Complements of Mathematics

Code:

EIC0009

Acronym:

CMAT

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2010/2011 - 2S

Active?	Yes
Responsible unit:	Mathematics Section
Course/CS Responsible:	Master in Informatics and Computing Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEIC	278	Syllabus since 2009/2010	1	-	6	56	162

Teaching language

Portuguese

Objectives

This course unit aims to act as a complement to other course units related to mathematics. It aims to train students on the application of mathematical tools and problem solving related to the themes of this Integrated Masters.
At the end of the semester, students should be capable of:
- solving differential equations
- calculating line and surface integrals
- representing Fourier series functions

Program

Scalar field functions. Limits and continuity. Partial derivatives. The chain rule. Gradient and directional derivatives. Level sets and applications to geometry of surfaces, tangent planes.
Vector field functions. Line integrals. Properties. Green's theorem. Surface integrals. Divergence and curl of vector function. Stokes' theorem. Gauss' theorem. Applications.
Differential equations. Study of second order linear equations with constant coefficients. Applications.
Laplace transform. Laplace transform of some important functions. Shift theorems. Laplace transform of Dirac function. Convolution theorem. Applications.
Fourier series. Euler formulas. Applications to the odd and even functions. Expansions. Trigonometric polynomial. Minimum square error. Applications.

Mandatory literature

APONTAMENTOS ELABORADOS PELO Prof. José Armando Rodrigues de Almeida E DISPONIBILIZADOS NO SIFEUP NA PÁGINA DA DISCIPLINA
SALAS-HILLE-ETGEN;CALCULUS-ONE AND SEVERAL VARIABLES-WILEY
TOM M. APOSTOL ;CALCULUS-GINN BLAISDELL
ERWIN KREYSZIG; ADVANCED ENGINEERIG MATHEMATICS-WILEY

Complementary Bibliography

Luisa Madureira; Problemas de equações diferenciais ordinárias e trasformadas de Laplace, FEUP-edições, 2000. ISBN: 972-752-040-5

Teaching methods and learning activities

Theoretical classes will be based on the presentation of the themes of the course unit. These classes are aimed to motivate students, where examples of application will be showed.
Theoretical-practical classes will be based on the analysis and on problem solving by students, where they have to apply tools and mathematical concepts taught in theoretical classes. These classes are aimed to assess students’ understanding and dexterity of the themes of the course unit.

keywords

Physical sciences > Mathematics > Mathematical analysis > Functional analysis

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	56,00
	Exame	5,00
	Total:	-	0,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
	Estudo autónomo	20
	Estudo autónomo	81
	Total:	101,00

Eligibility for exams

Students cannot miss more classes than allowed in the regulation.
Exception for working students.

Calculation formula of final grade

50% first test+ 50% second test. A final exam for those who miss the tests or do not reach 10. In the third evaluation students can do a global exam or improve first test or improve second test. The maximun grade of 20 is only possible with oral proof.

Special assessment (TE, DA, ...)

Final exam

Classification improvement

As FEUP regulation for a period of one year. In the third evaluation, students who already reached grade 10 or more in the 2 tests may improve classification. They can do ONE of the three tests: improve first part, improve second part or a global test.