Linear Analysis

Code:

M328

Acronym:

M328

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2014/2015 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:M	9	Plano de estudos a partir de 2009	1	-	7,5	-
			2
			3

Teaching language

Portuguese

Objectives

To give an exposure to common introductory topics of functional analysis of a first approach on the subject, exploring their connections to several problems on differential equations.

Learning outcomes and competences

Students should acquire knowledge on functional spaces, linear operators and their applications to integral and differential equations. They should deepen theoretical concepts that lead them to correctly identify, put into context and apply methods of problem solving.

Working method

Presencial

Program

Normed spaces, Euclidean spaces. Completion. Fourier Series. Riesz-Fisher representation theorem. Fourier and Laplace transforms. Continuous linear mappings. Dual space. Adjoint of an operator. Spectrum of a bounded operator. Compact operators. Integral operators. Fredholm theory. Linear operators in Hilbert spaces. Elliptic operators. Ordinary linear differential equations. Contour problems.

Mandatory literature

Smirnov Gueorgui V.; Curso de análise linear. ISBN: 972-592-153-4

Teaching methods and learning activities

The contact hours consist of theoretical and practical lessons, allowing teachers to organize and manage the time available for presenting the subject matter, solving problems, accomplishing tasks and practical work or using other teaching methods appropriate to the content of the discipline and the matters that are being addressed.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	100,00
Total:	100,00

Calculation formula of final grade

Final classification obtained by distributed evaluation with final exam: Final grade = 0.4xHW + 0.6xE where HW = average grade of 3 homeworks, E = grade of the final exam.
Final classification obtained by examination: grade of the final exam.

Examinations or Special Assignments

There will be 3 homeworks during the semester that may be used in the final exaluation.