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General information

Subject type: Basic

Coordinator: Joan Triadó Aymerich

Trimester: First term

Credits: 6

Teaching staff: 

Cristina Steegmann Pascual

Teaching languages

  • Catalan

Skills

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.

Description

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

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 partial (3 first 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 part-time will not need to take the final exam (the first part-time is subject-free). To opt for an average between the two exams, you must get a minimum of 5 points in the first exam and 4 points in the second exam. To the average grade obtained between the two exams, as long as it is a minimum grade of 4, the score obtained from the evaluable exercises will be added (20%).

 

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.

 

REFERENCES

Basic

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

Notes of the subject

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

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