General information

Subject type: Basic

Coordinator: Núria Masferrer Llabinés

Trimester: First and second quarters

Credits: 8

Teaching staff: 

Noemí Ruiz Munzón
Jose Ignacio Monreal Galán 
Marta Martínez Egea 

Teaching languages

  • Catalan
  • Spanish
  • 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 conceived 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 working methods that are especially suitable and useful to formalize economic situations.

In particular, the subject develops the fundamental aspects of mathematical calculus in one or more 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.

Learning outcomes

  • Master mathematical language as well as algebraic notation and manipulation in the context of univariate calculus.
  • Show knowledge of the basic concepts about the real line, real functions, univariate calculus and the properties of basic families of real functions, linear algebra and optimization in various variables.
  • Be able to identify and interpret simple mathematical models applied to economics.


Working methodology

Theoretical sessions

MD1. Master classes: Expository class sessions based on the teacher's explanation attended by all students enrolled in the subject.

MD3. Presentations: Multimedia formats that support face-to-face classes.

Autonomous learning

MD4. Video capsules: Resource in video format, which includes contents or demonstrations of the thematic axes of the subjects. These capsules are integrated into the structure of the subject and serve students to review as many times as necessary the ideas or proposals that the teacher needs to highlight from their classes.

MD9. Exercise and problem solving: Non-contact activity dedicated to the resolution of practical exercises based on the data provided by the teacher.

MD11. Non-contact tutorials: for which the student will have telematic resources such as e-mail and ESCSET intranet resources.

In the face-to-face sessions with the whole group, theory sessions will be combined with exercise resolution sessions. The theoretical presentation will include examples that will help the student to solve exercises autonomously.

In the non-contact sessions the students will have to work theoretical-practical knowledge from audiovisual material, documents Online and the material of the face-to-face sessions. The results of this work will be evaluated from questionnaires using the platform moodle or / and with the delivery of projects carried out individually.



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

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)

1.2 Limits and continuity

1.2.1 Limits


Lateral Boundaries

Infinite limits: Vertical asymptotes

Limits to infinity: Horizontal asymptotes

Graphic representation of the boundaries

Calculation of limits. Indeterminacies

1.2.2 Continuity

Definition and equivalent definitions

Types of discontinuity: avoidable, jumping and asymptotic

Continuity Problems

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

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

Hospital Rule

Intervals of growth and degrowth of a function

Calculation of extremes (maximums and minimums)

Definition of maximum and minimum

Null derivative theorem

Criteria for determining extremes

Concavity, convexity and inflection points.

The derivative 2ª theorem

Analysis of a function. Complete graphic study.



3. Integration.

3.1 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

3.2 Integral defined

Definition. Barrow's rule. Properties

Area calculation

Area between a curve and the axis of bscisses

Area between two or more curves

4. Linear Algebra.

4.1 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

4.2 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

5. Real functions of two or more variables

5.1 Real functions of two or more real variables


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 Function ends 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

Learning activities

In general the structure of the week is as follows:

Classroom activities Activities outside the classroom
  • 1 theoretical-practical session
  • 1 seminar session (in case of being present it is mandatory to bring your own computer)
  • Personal study, making exercise lists, reviewing notes, consulting the book and online material (autonomous).
  • Completion of Moodle questionnaires online (autonomous).
  • Individual task of solving evaluable exercises (autonomous).
  • Review (standalone)

This subject has methodological and digital resources to make possible its continuity in non-contact mode in the case of being necessary for reasons related to the Covid-19. In this way, the achievement of the same knowledge and skills that are specified in this teaching plan will be ensured.

The Tecnocampus will make available to teachers and students the digital tools needed to carry out the course, as well as guides and recommendations that facilitate adaptation to the non-contact mode.

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 (the type of examination will be determined by the indications derived from the PROCICAT plan):

- Three partial exams (P): 60% (if the examinations are carried out in person) or 45% (if the examinations are carried out online).

- Delivery of exercises, evaluation activities and participation (A): 40% (if the examinations are carried out in person) or 55% (if the examinations are carried out online).

Therefore the final note is obtained by applying the formula:

Attendance_note = 0,2 ·P2 + 0,2 ·P3 + 0,2 ·P4 + 0,4 ·A                   or            Note_not_present = 0,15 ·P2 + 0,15 ·P3 + 0,15 ·P4 + 0,55 ·A

On 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 first term, and P3 (requires a grade greater than or equal to 4 and removes subject) i P4 (a grade higher than or equal to 4 is required and eliminates subject) are the marks of the partial exams that will be held throughout the second term respectively, and A collects the note of participation 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 (P2, P3 oh P4). The final grade is calculated with the same formula that is applied in the continuous assessment (a grade greater than or equal to 4 in each is required).

In the recovery period of the second term the student will be able to be examined of the syllabus of the partial ones that remain to him to surpass (a qualification superior or equal to 4 in each is necessary). Students who have not taken the global exams (end of the second term) will not be eligible for the resit exam. The final grade is calculated using the same formula that applies in the continuous assessment.

The note of participation and delivery of exercises (A) it is not recoverable in any case and no grade will be saved from one academic year to another.

Summary of evaluation percentages based on:


Weighting (in case of face-to-face exams) 

Weighting (in case of NON-face-to-face exams) 

Participation in activities proposed in the classroom (participation)



Weekly individual work (project delivery) + Final block test (Tests)

10% + 20%

20% + 20%

Final exam (P2+P3+P4)




A student who did not appear in the first call NO (end of 2nd term) can apply for recovery.



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.

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


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

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