110002 - MATHEMATICS APPLIED TO LOGISTICS

Subject type: Basic

Coordinator: Jesus Ezequiel Martínez Marín

Trimester: First term

Credits: 6

• Catalan

The course material can be in Catalan, Spanish or English.

At the end of the subject, the student will know the basic and general mathematical tools for the approach and solution of logistical and economic problems that throughout his studies or in his professional future can be found. You will acquire mastery of these techniques by calculating and solving general problems and know their applications in the field of logistics. From a more general point of view, the student will acquire an overview of the need for mathematics and mathematical language as basic instrumental tools of the social sciences.

 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.

Evaluate through quantitative instruments different scenarios in the field of logistics.

• 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.

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, on-line documents and the material of the face-to-face sessions. 

0. Preliminaries.

The sets of numbers
Solving equations and inequalities

1. Real functions of a real variable.

Definition, types and properties
Expressions of a function: explicit form and implicit form
Graph of a function

Distance between two points
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)

2. Differential calculus with functions of a variable.

Derived from 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
Successive derivatives

Derivative applications
Calculation of the tangent line at a point
Limits

Definition Lateral Boundaries. Infinite limits: Vertical asymptotes. Limits to infinity: Horizontal asymptotes. Graphic representation of the boundaries. Hospital Rule. Calculation of limits. Indeterminacies.

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.

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
Optimization. Highs and lows with applications to the economy

3. Introduction to queuing theory

Model Kendal (M / M / 1)

4. Linear algebra

Arrays Definition of array.
Order of an array. Square matrices Transposed from an array. Symmetric matrices Operations with matrices Sum and product for a scalar Product of matrices. Identity Matrix Properties. Inverse Matrix. 

determinants
Definition. Determinants of order 2 and order 3. Sarrus rule Adjunct and complementary minors Properties of determinants Development of determinants applying their properties Applications of determinants: Calculation of the inverse matrix Solving matrix equations Range of a matrix.

Systems of linear equations
Definition. Equivalent systems. Homogeneous systems Matrices associated with a system. Matrix expression of a system Compatible, incompatible, determined and indeterminate systems Rouché-Fröbenius theorem. Application: Systems Discussion Compatible Systems Resolution: Cramer's Rule Systems Resolution by the Gaussian Method.

Transition matrices

5. Real functions of two or more variables

Real functions of two or more real variables
Definition Graphical representation Level curves Domain of functions of two variables.

Differential calculation of functions of two or more variables
Partial derivatives of a function Successive partial derivatives. Schwartz's theorem

6. Optimization with functions of two or more variables

Local optimization 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

In general the structure of the week is as follows:

The final grade will be the weighted arithmetic mean of the grades of the assessable activities performed. To pass the course, the final grade must be greater than or equal to 5 points out of 10. The continuous assessment will take into account the following aspects with the weights indicated:

- A Final exam (F): 60%.

- Online test activities (T): 20% (10% online periodic tests + 10% synthesis test)

- Delivery of exercises, evaluable activities and participation (A): 20%

The final grade is obtained by applying the formula:

Note = 0,6 ·F + 0,2 ·T + 0,2 ·A

On F (greater than or equal to 4) is the exam grade, T online tests and A collects the participation note.

In the recovery period of the first term the student will be able to re-examine (recoverable 60%).

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

Summary of evaluation percentages:

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.

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.

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

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