Algebra

Code:

EQ0058

Acronym:

A

Keywords
Classification	Keyword
OFICIAL	Physical Sciences (Mathematics)

Instance: 2009/2010 - 1S

Active?	Yes
Responsible unit:	Department of Chemical Engineering
Course/CS Responsible:	Master in Chemical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEQ	117	Syllabus	1	-	5	49	135

Teaching language

Portuguese

Objectives

This course aims to endow students with fundamental knowledge on Algebra (vectors, linear spaces, matrices, determiners, systems of linear equations) as is detailed is in the program of the course.

Program

1. VECTOR ALGEBRA
Operations with vectors; Linear dependence of vectors; Scalar product; Line equation; Plane equation; vector product; scalar triple product; repeated products of three or more vectors; distance from point to plane

2. LINEAR SPACES
Linear spaces: examples; Sub-spaces; Base and dimension; Linear spaces with inner product

3. MATRIX ALGEBRA
Linear transformations and matrices; Operations with matrices; Matrix decomposition; Linear transformations; R2 and R3 linear transformations: reflections, orthogonal projections, rotations, dilations and contractions

4. DETERMINANTS
Definition; Determinants: basic properties; Determinants calculation

5. LINEAR EQUATION SYSTEMS
Coefficient matrix and extended matrix; Gaussian elimination; Elementary operations; Equivalent systems; Matrix characteristics; General properties of solution of linear equation systems; Gauss-Jordan algorithm; Homogeneous systems; Linear space (Ax=0 solutions); Non-homogeneous systems; Linear dependence and characteristic; Singular matrices; Cramer’s rule; LU decomposition

6. INVERSE MATRIX AND RELATED MATRICES
Inverse matrix: properties; Adjunct matrix; Inverse matrix calculation by the adjunct matrix; Inverse matrix calculation by elementary operations

7. EIGENVALUES AND EIGENVECTORS
Characteristic determinant, characteristic polynomial and characteristic equation of a matrix; Determining eigenvalues and its eigenvalues; Eigenvalues: properties; algebraic multiplicity and geometric multiplicity

8. DIAGONALIZATION OF MATRICES
Diagonalizing a matrix: procedures

Mandatory literature

João Mendonça; Sebenta de Álgebra, DEQ/FEUP

Complementary Bibliography

Anton, Howard; Elementary linear algebra. ISBN: 0-471-17052-6

Teaching methods and learning activities

General theoretical-practical classes are based on the presentation of the themes of the course and examples are given.
The theoretical-practical classes, which are divided in groups, are intended to clarify students’ doubts about the exercises. Students are supposed to solve the exercises before class.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	62,40
	Teste
	Exame			2009-11-23
	Exame			2010-01-25
	Exame			2010-01-25
	Exame			2010-02-03
	Total:	-	0,00

Eligibility for exams

1- Students cannot exceed ¼ of the classes previously set
2- Students have to do at least 2-3 micro-tests
3- Students who were only admitted on the second phase, will be assessed depending on the date that they were admitted

Students who are repeating the course, and who were admitted to exams in the previous year, do not need to attend to classes.

Calculation formula of final grade

Final Mark will be based on one of the following formulas:
FM= 0,2*MT+0,4*T1+0,4*T2
Or
FM= 0,2*MT + 0,8* E

MT- Micro-tests
T1 and T2- Test 1 and Test 2
E- Exam

1- It will be calculated on the final mark the 6 best results of the micro-tests. As far as students who were only admitted on the second phase are concerned, it will be also considered the best results.
2- After the results of the first test (T1) are known, students have to inform the professor, if they either want to attend to the second test (T2) or to the complete final exam (E)
3- In recurso exam the final mark will only be based on the mark of the exam.

Students who do not need to attend classes:
FM= 0,5*T1 + 0,5*T2
Or
FM= E

Examinations or Special Assignments

Not applicable

Special assessment (TE, DA, ...)

Exam

Classification improvement

The marks of micro-tests will not be added to the Final Mark.

Observations

Students are not allowed to use calculators on micro-tests, tests and exams.