Linear Algebra and Analytic Geometry I

Code:

M1010

Acronym:

M1010

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2017/2018 - 1S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=281
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:B	1	Official Study Plan	3	-	9	84	243
L:F	0	Official Study Plan	2	-	9	84	243
			3
L:G	1	study plan from 2017/18	3	-	9	84	243
L:M	88	Official Study Plan	1	-	9	84	243
L:Q	0	study plan from 2016/17	3	-	9	84	243

Teaching language

Portuguese

Objectives

Understanding and ability to use the basic concepts and results related to the subjects of the syllabus.

Learning outcomes and competences

By completing this course, students should know, understand and be able to use the basic notions and results about vector spaces; Vector subspaces; subspace sums; direct sums of subspaces; linear independence; generating systems;finitely generated vector spaces; bases; dimension; linear applications; kernel and image of linear applications; inverse image of an element as translation of the kernel; characteristic of a linear transformation; linear operators; trace of a linear operator; matrices; matrix of a linear application with respect to fixed bases; change of basis; application of these concepts and results to solve systems of linear equations; Similar matrices; determinants; determinant of a linear operator; eigenvalues and eigenvectors; characteristic polynomial of a linear operator; cases in which there is a basis of eigenvectors.

Working method

Presencial

Program

1. Vector spaces; Vector subspaces; subspace sums; direct sums of subspaces; linear independence; generating systems; finitely generated vector spaces; bases; dimension.
2. Linear Applications; kernel and image of linear applications; inverse image of an element as translation of the kernel; characteristic of a linear transformation; linear operators; trace a linear operator.
3. Matrices; matrix of a linear application with respect to fixed bases; change of basis; application of these concepts and results to solve systems of linear equations; Similar matrices.
4. Determinants; determinant of a linear operator.
5. Eigenvalues and eigenvectors; characteristic polynomial of a linear operator; case in which there is a basis of eigenvectors.

Mandatory literature

Anton Howard; Elementary linear algebra. ISBN: 0-471-66959-8
Edwards jr. C. H.; Elementary linear algebra. ISBN: 0-13-258245-7
Monteiro António; Álgebra linear e geometria analítica. ISBN: 972-8298-66-8
Mansfield Larry E.; Linear algebra with geometric applications. ISBN: 0-8247-6321-1
Nomizu Katsumi; Fundamentals of linear algebra

Teaching methods and learning activities

Contact hours are divided into theoretical and theoretical-practical. The former consist of lectures on the contents of the syllabus, making use of examples to illustrate the concepts treated and to guide students. In the latter, theoretical and practical exercises and problems are solved. Support materials are available on the course page. In addition to the classes, there are weekly periods where students have the opportunity to ask for help on their difficulties.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

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

Eligibility for exams

Students with more than 7 absences to theoretical-practical classes (TP) will be excluded.
In order to not to be excluded, at least 6 (4 in the case of the second and third phase students) of the 10 minitests held in the TP classes are required; these tests will not count towards the final classification; for each minitest three types of questions will be given in advance, and in the minitest each student will be assigned randomly a question of one of the types.

Calculation formula of final grade

">Assessment will be based on three tests (the last one will take place on the date of the "exame da época normal), each of the first two tests being worth 4 points and the last one being worth 12 points.

To go to the second test, the student must achieve at least 1 point in the first test (unless they have entered the course in the second or third phase) and to go to the third test they should get at least 1 point in the second test, and should still get at least 4 points on the sum of the two tests (if they have entered in the second or third phase only 3 points are required).
">In the last test the student must obtain at least 3 points.


">There will be an exam (época de recurso), accessible to any student who has not passed in the regular season and who has not been excluded.

Ratings above 16 will only be awarded after a further test.

Special assessment (TE, DA, ...)

Any examination required under special statutes will consist of a written test which may be preceded by a previous oral or written test.