380025 - FUNDAMENTALS OF MATHEMATICS FOR BUSINESS

Subject type: Basic

Coordinator: Judith Turrión Prats

Trimester: First and second quarters

Credits: 8

Academic year: 2025

Teaching course: 2

• Catalan
• Spanish

Classes will be mainly in Catalan (Marc Guinjoan, Moisès Gómez, Josep Maynou) or Spanish (Nacho Monreal), although any student can address the teachers in either language. The basic materials in the virtual classroom are in Catalan. Other materials and audiovisual materials may be in Catalan, Spanish or English.

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.

The classroom (physical or virtual) is a safe space, free of sexist, racist, homophobic, transphobic and discriminatory attitudes, either towards students or teachers. We trust that together we can create a safe space where we can make mistakes and learn without having to suffer the prejudices of others.

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.

Optimization in one variable.

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

Review of maxima and minima with applications to economics

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

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

• Online quizzes will be given, each of which will be available for a limited time in the virtual classroom.
• Seminars will be held every quarter with activities that must be solved in small groups. In addition, exercises must be submitted individually and will be evaluated. During these seminars, the common competency called "Autonomy and Critical Thinking" will be explicitly worked on.
• At the end of each term, during the corresponding exam period, an exam will be held with the contents of the corresponding term, and a minimum grade will be required in each one in order to pass the subject.

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

• Quarterly exam grade: 30% of the final grade for the first quarter exam (called P1) and 30% for the second quarter final exam (called P2), with a minimum grade of 4 out of 10 required in both items to pass the subject.
• Online questionnaire grading: The average of the questionnaires taken each quarter (Q1 and Q2) will each count for 5% of the final grade.
• The seminars of each quarter will be evaluated in such a way that together they account for 30% of the final grade. Of this grade, a third (10% of the final grade) will correspond to the assessment of the competence in "Autonomy and Critical Thinking".

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) It is not recoverable under any circumstances. However, the grades from the quarterly exams (P1 and P2) can be recovered.

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

Summary of evaluation percentages:

A student who has not taken the quarterly exams will not be able to take the retake.

Any form of academic fraud will be sanctioned in accordance with the center's evaluation regulations. If signs of fraud are detected, including the improper use of generative artificial intelligence tools, the subject's teaching staff may call the student for an individual interview with the aim of verifying their authorship.

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

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

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

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

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

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