General information


Subject type: Basic

Coordinator: Enric Camón Luis

Trimester: First and second quarters

Credits: 8

Teaching staff: 

Jose Ignacio Monreal Galán

Teaching languages


  • English

Skills


Basic skills
  • B1_Students have demonstrated and understood knowledge in a field of study that is based on general secondary education, and is usually found at a level that, while supported by advanced textbooks, also includes some aspects involving knowledge from the forefront of their field of study

     

  • B5_That students have developed those learning skills necessary to undertake further studies with a high degree of autonomy

Specific skills
  • E9_Use mathematical tools and advanced statistical tools for decision making and contrasting various economic assumptions

     

General competencies
  • G2_Be able to innovate by developing an open attitude to change and be willing to re-evaluate old mental models that limit thinking

Transversal competences
  • T5_Develop tasks applying, with flexibility and creativity, the knowledge acquired and adapting it to new contexts and situations

     

Description


The subject "Fundamentals of Mathematics" is designed as an introductory subject of basic training for the student, as shown by its location in the first year. The course works on the use of mathematical language and the acquisition of work methods that are particularly suitable and useful for formalizing economic situations.

In particular, the subject develops the fundamental aspects of mathematical calculation in one or several variables (with optimization) and linear algebra that are most used in economics; in this sense, it is therefore an instrumental subject in which mathematical tools are provided that are used, mainly, in economic contexts.

In addition, it should be noted, due to the formative nature of this subject, that logical-deductive reasoning is promoted.

Contents


FIRST TRIMESTER

0. Preliminaries.

Basic algebraic operations.

Powers and logarithms.

Solving equations, systems of equations and inequalities.

Straight lines and parabolas.

Calculation of percentages.

1. Real functions of a real variable.

1.1 Definition, types and properties

Expressions of a function: explicit form and implicit form

Graph of a function

Domain and Path of a function

1.2 Operations with functions: sum, product for a scalar, product and quotient

Composition. Properties. Identity function and inverse function

Study of some elementary functions (polynomial, rational, with radical, exponential, logarithmic)

 

2. Differential calculus with functions of a variable.

2.1 Derivative of a function at a point: definition

Geometric interpretation of the derivative

Angular Points

Derivative and continuity theorem

Derived function

Function derived from elementary functions (Table of derivatives)

Derivative of operations: sum, product to scale, product, quotient

Derivative of the composition: Rule of the chain

Logarithmic derivation

Successive derivatives

2.2 Applications of the derivative

Calculation of the tangent line at a point

Calculation of limits: Hôpital's rule

Continuity

Calculation of the asymptotes of a function: horizontal, vertical and oblique

Intervals of growth and degrowth of a function

Calculation of extremes (maximums and minimums)

Concavity, convexity and inflection points.

Analysis of a function. Complete graphic study.

 

SECOND TERM

3. Integration.

3.1 Indefinite Integral.

definition Primitives of a function.

Properties of the integral.

Calculation of primitives.

3.2 Definite integral.

Definition. Barrow's rule. Properties

Area calculation

Area included between a curve and the abscissa axis

Area between two or more curves

4. Linear Algebra.

4.1 Matrix

Matrix definition. Order of an array. Square matrices. Identity Matrix

Transpose of a matrix.

Operations with matrices

4.2 Determinants

Definition.

Calculation of determinants. Rule of Sarrus

Basic properties of determinants.

4.3 Rank of a matrix.

Definition.

Range calculation.

4.4 Systems of linear equations.

classification Rouché-Frobenius theorem.

Systems resolution.

5. Real functions of two or more variables

5.1 Real functions of two or more real variables

Definition

Graphic representation

Level curves

Mastery of functions of two variables

5.2 Differential calculation of functions of two or more variables

Partial derivatives of a function

Successive partial derivatives. Schwartz's theorem

Compound derivation

5.3 Extremes of functions of two variables

Definition. Highs, lows and saddle points

Determination of extremes. Necessary condition

Singular points

Hessian matrix

Determination of extremes. Sufficient condition

6. Applications of functions to economics

6.1 Optimization with a variable

Highs and lows with applications to the economy

Two variables and an equality constraint.

6.2 Optimization with two variables

Maximum and minimum with applications to the economy

6.3 Optimization with constraints: Linear programming

Concept and formulation

Graphic technique

Matrix formulation

General problem

Evaluation system


The evaluation of the subject will take into account the following evaluable aspects:

  • There will be online quizzes each of which will be available for a limited time.
  • There will be seminars with activities that will have to be solved in groups.
  • Activities will be done in the classroom that can be graded. 
  • In addition, there will be two exams per term throughout the two terms. The quarterly exam grade (Ex1 and Ex2) will be a weighted arithmetic average of the grades in these exams, and a minimum mark will be required for each of the exams taken in order to be able to make this average.

Then the final grade of the subject will be calculated with the following weights:

  • Quarterly exam grade: 60%, i.e. 30% of each of the 2 terms (Ex1 and Ex2, a grade of 4 or more out of 10 is required in both items to pass the subject).
  • Continuous assessment activities (CA), made up of the other assessable aspects: 40%.

To pass the subject, the final grade must be equal to or higher than 5 points out of 10.

The continuous assessment grade (AIR CONDITIONING) is not recoverable under any circumstances. Yes, the grades of the quarterly exams (Ex1 and Ex2) can be recovered.

No grade from one academic year will be saved for another.

Summary of evaluation percentages:

System

Weighting 

First term exam notes

30%

Second term exam notes

30%

Continuous Assessment (online quizzes, seminars, assignment of problems, class participation...)

40%

 

All the exams that are taken will require a minimum qualification to count in the evaluation.

A student who has not taken the final exam (at the end of the 2nd term) will not be able to take the retake.

REFERENCES


Basic

HAEUSSLER, JR., ERNEST, F., RICHARS D. PAUL, RICHARD J. WOOD (2008): Mathematics for administration and economics. Ed Pearson.

Complementary

GARCÍA, P., NÚÑEZ, J., SEBASTIÁN, A. (2007): Initiation to the university mathematics. Ed. Thomson.

LARSON, HOSTETLER, EDWARDS (2006): Calculus. Eighth edition. Mc Graw-Hill.

STTAN (1998): Mathematics for administration and economics. International Thomson Publishers.

LÓPEZ, M. VEGAS, A. (1994): Basic course of mathematics for the economy and the direction of companies. Vol I and II. Ed Pyramid.

 

BITTINGER, MARVIN, L. (2002): Calculus for economic-administrative sciences. Seventh education. Ed Pearson.