Mathematics II

Code:

M194

Acronym:

M194

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2013/2014 - 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	5	Plano de estudos a partir de 2008	3	-	7,5	-
L:G	84	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	99	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 Vector 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. Lines and planes

2. Real vector spaces.

3. Linear functions.

PART II – VECTOR CALCULUS

4. Parameterized curves in R^n.

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

6. 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 with final exam

Assessment Components

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

Calculation formula of final grade

Students may obtain approval on this discipline either by performing 3 tests or through a mixed score obtained between the tests and the final exam (see details below).

 

Tests: will be held 3 tests lasting 1 hour on the following dates:

• Friday, March 21, from 17:00 to 18:00
• Wednesday, April 30, from 18:30 to 19:30
• Monday, June 9, from 11:00 to 12:00

In each of these tests will be evaluated all topics given until the week prior to the week where the test take place. More precise details will be posted on Moodle course page in the vicinity of the respective test. The tests will all have the same weight in the calculation of the final score.

Exams: Final exams will be divided into three parts, each corresponding to each test (1st part corresponds to the 1st test, and so on). The topics assessed in each part correspond to the topics assessed in the respective test. Therefore, the three parts of the final exams have all the same weight. However, students can only answer to one or two of these three parts of their choice (see below how to determine the final score). The final exam will last for 2 hours.

Calculation of the final score of tests and exams:

Tests: average of three tests (on a scale of 0 to 20)

Exams: In the parts solved in the exam, the student keep the score obtained in the exam. In the parts that have not been solved in the exam, the student keep the score obtained in the respective test. The final grade will be the average of these three parts (on the scale of 0 to 20).

Final classification of the 1st evaluation season:

• It is the final score of the exam if the student takes it and do not withdrawn
• It is the final score of the tests if the student doesn't take the final exam or takes it but withdraw

I draw attention to the fact that if a student has obtained final grade in the tests above 9.5 and has completed an examination of the normal season with final rating lower than 9.5 (and has not withdrawn), then he will reprove the normal season.

Final classificationof the 2nd evaluation season:

• It is the final score of the corresponding exam.

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 final score for the written exam is calculated following the rules described above unless the student proves that he couldn't go to any of the three written tests. In the case where the student proves that he couldn't go to any of the three tests, the student can do all the three parts of the written exam and has three hours to do the written exam.

 

Classification improvement

The final score of an exam taken to improved grades is calculated using the rules described above.

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.