Mathematical Analysis II

Code:

L.EMAT006

Acronym:

AM II

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2021/2022 - 2S

Active?	Yes
Web Page:	http://consultoriodigitalmatematica.pt/
Responsible unit:	Department of Metallurgical and Materials Engineering
Course/CS Responsible:	Bachelor in Materials Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L.EMAT	54	Syllabus	1	-	6	52	162

Teaching language

Portuguese

Objectives

It aims to act as a continuation of Mathematical Analysis I.

Learning outcomes and competences

It is intended that students acquire the foundations of mathematical analysis necessary for the study of scientific disciplines where necessary as well as for their future needs for professionals.

Acquiring proficiency with knowledge of Mathematical Analysis and be able to apply them in engineering problems;

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Skills Analysis Matewmática I

Program

- Functions of multiple variables. Limits, continuity, partial derivatives. Differential equations: definitions and examples; first order differential equations; solutions; isoclines; separable variables equations; first order linear equations; Bernoulli equations; total differential equations; orthogonal trajectories; first and superior order differential equations; solutions; reducible second order equations; first and superior linear differential equations; general properties; second order homogeneous linear differential equations with constant coefficients; second order nonhomogeneous linear differential equations with constant coefficients; nonhomogeneous linear equations of order n; systems of differential equations; - Double integrals: Definition and properties; calculation of a double integral; calculation of areas and volumes; double integral in polar coordinates; calculation of surface areas; variable density mass; moment of inertia plane figures; centre of gravity of plane figures. - Triple integrals: definition and properties; calculation of a triple integral; volume calculation; variable change; cylindrical and spherical coordinates. - Line integrals: definition and properties; calculation of a line integral.

Mandatory literature

N. Piskuonov; Cálculo Diferencial e Integral, Vol I e II, Lopes da Silva Editora, 2002

Complementary Bibliography

B Demidovitch; Problemas de Análise Matemática, McGraw Hill
Apostol, Tom M.; Calculus. ISBN: 0-471-00005-1(vol.1)

Teaching methods and learning activities

Theoretical-practical classes – presentation of the themes along with exercised solved by the students under professor’s supervision.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	60,00
Teste	40,00
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

The number of faults does not exceed 1/4 of the classes

Calculation formula of final grade

The distributed evaluation consists of 3 evaluation moments:

1) 1st Test;
2) 2nd Test;
3) Exam (Minimum score of 7 points to pass).

The final grade is calculated as follows:

Final grade = 0.2 * Grade 1 Test + 0.2 * Grade 2 Test + 0.6 * Grade of the exam.

It is approved that you obtain a Final Score greater than or equal to 10 points.

Special assessment (TE, DA, ...)

Classification improvement

Students who wish to undertake improvement of classification shall be subject to an exam.

 

Observations

 Calculus, T Apostol