Mathematics II

Code:

EM192

Acronym:

EM192

Keywords
Classification	Keyword
OFICIAL	Basic Sciences

Instance: 2014/2015 - 2S

Active?	Yes
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	67	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 IRⁿ
Vectors. Lines, planes, conics and quadrics in IR³ 
Dot product in IRⁿ. Cross product in IR³

Real vector spaces.
Linear maps. Eigenvectors and eigenvalues.

Maps from IRⁿ  to IR^m
Continuity and differentiability.
Parametrized curves in  IRⁿ
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:
Exposure of the material of the program and resolution of exercises.

* Pratical Classes:
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

If the limit of absences is exceeded the student will not be admited access to examination, either in time or normal use (except for students exempted from frequency)

Calculation formula of final grade

There wil be two components of assessment:
• Continuous Evaluation (optional): based on test results and itcan be corrected by the assessment practices in the classroom (including level of participation and performance in class) *.
• final written exam with a total duration not exceeding 3 hours
-.-.-.-.-.-.-.-.-.-.-.-.-.-
The evaluation will be done through two tests required and the final exam.
Admission to the second test will be conditional upon a minimum grade of 8.0 values.

Minimum grade of second test 6 values
The tests may replace the exam.
The notice of exemption will not necessarily be the arithmetic mean of test scores *
The student with a grade exceeding eighteen values in tests or final examination may eventually be subjected to an extra proof.

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.