Mathematics II

Code:

EM192

Acronym:

EM192

Keywords
Classification	Keyword
OFICIAL	Basic Sciences

Instance: 2015/2016 - 2S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=832
Responsible unit:	Department of Mathematics
Course/CS Responsible:	First Degree in Engineering Sciences

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:CE	66	PE2007- Perfil Engenharia Geográfica	1	-	7,5	-
		PE2007- Perfil Engenharia Electrotécnica	1	-	7,5	-
		PE2007- Perfil Engenharia Alimentar	1	-	7,5	-
		PE2007- Perfil Engenharia Agronómica	1	-	7,5	-

Teaching language

Portuguese

Objectives

To undestand the Euclidean space, its geometry , continuity and differentiability.

Learning outcomes and competences

Problem-solving skills. Theoretical understanding.

Working method

Presencial

Program

The euclidean space Rⁿ
Vectors. Lines, planes, conics and quadrics in R³. Dot product in Rⁿ. Cross product in R^3.

Real vector spaces. Linear maps. Eigenvectors and eigenvalues.

Maps from Rⁿ  to R^m
Continuity and differentiability. Parametrized curves in  Rⁿ. Real multivariable functions. Derivatives of multivariable functions. Maxima and minima of real valued multivariable functions.

Multivariable integrals.
Polar, cylindrical and spherical coordinates

Mandatory literature

Marsden Jerrold E.; Vector calculus. ISBN: 7167-4992-0
Adams Robert A.; Calculus. ISBN: 0-201-82823-5

Complementary Bibliography

Marsden Jerrold; Calculus iii. 2nd ed. ISBN: 0-387-90985-0
Lipschutz S.; Algebra Linear
Anton Howard; Elementary linear algebra. ISBN: 0-471-66959-8

Comments from the literature

The most important "bibliography" is what is given in the lectures.

Teaching methods and learning activities

* Lectures:
Presentation of the content of the program and resolution of exercises.

* Tutorials:
Resolution, by the students, of the proposed exercises and answering questions about the resolution of problems and proposed work.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

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

Eligibility for exams

All registered students are considered to have attended the course.

Calculation formula of final grade

The assessment will be done through two non-compulsory tests and a final exam. There are no requirements for admission to the tests or to the exam.

The grade resulting from the tests is the average of the test grades.
Students approved through the tests are exempt from the final exam. They may, nevertheless, participate in the final exam, in which case their final grade will be the best between the grades resulting from the tests and from the exam.

The student with a grade exceeding eighteen values in tests or final examination may eventually be subjected to an extra evaluation.

Special assessment (TE, DA, ...)

 According to the General Evaluation Rules.

 

Classification improvement

For students under normal conditions with access to examination and which have succeeded the distributed evaluation (score above or equal to 10/20), the final classification is obtained by the highest ranking achieved in the distributed evaluation and / or examination.