General information

Subject type: Basic

Coordinator: Joan Triadó Aymerich

Trimester: Second term

Credits: 6

Teaching staff: 

Carlos Paul Recarens

Teaching languages

  • Catalan


Specific skills
  • CE1: Train for the solution of mathematical problems that may arise in engineering. Ability to apply knowledge about: ¿¿linear algebra; geometry; differential geometry; differential and integral calculus; differential equations and partial derivatives; numerical methods; numerical algorithm; statistics and optimization.

Transversal competences
  • CT2: That students have the ability to work as members of an interdisciplinary team either as one more member, or performing management tasks in order to contribute to developing projects with pragmatism and a sense of responsibility, assuming commitments taking into account count available resources.


The subject provides a second mathematical level to students, completing the analysis of one variable with the integral and the analysis of functions in several variables.

New vector concepts related to derivation and integration with practical applications in electrical and mechanical engineering are introduced.

At the end of the course, the student must be able to:

  1. Calculate integrals by basic methods
  2. Calculate areas and volumes using Integral Calculation resources
  3. Solve the differentiability in several variables.
  4. Solve elementary situations of differential geometry
  5. Calculate the ends of the graph of functions of several variables
  6. Familiarize yourself with the vector notation of fields.



1. Integral

1.1 Concept of Antiderivative
1.2 Areas and distances
1.3 Integral Defined
1.4 Fundamental theorem of calculus
1.5 Indefinite Integrals
1.6 The variable change rule

2. Applications of Integration I

2.1 Areas between curves
2.2 Volumes
2.3 Volumes by cylinders
2.4 Work
2.5 Average value of a function

3. Integration Techniques

3.1 Integration by parts
3.2 Trigonometric integrals
3.3 Trigonometric substitution
3.4 Integration of rational functions by means of partial fractions
3.5 Integrals using Integral Tables
3.6 Improper Integrals

4. Applications of Integration II

4.1 Arc length
4.2 Area of ​​a surface of revolution
4.3 Moment of center of mass
4.4 Pappus' theorem
4.5 Concepts of probability
4.6 Concept of differential equation

5. Vectors and Geometry in Space

5.1 Three-dimensional coordinate systems
5.2 Scalar Product
5.3 Vector Product
5.4 Vector Functions

6. Partial Derivatives

6.1 Functions of Various Variables
6.2 Limits and Continuity
6.3 Partial Derivatives
6.4 The Chain Rule
6.5 Gradient
6.6 Maximum and Minimum Values
6.7 Lagrange Multipliers

7. Multiple Integrals

7.1 Double integers in rectangular coordinates
7.2 Double integrals in polar coordinates
7.3 Triple integrals in rectangular coordinates
7.4 Triple integrals in cylindrical coordinates
7.5 Triple integrals in spherical coordinates
7.6 Jacobian of the coordinate transformation

8. Vector Calculus

8.1 Vector fields
8.2 Line integrals
8.3 Green's theorem
8.4 Rotational and Divergence
8.5 Stokes' theorem
8.6 Divergence Theorem



Evaluation system

The evaluation system consists of three parts identified as follows. An exam at the end of the term in which all the content of the subject is assessed. There are two sessions of problems solved individually; the first at one-third of the quarter and the second at two-thirds of the quarter.

The final grade is the weighted sum of the final exam and the individual problem sessions, with the following weights:

FINAL GRADE = EXAM x 0,6 + PROBLEMS1 x 0,2 + PROBLEMS2 x 0,2

There will be an extraordinary exam recovery session for all students who do not pass the subject in the ordinary assessment.

The grade of this recovery will replace the exam grade obtained in the ordinary assessment.



Notes of the subject

James Stewart. Calculation of a variable.

James Stewart. Calculation of several variables.