General information

Subject type: Basic

Coordinator: Núria Masferrer Llabinés

Trimester: First and second quarters

Credits: 8

Teaching staff: 

Jose Ignacio Monreal Galán

Teaching languages

  • Spanish
  • Catalan
  • English

Check the schedules of the different groups to know the language of teaching classes. Although the material can be in any of the three languages.


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



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.



0. Preliminaries.

The sets of numbers

Solving equations and inequalities

Solving systems of linear and nonlinear equations

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


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.



3. Linear Algebra.

3.1 Matrix

Matrix definition. Order of an array. Square matrices

Transposed from an array. Symmetrical matrices

Operations with matrices

Sum and product for a scalar

Matrix product. Properties

Identity Matrix. Inverse Matrix

3.2 Determinants

Definition. Determinants of order 2 and order 3. Sarrus rule

Complementary deputies and minors

Properties of determinants

Development of determinants applying their properties

Applications of determinants:

Reverse matrix calculation

Solving matrix equations

Range of an array

4. Real functions of two or more variables

4.1 Real functions of two or more real variables


Graphic representation

Level curves

Mastery of functions of two variables

4.2 Differential calculation of functions of two or more variables

Partial derivatives of a function

Successive partial derivatives. Schwartz's theorem

Compound derivation

4.3 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

5. Applications of functions to economics

5.1 Optimization with a variable

Highs and lows with applications to the economy

Two variables and an equality constraint.

5.2 Optimization with two variables

Maximum and minimum with applications to the economy

5.3 Optimization with constraints: Linear programming

Concept and formulation

Graphic technique

Matrix formulation

General problem

6. Integration.

6.1 Indefinite Integral

Definition. Primitives of a function

Table of immediate integrals

Application of the chain rule in the integration of functions

Properties of the integral

Integration by parts

Integration of rational functions

6.2 Integral defined

Definition. Barrow's rule. Properties

Area calculation

Area included between a curve and the abscissa axis

Area between two or more curves

Evaluation system

Eliminatory evaluations of the subject will be carried out throughout the two quarters. The final grade will be the weighted arithmetic mean of the grades of the evaluation activities carried out in the first and second quarters. To pass the course, the final grade must be greater than or equal to 5 points out of 10.

The continuous evaluation will take into account the following aspects with the weights indicated:

- Two partial exams (P): 60%.

- Delivery of exercises, evaluation activities and participation (A): 40%.

Therefore, the final grade is obtained by applying the formula:

final_note = 0,3·P1 + 0,3 ·P2 + 0,4 ·A                  

On P1 (a grade higher than or equal to 4 is required and eliminates subject) is the mark of the partial exam that is carried out during the first term and P2 (requires a grade greater than or equal to 4 and eliminates subject) is the mark of the midterm exam that is conducted throughout the second quarter, and A collects the note of continuous evaluation of the first and second trimester.

At the end of the exam period of the second term, the student will be able to be examined on the syllabus of the partials that he / she has yet to pass (P1 o P2). The final grade is calculated using the same formula that is applied in the continuous assessment (a grade of 4 or higher is required in each).

In the recovery period of the second term, the student will be able to examine the syllabus of the partials that he has yet to pass (a grade of 4 or higher is required in each). The student who has not taken the global exams (end of the second term) will not be able to take the make-up exam. The final mark is calculated using the same formula that is applied in the continuous assessment.

The note of participation, activities in the classroom and delivery of exercises (A) it is not recoverable under any circumstances and no grade from one academic year will be saved for another. It is necessary to obtain an average grade of 5 or higher (out of 10) in the Online Test model so that it is included in the weighting of the final assessment.

Summary of evaluation percentages based on:



Participation in activities proposed in the classroom (seminars-participation)


Individual work: Control 1 and Control 2 + Online quizzes

20% + 10%

Final exam (P1+P2)



Exams require a minimum grade to be counted in the evaluation.

A student who has not appeared in the first call (end of the 2nd term) CANNOT appear in the make-up.



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


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.