Calculus

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

Teachers

Person in charge

• Rafael Ramirez Ros ( )

Others

• Jordi Villanueva Castelltort ( )

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. Grasp the concept of real i complex number
   Related competences: CT6, CB1,
2. Ability to cope with interval calculus and inequalities
   Related competences: CE1, CT5, CT6, CB1,
3. Modeling of problems of numerical optimization
   Related competences: CE1, CT6, CG2, CB1,

Contents

1. Numbers
   Rational, and real numbers. Absolute value. Operations and expressions.
2. Functions
   Qualitative study of the most common functions and their inverses. Limits and continuity.
3. Derivation
   Derivative of a function. Derivative of a composition of functions and of the inverse function. Also for a function implicitly defined. Relative extremes. The mean value theorem. The L'Hôpital rule. The Taylor formula. Lagrange error formula. Optimization problems. Partial derivatives and gradient. Directional derivatives and tangent plane.
4. Integration
   Computation of primitive functions: changes of variable, integration by parts formula; rational, trigonometric and irrational integrals. Integral of a function defined on an interval. Calculus Fundamental Theorem. Mean Value Theorem for integrals. Leibniz's Formula. Improper integrals: definition and comparative criteria. Euler's Gamma function.
5. Sequences and series
   Sequances. Calculation of limits. Series of real and complex numbers. Convergence criteria. Power series. Radius of convergence. Differentiation and integration of power 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, 2011. ISBN: 9786071505019
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991003865579706711&context=L&vid=34CSUC_UPC:VU1&lang=ca

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