the most suitable method to calculate the indefinite integral of a function; more specifically, to be able to decide whether this requires a change of variables, integration by parts or integration of rational functions.
- To understand the geometrical interpretation of the Riemann definite integral.
- To know how to apply the main properties of the definite integral
- To be able to relate the concepts of indefinite integral and definite integral.
- To be able to able to apply the second fundamental theorem of calculus to obtain the value of a definite integral.
- To know how to make a change of variables in a definite integral.

Introduction

Mathematics I is a basic-training subject with a value of** **6 ECTS credits and it is taught during the first semester of the first year. It is complemented by Mathematics II, a subject in the second semester of the first year. The teaching of Mathematics I is assigned to the Department of Economic Analysis of the University of Zaragoza, which is also responsible for the teaching of other subjects closely related to Mathematics, such as Microeconomics, Macroeconomics, and Econometrics.

The goal of Mathematics I is to increase the students’ existing mathematical knowledge of matrix algebra and univariate functions and to present the calculus of multivariate functions, thereby training the students to assimilate the mathematical tools most widely used for Economic Analysis, especially in the fields of Economic Theory and Econometrics. This subject helps students progress from their predominantly arithmetic knowledge, typical of Mathematics in Secondary Education, towards the precision and abstraction typical of the Mathematical Sciences. This will allow the students to handle other subjects of the Degree which use mathematical techniques and prospective challenges in their careers.

On completing Mathematics I, the students will have gained a more precise command of mathematical language, which will allow them to understand some economic concepts and to interpret some results with a certain rigour. They will also master a number of mathematical tools and methods for the resolution of simple economic problems.