What are you looking for?
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 re-evaluate 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 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.
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.
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
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
The evaluation of the subject will take into account the following evaluable aspects:
Then the final grade of the subject will be calculated with the following weights:
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) is not recoverable under any circumstances. Yes, the grades of the quarterly exams (Ex1 and Ex2) can be recovered.
No grade from one academic year will be saved for another.
Summary of evaluation percentages:
System |
Weighting |
First term exam notes |
30% |
Second term exam notes |
30% |
Continuous Assessment (online quizzes, seminars, assignment of problems, class participation...) |
40% |
All the exams that are taken will require a minimum qualification to count in the evaluation.
A student who has not taken the final exam (at the end of the 2nd term) will not be able to take the retake.
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.
STTAN (1998): Mathematics for administration and economics. International Thomson Publishers.
LÓPEZ, M. VEGAS, A. (1994): Basic course of mathematics for the economy and the direction of companies. Vol I and II. Ed Pyramid.
BITTINGER, MARVIN, L. (2002): Calculus for economic-administrative sciences. Seventh education. Ed Pearson.