Credits
7.5
Types
Compulsory
Requirements
This subject has not requirements, but it has got previous capacities
Department
MAT
Introduction to differential and integral calculus. From the starting point of numbers (rational, real, complex) and going up to some notion of multivariate calculus.

Teachers

Person in charge

  • Jose Tomas Lazaro Ochoa ( )

Others

  • Rafael Ramirez Ros ( )

Weekly hours

Theory
3
Problems
2
Laboratory
0
Guided learning
0.5
Autonomous learning
7

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 - 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, real and complex numbers. Absolute value. Operations and expressions. Fundamental theorem of algebra.
  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. Optimization problems. Partial derivatives and gradient. Introduction to Optimization in several variables.
  4. Integration
    Integral of a function over an interval. The Fundamental Theorem of Calculus. Calculation of primitives. Improper integrals.
  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


Midterm exam


Objectives: 1 2
Week: 10 (Outside class hours)
Type: theory exam
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
2h
Autonomous learning
5h

Final exam


Objectives: 2 3
Week: 15 (Outside class hours)
Type: final exam
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
2h
Autonomous learning
10h

Numbers



Theory
3h
Problems
4h
Laboratory
0h
Guided learning
0h
Autonomous learning
18h

Functions study



Theory
8h
Problems
5h
Laboratory
0h
Guided learning
0h
Autonomous learning
18h

Differentiability



Theory
12h
Problems
8h
Laboratory
0h
Guided learning
0h
Autonomous learning
18h

Integrability



Theory
12h
Problems
8h
Laboratory
0h
Guided learning
0h
Autonomous learning
18h

Sequences and series



Theory
10h
Problems
5h
Laboratory
0h
Guided learning
0h
Autonomous learning
18h

Teaching methodology

Lectures introduce the concepts, results and algorithms needed to achieve the required level of understanding

These concepts are put into practice ex
problem and laboratory sessions.

The teacher poses problems related to the current topic prior to each problem session.

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.

Bibliography

Basic:

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
    http://cataleg.upc.edu/record=b1494388~S1*cat

Previous capacities

Knowledge on basic calculus theory at level 2n Batxillerat

Addendum

Contents

NO HI HA CANVIS RESPECTE LA INFORMACIÓ PUBLICADA A LA GUIA DOCENT

Teaching methodology

NO HI HA CANVIS RESPECTE LA INFORMACIÓ PUBLICADA A LA GUIA DOCENT

Evaluation methodology

NO HI HA CANVIS RESPECTE LA INFORMACIÓ PUBLICADA A LA GUIA DOCENT

Contingency plan

En el cas que una emergència sanitària requerís la no-presencialitat, el curs es desenvoluparia durant els mateixos horaris de classe i de manera online.