Introduction to the basic calculus tools for functions of one variable (continuity, derivation, integration and series) as well as some basic notions of calculus for functions of several variables. The presentation is used to introduce some basic numerical calculation tools.
Teachers
Person in charge
Jordi Villanueva Castelltort (
)
Others
Jose Tomas Lazaro Ochoa (
)
Rafael Ramirez Ros (
)
Weekly hours
Theory
3
Problems
2
Laboratory
0
Guided learning
0
Autonomous learning
7.5
Competences
Technical Competences
Technical competencies
CE1 - Skillfully use mathematical concepts and methods that underlie the problems of science and data engineering.
Transversal Competences
Transversals
CT5 - Solvent use of information resources. Manage the acquisition, structuring, analysis and visualization of data and information in the field of specialty and critically evaluate the results of such management.
CT6 [Avaluable] - Autonomous Learning. Detect deficiencies in one's own knowledge and overcome them through critical reflection and the choice of the best action to extend this knowledge.
Basic
CB1 - That students have demonstrated to possess and understand knowledge in an area of ??study that starts from the base of general secondary education, and is usually found at a level that, although supported by advanced textbooks, also includes some aspects that imply Knowledge from the vanguard of their field of study.
Generic Technical Competences
Generic
CG2 - Choose and apply the most appropriate methods and techniques to a problem defined by data that represents a challenge for its volume, speed, variety or heterogeneity, including computer, mathematical, statistical and signal processing methods.
Objectives
Elementary functions, continuity, limit and associated concepts
Related competences:
CB1,
CT6,
The derivative and its use as a basic calculation tool.
Related competences:
CB1,
CT5,
CT6,
CE1,
CG2,
Calculation of primitives and definite integrals.
Related competences:
CB1,
CT5,
CT6,
CE1,
CG2,
Discussion of the convergence of improper integrals, sequences and series and calculation of their limit in simple cases where it is approachable.
Related competences:
CB1,
CT5,
CT6,
CE1,
CG2,
Contents
Functions
Rational and real numbers. Absolute value. Qualitative study of the most usual functions and their inverses. Limit and continuity. Theorem of Bolzano and theorem of the intermediate value.
Derivation
Derivative of a function. Direct applications of the derivative. Rolle's and mean value theorems. Rule of L'Hôpital. Taylor's formula and applications. Introduction to the functions of several variables. Numerical derivation. Numerical computation of zeros of functions.
Integration
Calculation of primitives. Definite integrals. Numerical integration. Improper integrals and their convergence criteria. Euler's Gamma function.
Sequences and series
Sequences and their limit. Numerical series and their convergence criteria. Power series. Taylor series.
Lectures introduce the concepts, algorithms and results needed to reach athe required level of understanding. These concepts are put into practice in the problem classes in which, due to its structure, it is easier to encourage the active participation of students. The practice note is aimed at encouraging the most creative and transversal aspects of the subject since it involves the completion of problems that involve the understanding of concepts and the use of tools that we could hardly fit into the regulated exhibition.
Evaluation methodology
Final grade = max(0.1*NPract + 0.9*NExFinal, 0.1*NPract + 0.3*NExParcial + 0.6*NExFinal)
on
[NPract]: numerical methods exam
[NExParcial]: midterm exam
[NExFinal]: final examen grade
In case of reevaluation, the new grade will replace the previous.
Primer dels tres volums dels divulgadors Edwin Herman i Gilbert Strang, professors del MIT,
editats per OpenSatx sota llicència gratuïta. Gairebé 3000 pàgines amb una gran quantitat d'exemples, figures i problemes resolts. https://openstax.org/details/books/calculus-volume-1
Segon dels tres volums dels divulgadors Edwin Herman i Gilbert Strang, professors del MIT,
editats per OpenSatx sota llicència gratuïta. Gairebé 3000 pàgines amb una gran quantitat d'exemples, figures i problemes resolts. https://openstax.org/details/books/calculus-volume-2
Tercer dels tres volums dels divulgadors Edwin Herman i Gilbert Strang, professors del MIT,
editats per OpenSatx sota llicència gratuïta. Gairebé 3000 pàgines amb una gran quantitat d'exemples, figures i problemes resolts. https://openstax.org/details/books/calculus-volume-3