Complements of Mathematics

Code:

EIC0009

Acronym:

CMAT

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2014/2015 - 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	233	Syllabus since 2009/2010	1	-	6	56	162

Teaching language

Suitable for English-speaking students

Objectives

1- BACKGROUND The main aim is to introduce fundamental mathematical concepts by developing the ability to analyze problems and results and also to acquire mathematical precision. These aspects form an educational background for other subjects in the curricula.

2- SPECIFIC AIMS Enhance the students reasoning capacity and knowledge of essential mathematical concepts. The students should acquire solid theoretical and practical training on the main concepts and results of differential and integral calculus of several variables, including the basic theorems of calculus.

 3- PREVIOUS KNOWLEDGE Functions and graphs. Differential and integral calculus in R1, R2 and R3. Matrix Algebra.

4- PERCENTAGE DISTRIBUTION Scientific component:75% Technological component:25%

5- LEARNING OUTCOMES Knowledge and understanding: Partial and directional derivatives for real-valued and vector-valued functions; gradient vector. The chain rule for real-valued and vector-valued functions including implicit functions. Apply parametric curves and surfaces in R3 to calculate line and surface integrals. Establishment of the relationship between the line integral and the surface integral based on the Green’s, Stokes and Gauss Theorems.

 

Learning outcomes and competences

Students should deepen their knowledge on the concepts of line, surface, double and triple, integrals and their applications and improve the knowledge of vector and scalar fields.  Students should be able to apply these concepts in engineering problems

Working method

Presencial

Program

1- VECTOR FUNCTIONS. Properties. Curves. Arc length. Curvature. 2- FUNCTIONS OF SEVERAL VARIABLES. Quadric surfaces. Level curves and level surfaces. Partial derivatives. Limits and continuity. 3-GRADIENTS. Differentiability and gradient. Gradients and directional derivatives. The mean-value theorem. Chain rules. Maximum and minimum values. Differentials. 4- DOUBLE AND TRIPLE INTEGRALS. The double integral over a region. Evaluating double integrals using polar coordinates. Triple integrals. Cylindrical coordinates. Spherical coordinates.  Jacobians; changing variables in multiple integration. 5- LINE INTEGRALS AND SURFACE INTEGRALS. Line integrals. Properties. Line integrals respect to arc length. Green’s theorem. Parametrized surfaces. Surface área. Surface integrals. Divergence and curl. The divergence theorem. Stokes’s theorem

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

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

Designation	Weight (%)
Participação presencial	0,00
Teste	100,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

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.