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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
E9_Use mathematical tools and advanced statistical tools for decision making and contrasting various economic assumptions
G2_Be able to innovate by developing an open attitude to change and be willing to reevaluate old mental models that limit thinking
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 logicaldeductive reasoning is promoted.
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 facetoface 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: Noncontact activity dedicated to the resolution of practical exercises based on the data provided by the teacher. MD11. Noncontact tutorials: for which the student will have telematic resources such as email and ESCSET intranet resources. 
In the facetoface 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 noncontact sessions the students will have to work theoreticalpractical knowledge from audiovisual material, documents Online and the material of the facetoface 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.
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
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
Definition
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.
SECOND TERM
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
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 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
In general the structure of the week is as follows:
Classroom activities  Activities outside the classroom 


This subject has methodological and digital resources to make possible its continuity in noncontact mode in the case of being necessary for reasons related to the Covid19. 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 noncontact 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):
 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:
System 
Weighting (in case of facetoface exams) 
Weighting (in case of NONfacetoface exams) 
Participation in activities proposed in the classroom (participation) 
10% 
15% 
Weekly individual work (project delivery) + Final block test (Tests) 
10% + 20% 
20% + 20% 
Final exam (P2+P3+P4) 
60% 
45% 
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 GrawHill.
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 economicadministrative sciences. Seventh education. Ed Pearson.