This course presents subjects of mathematics that extend or complement those introduced in the courses on Algebra and Calculus of the first semester.
Person in charge
Jordi Quer Bosor (
Jordi Guardia Rubies (
CE1 - Skillfully use mathematical concepts and methods that underlie the problems of science and data engineering.
CT5 - Solvent use of information resources. Manage the acquisition, structuring, analysis and visualization of data and information in the field of specialty and critically evaluate the results of such management.
CT6 [Avaluable] - Autonomous Learning. Detect deficiencies in one's own knowledge and overcome them through critical reflection and the choice of the best action to extend this knowledge.
CB1 - That students have demonstrated to possess and understand knowledge in an area of ??study that starts from the base of general secondary education, and is usually found at a level that, although supported by advanced textbooks, also includes some aspects that imply Knowledge from the vanguard of their field of study.
Generic Technical Competences
CG2 - Choose and apply the most appropriate methods and techniques to a problem defined by data that represents a challenge for its volume, speed, variety or heterogeneity, including computer, mathematical, statistical and signal processing methods.
CG5 - To be able to draw on fundamental knowledge and sound work methodologies acquired during the studies to adapt to the new technological scenarios of the future.
Extension of knowledge of Algebra and Calculus.
Recognize and apply the concepts of Algebra and Calculus related to multidisciplinary problems.
Achieve a mastery of software that allows you to solve problems of greater complexity from the knowledge acquired.
Riemann integral of functions of several variables. Rectangle; arbitrary domains; improper integrals. Fubini's Theorem. Iterated integrals. Normal domains. Change of variables theorem. Polar and spherical coordinates. Numerical methods. Quadrature formulas. Monte Carlo mehtod.
Fourier series and Fourier transform
Spaces of funcions. Sequences and series of funcions. Trigonometric and exponential Fourier series. Parity. Fourier transform. Properties: symmetries, shift, scaling, convolution, conservation of energy. Generalized functions. Dirac Delta. Functionals. Distributions.
Quadratic forms and extrema
Quadratic forms and symmetric matrices. Definite, indefinite, semidefinite. Diagonalization. Signature. Restriction to subspaces. Gradient, Jacobian, Hessian. Local extrema of functions of several variables. Critical points. Constrained extrema. Lagrange multipliers. Global extrema on compact sets.
Development of topic 1 of the course
Theory classes and Problems of the topic 1 Objectives:123
Development of topic 2 of the course
Theory and Problems classes on topic 2 Objectives:123
Development of topic 3 of the course
Theory and problem classes on topic 3 Objectives:123 Contents:
Theory classes will be in the form of master classes in which the contents of the subject will be explained and examples and illustrative problems will also be given.
In the problem classes, problems will be solved on the topics studied in theory.
Algebra, topology, differential calculus, and optimization theory for computer science and engineering -
Gallier, Jean; Quaintance, Jocelyn,
University of Pennsylvania. Department of Computer and Information Science, 2018.