Linear Algebra and Analytic Geometry

Code:

M1004

Acronym:

M1004

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2018/2019 - 1S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=501
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Physics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:F	62	Official Study Plan	1	-	6	56	162
			3
L:G	0	study plan from 2017/18	3	-	6	56	162
MI:EF	93	study plan from 2017/18	1	-	6	56	162

Teaching language

Suitable for English-speaking students

Objectives

Upon completing this course, the student should master the main concepts of Linear Algebra and Analytic Geometry. Namely, he must understand, be able to work with and use the main properties of the concepts of matrix, determinant, vector space and linear function.

Learning outcomes and competences

Upon completing this course, the student should be able to: make the main matrix operations; solve systems of linear equations using matrices; using matrices to discuss systems of linear equations; calculate determinants; apply the properties of determinants; recognize real vector subspaces; determine bases for real vector spaces; calculate the dimension of vector spaces; recognize linear functions, and their main properties; determine or justify why there are no linear functions satisfying certain conditions; work with matrices associated with linear functions; determine eigenvectors and eigenvalues ​​of matrices; diagonalize a matrix (if possible); using some properties of matrix diagonalization.

Working method

Presencial

Program

1. Linear systems and matrices


2. Matrices


3. Determinants of square matrices


4. Vector spaces


5. Linear functions


6. Eigenvectors and eigenvalues and diagonalization of matrices


7. Conic sections

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

Teaching methods and learning activities

Contact hours are divided into theoretical and practical classes. In the first, the contents of the course are presented using examples to illustrate them and to guide the students. In the practical classes, previously announced exercises and problems are solved. Support materials are available on the Moodle course webpage. In addition to the classes, there are periods of attendance per week where students have the opportunity to ask questions.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Exame	50,00
Teste	50,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

N/A

Calculation formula of final grade

The content of this course will be divided into two parts: P1 and P2.

Regular season final grade: average(N1,N2) where Ni is the grade of part Pi in the regular season.

• P1: assessed by test on October 31st, from 11:30 until 13:00.
• P2: assessed on the date set for the examination of this UC during the regular season (duration: 1h30m). 
• P1 will not be assessed in the regular season exam.

Second examination season exam: divided into two optional parts, of 1h30m each, assessing respectively P1 and P2.

• Ei: grade obtained in part Pi if the student has done it in the second examination season exam.

Second examination season final grade: average(R1,R2) where Ri is the grade of part Pi in the second examination season.

• Grade improvement exam: Ri=Ei.

Other students:

• Ri=Ni if the student has not done part Pi in the second examination season exam.
• Ri=maximum{Ni,Ei} if Ei≥0,75×Ni.
• Ri=average{Ni,Ei} if Ei<0,75×Ni.

Special assessment (TE, DA, ...)

Any examination required under special statutes consist of a written exam that can be preceded by an oral or written evaluation.

Classification improvement

• Students wishing to take a grade improvement examination in the regular season will have to follow the rules indicated above for the evaluation of the remaining students during the regular season.


• Students who want to improve their grades at the second examination season will have to do both parts on the day scheduled for the second season exam and the final grade will be the average of those two parts. 

Observations

Any student can be asked to do an oral examination in case there are some dougts about the written examination.