Algebra

Code:

L.EQ001

Acronym:

ALG

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2024/2025 - 1S

Active?	Yes
Responsible unit:	Department of Chemical and Biological Engineering
Course/CS Responsible:	Bachelor in Chemical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L.EQ	89	Syllabus	1	-	6	52	162

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.

Learning outcomes and competences

Knowledge about basic principles of Algebra as described in the course program.

Working method

Presencial

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; Linear transformations; R2 and R3 linear transformations. 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
José Augusto Trigo Barbosa; Noções sobre matrizes e sistemas de equações lineares. ISBN: 972-752-069-3 972-752-065-0
José Augusto Trigo Barbosa; Noções sobre álgebra linear. ISBN: 978-972-752-142-5
F. Xavier Malcata; Mathematics for Enzyme Reaction Kinetics and Reactor Performance, John Wiley & Sons Ltd., 2020. ISBN: 9781119490319

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 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 without final exam

Assessment Components

Designation	Weight (%)
Teste	100,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	60,00
Frequência das aulas	40,00
Total:	100,00

Eligibility for exams

Do not exceed 1/4 of unexcused absences in practical-theoretical (TP) classes relative to the total number of scheduled TP classes. Students who have already fulfilled attendance requirements in a previous year are exempt from attending again.

Calculation formula of final grade

Continuous Assessment:

Continuous assessment consists of 5 tests:

Tests 1 to 4 – Partial assessment of the material taughtMaximum duration: 30 minutes each
Weight: 10% each

Test 5 – Comprehensive assessment covering all the material taughtMaximum duration: 70 minutes
Weight: 60%

Notes:
Absences from Tests 1 to 4:Justified (e.g., student workers, illness) – the percentage of the missed test will be transferred to Test 5
Unjustified – score of 0
Test 5 is the same for all students and is mandatory to pass the continuous assessment.
To pass, students must score above 6.5 on Test 5 and have a final grade (CF) above 9.5 in the course.

Final Grade (CF) Calculation: CF = 0.1 * T1 + 0.1 * T2 + 0.1 * T3 + 0.1 * T4 + 0.6 * T5


Recurso (for approval or grade improvement):
CF = Exam

Examinations or Special Assignments

Not applicable

Special assessment (TE, DA, ...)

Exam

Classification improvement

Appeal exam

Observations

The use of calculators is not allowed in tests and exams. However, in Test 5 and exams, students will be permitted to consult a formula sheet individually prepared by each student, according to guidelines to be provided later.