Titular Professors
Professors
Mathematical Foundations and Differential and Integral Calculus
The Learning Outcomes of this subject are:
LO.1. Knowledge of multivariate mathematical analysis.
LO.2. Practical application of the acquired knowledge to problem solving.
LO.3. The basic principles of signal processing are understood.
LO.4. General knowledge of signal processing and transmission is acquired.
Module 1: Functions of several variables.
Module 2: Differentiation and integration of functions of several variables.
Module 3: Optimization of functions of several variables.
Module 4: Approximation of functions of several variables.
Module 5: Introduction to signals and signal processing.
Module 6: Signal analysis in the time domain.
Module 7: Fourier transform and analysis in the frequency domain.
Module 8: Discrete Fourier transform and spectral analysis.
The course is taught in 5 weekly lessons lasting 50 minutes each. The usual dynamics of each class will consist of a combination of theoretical explanations always followed by exercises that exemplify what has just been explained. Applied methodologies: master class, problems and exercises class.
Additionally, the eStudy provides resources for the student to carry out self-learning activities (online resources and videos indexed according to their contents). Applied methodology: self-paced learning.
To achieve an applied view of the concepts presented in class, two practical exercises using MATLAB software will be undertaken. Applied methodology: challenge-based learning.
To evaluate each of the skills, 3 different evaluation activities have been specified:
E1. Exams (60%)
Of all kinds: open answer, test, with or without lecture notes, etc.
E2. Exercises, problems and practices (30%)
MATLAB. Individual or in group. The student has at their disposal the appropriate consultation materials. It shows the degree of mastery of learning beyond the mere memorization of information.
E3. Participation in class (10%)
Participation in class, workshop or laboratory. It may include attendance, attitude, oral and/or written tests carried out in class, participation in discussion forums, answering questions and/or resolving situations through actions, among others.
In ordinary call:
The exam mark (NE) is obtained from the control point mark (NEM) and the final exam mark of the semester (NEF):
NE = max{ NEF, 0.6*NEF + 0.4*NEM}
To apply this formula, NEF must be >= 3.5. Otherwise, NE = NEF.
The final grade of the course (NFinal) is computed with the grades of exams (NE), problems and practices (NP) and class participation (NA) according to the following expression:
NFinal = max{ NE, 0.6*NE + 0.3*NP + 0.1*NA }
To apply this formula, NE must be >= 3.5. Otherwise, NFinal = NE and the course is not passed.
The course is passed in ordinary call if NFinal is >= 5.
If the course is not passed in ordinary call (end of the semester):
In July there will be the extraordinary call, which consists of a recovery exam of the entire course (including the MATLAB practices), with recovery mark (NR).
The final grade of the course in July is calculated according to the following expression:
NFinal = max{ NR, 0.6*NR + 0.3*NP + 0.1*NA }
To apply this formula, NR must be >= 4. Otherwise, NFinal = NR and the course is not passed.
The course is passed in extraordinary call if NFinal is >= 5.
J.H. Hubbard, B.B. Hubbard, "Vector Calculus, Linear Algebra, and Differential Forms - A Unified Approach", Matrix Editions.
A.V. Oppenheim, R.W. Schafer, "Discrete-time signal processing", Prentice Hall.
T.K. Rawat, "Signals and systems", Oxford University Press.
G.B. Folland, "Fourier Analysis and its Applications", American Mathematical Society.
W. Rudin, "Principles of Mathematical Analysis", McGraw-Hill.
E.M. Stein, R. Shakarchi, "Fourier Analysis: An Introduction", Princeton University Press.