Algebra

Code:

EEC0004

Acronym:

ALGE

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2007/2008 - 1S

Active?	Yes
Responsible unit:	Fundamental Sciences and Electrotechnics
Course/CS Responsible:	Master in Electrical and Computers Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
LEEC	0	Plano de estudos de transição para 2006/07	1	6	6	75	160
MIEEC	446	Syllabus since 2006/2007	1	-	6	75	160
		Syllabus since 2007/2008	1	-	6	75	160
		Plano para alunos que em 2006 estiveram no 3º ano	1	-	6	75	160
		Plano para alunos que em 2006 estiveram no 5º ano	1	-	6	75	160
		Plano para alunos que em 2006 estiveram no 4º ano	1	-	6	75	160

Teaching language

Portuguese

Objectives

This course aims to provide concepts of Linear Algebra, which are of crucial importance to the qualification of the Electrical Engineering undergraduates. The fundamental concepts include algebraic structures, linear or vector distance, matrix analysis and linear transformations. It is aimed that the students develop algebraic manipulation skills, analytical and independent thinking and the ability to apply mathematical concepts to the resolution of practical problems.

Program

Algebraic Structures: groupoid, group, ring and body. The body of real numbers and the body of the complex numbers.
Vectorial Space over a body: definition and examples; linear dependency and independency; subspace; basis; isomorphism. Euclidean distance: internal product, projections, rules and ortonormal basis.
Matrixes: definitions and basic operations. Characteristic and determinants. Matrixes’ inversion. Solving equation systems. Gaussian elimination.
Linear Transformation: definition, nucleous, image and characteristic. Matrix representation of linear transformations. Change of basis. Matrix similarity.
Specific Values and vectors: definition and properties. Calculation of specific values and vectors. Repeated specific values and Jordan’s shape. Matrix diagonalization.

Mandatory literature

Notas a disponibilizar pelos docentes durante o Semestre (ver página da web)
Noble, Ben; Applied linear algebra. ISBN: 0-13-041260-0

Complementary Bibliography

Gregório Luís e C. Silva Ribeiro; Álgebra Linear, McGraw-Hill.
Gilbert Strang ; Applied Algebra and Its applications , Saunders HBJ
E. Giraldes, V. H. Fernandes M. Smith ; Álgebra Linear e Geometria Analítica, McGrawHill

Teaching methods and learning activities

In theoretical classes important concepts and associated results will be presented, giving special emphasis to geometrical interpretations and their practical applications. Aiming to clarify the definitions and theorems presented, demonstrations will be given each and every time that these might help to achieve that understanding and the students will be given illustrative exercises to solve.
The theoretical-practical classes aim to better orientate the study of this course by making exercises that apply the taught information.
The practical classes are used to help the student solving exercises and to clarify their doubts.
The teachers of this course will also set a Schedule to receive the students beyond class time.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Subject Classes	Participação presencial	68,00
	Trabalho escrito	22,00
	Exame	0,50
	Exame	0,50
	Exame	0,50
	Exame	0,50
	Exame	2,00
	Total:	-	0,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
	Estudo autónomo	68
	Total:	68,00

Eligibility for exams

Regardless of the classification in the distributed component, every student will attain frequency as long as he doesn’t exceed the absence limit.

Calculation formula of final grade

Final Grade = Grade of the distributed component*20% +
Grade of the final exam*80%.

Special assessment (TE, DA, ...)

Special Evaluation Students:
The students who, throughout the year, have the statute either of working students or of the military are dismissed from frequency and the compulsory distributed evaluation component. For these students, the evaluation in this course will be done with the final written exam, which will represent 100% of the final classification. Nevertheless, the students with these statutes that do the mini-test will be evaluated with it and with the final exam, with the proportion of 20% and 80%.


Students that attained frequency in 2003/2004:
The students who attended Algebra in 2003/2004 that had negative results but attained frequency (see grid) may, in concord with the general evaluation rules, be dismissed from attending classes this year. This also means that they don’t need to enrol on this year classes. Under those circumstances, the evaluation will be done only with the final exam, unless:
a) They do the mini-test, in which case they will be evaluated with it and the final exam, with the proportions of 20% and 80%.
b) They choose to keep the result of the distributed component of last year. This represents 20% of the final grade. These students must get in touch with the teacher by e-mail to sergio@fe.up.pt until December 19th, 2004.

Classification improvement

Classification improvement will be done with the final written exam. The result represents 100% of the final classification.

Observations

Horário de atendimento de alunos (efectuar marcação prévia por e-mail):


Language of instruction: Portuguese.