TecnoCampus Foundation
eCampus
University Business
eCampus

What are you looking for?

General information

Subject type: Basic

Coordinator: Joan Triadó Aymerich

Trimester: Second term

Credits: 6

Teaching staff: 

Carlos Paul Recarens

Academic year: 2025

Teaching course: 1

Languages ​​of instruction

  • Catalan

Competencies / Learning Outcomes

Specific skills

  • K2. Identify the basic methodologies of linear algebra; geometry; differential geometry; differential and integral calculus; differential and partial differential equations; numerical methods; numerical algorithm; statistics, and optimization that are applied in engineering.

  • S1. Solve, through the use of mathematics and statistics, the possible problems that may arise in engineering.

  • S31. Apply critical thinking using different strategies depending on what needs to be learned and in the context in which it needs to be learned.

Presentation of the subject

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.

The classroom (physical or virtual) is a safe space, free of sexist, racist, homophobic, transphobic and discriminatory attitudes, either towards students or towards teachers. We trust that together we can create a safe space where we can make mistakes and learn without having to suffer prejudice from others.

Contents

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 using 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 Several Variables
6.2 Limits and Continuity
6.3 Partial Derivatives
6.4 The Chain Rule
6.5 Gradient
6.6 Maximum and Minimum Values

7. Multiple Integrals

7.1 Double integrals 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



 

 

Activities and evaluation system

The evaluation system consists of three parts identified as follows. An exam at the end of the term, where all the content of the subject is evaluated. There are two sessions of problems solved individually; the first (Problems1) at one-third of the term and the second (Problems2) at two-thirds of the term.

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 only the exam grade obtained in the ordinary assessment.

The subject is taught in person and, therefore, class attendance is essential. In the same way that attendance at practical activities is essential.

Bibliography

Basic

Notes of the subject

James Stewart. Calculation of a variable.

James Stewart. Calculation of several variables.