Mathematics II

Code:

EBE0007

Acronym:

MAT2

Keywords
Classification	Keyword
OFICIAL	Basic Sciences

Instance: 2009/2010 - 2S

Active?	Yes
Course/CS Responsible:	Master in Bioengineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIB	72	Syllabus	1	-	6	80	162

Teaching language

Portuguese

Objectives

This course unit aims to familiarise students with mathematical concepts and tools to study functions of various variables, as well as to develop their analytical reasoning, critical spirit and interest in mathematics.

Program

Curves in a plane and space and their parametric representation
Vector functions; Surfaces in three dimensional space
Real functions and vector functions of various variables
Partial derivatives; Directional derivatives and gradient
Derivation of compound functions; Implicit functions and their derivatives
Free maximum and minimum with restrictions: Lagrange multiplier method
Double integrals in R rectangular domains
Double integrals in arbitrary limited domains in R
Applications of double integrals
Double integrals in polar coordinates
Triple integrals; Applications of triple integrals
Triple integrals in cylindrical and spherical coordinates
Line integrals; Green’s theorem
Divergence and rotation of a vector field
Surface integrals; Stokes’ and divergence theorems

Mandatory literature

Serge Lang; Calculus of Several Variables, 3rd edition, Springer, 1987. ISBN: 0-387-96405-3
Serge Lang; Calculus of Several Variables, 3rd edition, Springer, 1987. ISBN: 0-387-96405-3

Teaching methods and learning activities

Classes are theoretical and practical; therefore classes will be based on the presentation of the program and examples, along with problem solving by the students under professor supervision. It will be used the board, and occasionally the overhead projector, to give classes.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	56,00
	Total:	-	0,00

Eligibility for exams

To be admitted to exams, students have to attend the tests.

Calculation formula of final grade

Final Grade will be based on the following components:

- 1st test (T1) – a mandatory test (date will be later announced)
- 2nd test (T2) - only for students who reached a minimum grade of 10 (out 20) in T1. It will not cover the themes of T1.

- Final Exam (FE) – it will take place at the same time as T2 and it is a mandatory exam to students who did not reach a minimum grade of 10 (out of 20) in T1. However, any student can attend this exam, which will cover the entire program.
- Recurso (resit) Exam- RE- Only for students who did not complete the course or want to improve their grades.

Final Grade will be based on the following formula:
FG= (T1+T2)/2 or FG= FE or FG= RE

Special assessment (TE, DA, ...)

Normal season of exams

Classification improvement

Recurso (resit) exam