Teaching Plan Information

1. General information

Mathematics for Telecommunications aims to show various mathematical contents related to linear ordinary differential equations, Laplace transform, series and Fourier transform and resolution of the equations in partial derivatives of mathematical physics (wave, heat and Laplace equations). We present simple numerical methods to solve initial value and boundary problems, and some models in Telecommunications that use these mathematical contents.

It is recommended to have a precise knowledge of the contents of the Calculus and Algebra subjects of the previous term.

2. Learning results

The contents of this subject should provide students with sufficient techniques and skills to enable them to address the following issues and problems related to the following aspects:

1.- Use elementary methods to solve first order ordinary differential equations and linear differential equations of arbitrary order.

2.- To know the properties of the Laplace transform and its application to the solution of differential and integro-differential equations.

3.- To know the Fourier series developments of periodic functions and their application to the resolution of contour problems.

4.- To know the properties of the Fourier transform and its application to the solution of differential equations.

5.- Use scientific software to solve problems related to differential equations and signal reconstruction.

As a consequence of the previous learning results, the student should be able to analyze a problem and select the most appropriate technique to solve it effectively, interpret the results obtained and question its validity. 

It is also important to know how to analyze and communicate with rigor and precision the results obtained, their scope and their limitations.

Finally, the student must learn to relate the concepts developed in the course with the specific contents of other subjects of the degree. 

3. Syllabus

The program of the subject is divided into the following topics:

Topic 1. First Order Ordinary Differential Equations and Linear Equations of Arbitrary Order.

Topic 2. Laplace transform.

Topic 3. Applications of Differential Equations in Telecommunications. 

Topic 4. Fourier series.

Topic 5. Fourier transform.

Topic 6. Applications of Fourier Methods in Telecommunications.

Topic 7. Applications to Partial Differential Equations. 

4. Academic activities

The subject is developed through an appropriate combination of the following activities:

Participatory lectures 36 hours

Theoretical contents and results are presented, complemented with some problems and practical exercises.

Problem solving classes: 12 hours

In small groups, models are presented in which some of the mathematical aspects of the subject are presented, solved in class or as autonomous work material for the student.

Practical classes: 12 hours

In small groups a scientific software is used to solve the proposed exercises related to some numerical methods and applications in Telecommunications of the mathematical contents.

Teaching jobs: 17 hours

Preparation of the final questionnaires for the laboratory sessions

Personal study: 70 hours

Evaluation tests: 3 hours

5. Assessment system

The subject is evaluated in the global evaluation modality through the following activities:

* Final exam (80%) with theoretical-practical questions, exercises and problems corresponding to the topics developed in the master classes and in the problem classes.

* Laboratory practical work (20%). The requested reports will be evaluated. Students who do not complete or do not pass this evaluation activity will be able to take an exam.

6. Sustainable Development Goals

4 - Quality Education
5 - Gender Equality