Mathematics II

Code:

M194

Acronym:

M194

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2015/2016 - 2S

Active?	Yes
Web Page:	http://moodle.up.pt/course/view.php?id=307
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Geology

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	4	Plano de estudos a partir de 2008	3	-	7,5	-
L:G	70	P.E - estudantes com 1ª matricula anterior a 09/10	1	-	7,5	-
		P.E - estudantes com 1ª matricula em 09/10	1	-	7,5	-
L:Q	61	Plano de estudos Oficial	1	-	7,5	-

Teaching language

Portuguese

Objectives

One intends that the students are capable of understanding and using the concepts and the results of Linear Algebra and Vector Calculus covered in the course.

Learning outcomes and competences

Ability to make use of the concepts and results of Linear Algebra and Vector Calculus covered in the course.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

It is assumed in this course that the student is familiar and is capable of using the basic notions of Linear Algebra and Calculus given in Matemática I (M193). Namely, the students must know how to work with matrices, how to solve and how to characterize linear systems of equations, and how to calculate determinants; and they must know how to calculate derivatives and integrals of functions in one variable. 

Program

PART I – LINEAR ALGEBRA

1. Matrices and linear sistems

2. Lines and planes (R^2 and R^3)

3. Real vector spaces (R^n and its subspaces).

4. Linear functions.

PART II – VECTOR CALCULUS

5. Parameterized curves in R^2 and R^3.

6. Real multivariable functions (basic notions, derivatives and maxima and minima of real valued multivariable functions).

7. Real scalar functions (gradient, local maxima and minima, multivariable integrals) .

Mandatory literature

Adams Robert A.; Calculus. ISBN: 0-321-27000-2
Anton Howard; Elementary linear algebra. ISBN: 0-471-66959-8
Marsden Jerrold E.; Vector calculus. ISBN: 7167-4992-0
Stewart James; Cálculo. ISBN: 85-221-0479-4 (Vol. I)

Teaching methods and learning activities

The course material will be presented in the theoretical classes with the help of slides. These slides will be complemented with the resolution of several examples on the blackboard to help to understand the course material and to pinpoint usual mistakes and difficulties.

Sheets with exercises will be available to the students for them to try to solve and to try to identify their own difficulties. A list of exercises to be addressed in the practical sessions will be announced weakly. The students should try to solve these exercises prior to the practical sessions so that they can clarify all their doubts in these sessions.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

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

Calculation formula of final grade

The content of this course will be divided into three parts, each evaluated by a test. The final grade is the everage of the three parts, but it is required to have a test score higher than 4 points in the 3rd part to get approval to this course. The dates for the completion of the three tests are:

• 1st test: March 16th, from 18:30 until 19:30.
• 2nd test: April 27th, from 18:30 until 19:30.
• 3rd test: the examination date scheduled for the 1st examination season

1st evaluation season:

• The final grade of the 1st evaluation season is the average of 3 tests. Note that the students must have score higher that 4 points in the 3rd part to be approved (it is not enough to have the average positive). The students who want to improve their grades in the 1st evaluation season must do the three tests scheduled above.

2nd evaluation season:

• In the 2nd evaluation season exam, the students can repeat again all three tests or only some of them.
• The grade of each part in the 2nd evaluation season is the best among the respective classification in the 1st evaluation season and the grade from the respective test done in the 2nd evaluation season.
• The final grade of the 2nd evaluation season is the average of the grades of the three parts obtained as explained above. Note that the students must have score higher that 4 points in the 3rd part to be approved (it is not enough to have the average positive).

Special assessment (TE, DA, ...)

Students with special status are evaluated in the same way as regular students in the first and second evaluation season.

In any special evaluation season, the written exam might be preceded by an eliminatory oral test to assess whether the student satisfies minimum requirements to tentatively pass the written exam. The tests cannot be used in any special evaluation season.

 

Classification improvement

• Students who have passed this course in the previous year and want to improve their grades in the 1st evaluation season will have to make the three tests scheduled for the 1st evaluation season (2 during the semester and one in the 1st evaluation season).


• Students wishing to undertake a classification improvement exam in the 2nd evaluation season can take advantage of the results obtained in the 1st evaluation season. If they want to take advantage of the classification of a part of the 1st evaluation season, they should not do the respective test in the 2nd evaluation season. However, if a student do a particular test at the 2nd evaluation season, he loses the grade obtained in the 1st evaluation season for that part.

Observations

It may be asked to any student to take an extra oral or written examination if any doubt concerning his/her performance occurs on certain assessment pieces.