300123 - FUNDAMENTALS OF MATHEMATICS FOR BUSINESS

Subject type: Basic

Coordinator: Alex Araujo Batlle

Trimester: First and second quarters

Credits: 8

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.

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.

• 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, 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.

The classroom (physics or virtual) it is a safe, free space of attitudes sexists, racists, homophobic, transphobic i discriminatory, ja be towards the students or towards the faculty. we trust that among all and all we can create a space sure on ens can to err i to learn sense having to suffer prejudice others.

FIRST TRIMESTER

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

Limits 

Hospital 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.

SECOND TERM

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

Definition

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 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

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 between a curve and the abscissa axis

Area between two or more curves

In general the structure of the week is as follows:

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.

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):

- Two partial exams (P): 60% (if the examinations are carried out in person).

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

Therefore the final note is obtained by applying the formula:

Attendance_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 with the same formula that applies in the continuous assessment (a grade greater than or equal to 4 is required in each).

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, activities in the classroom 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:

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.