TecnoCampus Foundation
eCampus
University Business
eCampus

What are you looking for?

General information

Subject type: Basic

Coordinator: Joan Triadó Aymerich

Trimester: First term

Credits: 6

Teaching staff: 

Cristina Steegmann Pascual

Academic year: 2025

Teaching course: 2

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.

  • S32. 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

This is the last subject of mathematics and provides basic tools in the training of the engineer. The subject enables the student to understand and/or solve mathematical problems that may arise in engineering, related to analysis and linear algebra.

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

Topic 1: Introduction to complex numbers

  1. Origin of numbers C and operations with C
  2. Polar shape of the C
  3. Trigonometric shape - exponential
  4. Complex roots of an equation

Topic 2: Limits and derivatives in complexes

  1. Complex functions
  2. Derivability of complex functions
  3. Integration of complex functions. Primitives

Topic 3: Elementary functions

  1. Complex polynomial function
  2. Complex exponential function
  3. Complex logarithmic function
  4. Complex trigonometric functions

Topic 4: Diagonalization of matrices

  1. Linear application
  2. Characteristic polynomial, vaps and veps
  3. Diagonalization of matrices_I
  4. Diagonalization of matrices_II

Topic 5: Ordinary Differential Equations (ODE)

  1. Separable ordinary differential equations
  2. Linear ordinary differential equations
  3. Exact ordinary differential equations
  4. Exercises EDO I
  5. Exercises EDO II
  6. Mathematical models
  7. Mathematical model exercises

Topic 6: Laplace transform (TL)

  1. Laplace transform
  2. Inverse Laplace transform

Activities and evaluation system

20% Assessable individual exercises:

They will be evaluated on the basis of the resolution, within a fixed period of days, of four exercises, personalized, corresponding, each of them, to a subject of the course.

 

80% Tests:

There will be two exams during the course (40% each test), a first midterm (first 3 topics) and a final exam with 5 questions each. Those who have failed the first exam will have to take this part in the final exam. Those who have passed the first midterm will not have to take this part in the final exam (the first midterm is subject-free). To qualify for an average between the two exams, a minimum of 5 points must be obtained in the first exam and 4 points in the second exam. The score obtained in the assessable exercises (4%) will be added to the average grade obtained between the two exams, provided that it is a minimum grade of 20. In the event of a coincidence in the final grade, the grade of the second midterm will prevail to qualify for the MH.

Students who fail the final exam will go to recovery. The maximum grade for the retake is 6 points and the evaluable exercises are not compatible with the retake.

 

Important: 

Any form of academic fraud will be sanctioned in accordance with the center's assessment regulations. If signs of fraud are detected, including the improper use of generative artificial intelligence tools, the subject's teaching staff may call the student for an individual interview with the aim of verifying their authorship.

 

 

Bibliography

Basic

Notes of the subject

Boyce, W .; DiPrima, R. (1990). Differential equations. Mexico: Limusa Noriega Editores.

Krasnov, m et al. 1990. Higher mathematics course for engineers. Mir. Moscow

Schaum (1971). Complex variable. Madrid: Mc Graw-Hill