Calculus

• Teachers
• Weekly hours
• Competences
• Objectives
• Contents
• Activities
• Teaching methodology
• Evaluation methodology
• Bibliography
• Web links
• Previous capacities

Teachers

Person in charge

• Jordi Villanueva Castelltort ( )

Others

• Jose Tomas Lazaro Ochoa ( )
• Rafael Ramirez Ros ( )

Weekly hours

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

1. Elementary functions, continuity, limit and associated concepts
   Related competences: CT6, CB1,
2. The derivative and its use as a basic calculation tool.
   Related competences: CE1, CT5, CT6, CG2, CB1,
3. Calculation of primitives and definite integrals.
   Related competences: CE1, CT5, CT6, CG2, CB1,
4. Discussion of the convergence of improper integrals, sequences and series and calculation of their limit in simple cases where it is approachable.
   Related competences: CE1, CT5, CT6, CG2, CB1,

Contents

1. 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.
2. 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.
3. Integration
   Calculation of primitives. Definite integrals. Numerical integration. Improper integrals and their convergence criteria. Euler's Gamma function.
4. Sequences and series
   Sequences and their limit. Numerical series and their convergence criteria. Power series. Taylor series.

Activities

Activity Evaluation act

Teaching methodology

Evaluation methodology

Bibliography

Basic:

• Análisis matemático - Apostol, Tom M, Reverté, 1977. ISBN: 8429150048
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991000520829706711&context=L&vid=34CSUC_UPC:VU1&lang=ca
• Cálculo infinitesimal de una variable - Burgos Román, J., McGraw-Hill, 2007. ISBN: 9788448156343
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991003471409706711&context=L&vid=34CSUC_UPC:VU1&lang=ca
• Cálculo - Larson, R.; Edwards, B, McGraw Hill, 2016. ISBN: 9786075220154
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991004174869706711&context=L&vid=34CSUC_UPC:VU1&lang=ca
• Cálculo de una variable: trascendentes tempranas - Zill, D.G, McGraw Hill, 2019. ISBN: 9781456272340
  

Complementary:

• Calculus made easy : being a very-simplest introduction to those beautiful methods of reckoning which are generally called by the terrifying names of the differential calculus and the integral calculus - Thompson, Silvanus Phillips; Gardner, Martin, Macmillan and co., limited , 1998. ISBN: 9781514779545
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991004118869706711&context=L&vid=34CSUC_UPC:VU1&lang=ca

Web links

• 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
• Material seleccionat i elaborat pel professor Rafael Ramírez amb multitud de vídeos de contingut matemàtic adaptat directament al temari de l'assignatura. https://web.mat.upc.edu/rafael.ramirez/ACcY/index.html

Previous capacities