110002 - MATHEMATICS APPLIED TO LOGISTICS

Subject type: Mandatory

Coordinator: Valeria Bernardo

Trimester: First term

Credits: 6

Academic year: 2026

Teaching course: 1

• Catalan

Classes will be held in Catalan. In case of any language difficulties, please contact the teachers as soon as possible.

The basic course material is in Catalan. The rest of the course materials can be in Catalan, Spanish or English.

Upon completion of the subject, the student will know the basic and general mathematical tools for approaching and resolving logistical and economic problems that they may encounter throughout their studies or in their professional future.

You will acquire mastery of these techniques through the calculation and resolution of general problems and will learn about their applications in the field of logistics.

From a more general point of view, the student will acquire a global vision of the need for mathematics and mathematical language as basic instrumental tools in the social sciences.

L'class (physical or virtual) is a safe space, free from sexist, racist, homophobic, transphobic and discriminatory attitudes, whether towards students or teachers. We hope that together we can create a safe space where we can make mistakes and learn without having to suffer prejudice from others.

0. Preliminaries.

Basic algebra

Solving equations and inequalities

1. Real functions of a real variable.

Definition, types and properties

Expressions of a function: explicit 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)

Concept of limit. Graphical determination of lateral limits, the limit at a point and the limit at infinity. Analytical determination.

Definition of vertical and horizontal asymptotes and graphical determination.

Continuity: Definition, types of discontinuities.

2. Differential calculus with functions of a variable.

Derivative of a function at a point: Definition and geometric interpretation of the derivative

Derivative function. Derivatives of elementary functions.

Properties of the derivative operator: sum, dot product, product, quotient, chain rule.

Calculation of the tangent line at a point

2nd derivative

Calculation of limits: Arithmetic of infinity, Indeterminacy and Hôpital's rule.

Derivative and continuity theorem. Non-differentiability: Angular points.

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

Intervals of growth and decrease of a function. Calculation of stationary points (maximum and minimum) with the derivative.

Concavity, convexity and inflection points. 2nd derivative theorem for the classification of stationary points.

Analytical study of a function to determine its graph.

Optimization. Highs and lows with applications to the economy

3. Linear algebra

Matrices: Definition, types, order.

Operations with matrices: addition, dot product, matrix product, transpose of a matrix. definition of inverse matrix.

Determinants: Definition, calculation of determinants of order 2 and order 3 (Sarrus rule). Adjoints and complementary minors. Properties of determinants.

Applications of determinants: Calculating the inverse matrix

Rank of a matrix: definition and calculation with determinants. Calculation with Gaussian transformations.

Systems of linear equations: Matrix form of a system. Classification according to the number of solutions. Rouché-Fröbenius theorem.

Solving systems: Cramer's rule and Gauss's method.

4. Real functions of two or more variables and optimization.

Real functions of two or more real variables

Domain of functions of two variables.

Differential calculus of functions of two or more variables: Partial derivatives of a function, successive partial derivatives. Schwartz's theorem. Hessian matrix.

Stationary points of functions of two variables: Maxima, minima and saddle points.

Determination of stationary points (2 variables): Necessary condition on first partial derivatives. Sufficient condition on Hessian Matrix.

The final grade will be the weighted arithmetic average of the grades of the assessable activities carried out.

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

• Exam: A retrievable final exam (F), with a minimum grade of 4 points out of 10: 60%.
• Non-recoverable continuous assessment:
  • Online quiz activities (Q): 10%.
  • Compulsory attendance seminars, where individual submission of exercises will be required (S): 30%.

The final grade is obtained by applying the formula:

                                                               Note = 0,6·F + 0,1·Q + 0,3·S

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

During the recovery period of the first trimester, the student will be able to retake the exam (F).

The student who has not taken the final exams (ordinary call for December) will not be able to take the resit exam.

Note: This subject will assess the Common Tecnocampus Competency ofAutonomy and Critical ThinkingYour grade will be one third of the seminar grade, that is, 10% of the final grade for the subject.

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