Mathematical Analysis II

Presentation

The present curricular unit (CU) belongs to the curricular plan of this 1st cycle degree.

In this CU it is intended to introduce the fundamental concepts about the theory of errors, the methodologies and applications of integral calculus and the techniques for solving differential equations of 1st and 2nd orders.

Programme

IT Engineering

Level of Qualification|Semesters|ECTS

| Semestral | 6

Year | Type of course unit | Language

1 |Mandatory |Português

Code

ULP452-551

Recommended complementary curricular units

Mathematical Analysis I

Professional Internship

Não

Syllabus

PART I - Theory of Errors

1 - Absolute error, relative error and uncertainty

2 - Rounding

3 - Propagation of errors

PART II - Integral calculation

1 - Undefined Integral

1.1 - Definition and Properties

1.2 - Immediate primitives

1.3 - Integration methodologies (immediate primitiveness, by substitution and by parts)

1.4 - Integration of certain classes of functions: polynomial, rational, irrational and transcendent

2 - Defined integral

2.1 - Definition, properties and geometric meaning

2.2 - Calculation and applications

3 - Improper integrals

4 - Integration of functions with more than one variable

4.1 - Fundamental concepts, calculation and applications

Part III - Ordinary differential equations (EDO)

1 - Definitions

2 - Initial and boundary conditions

3 - Integration of the main 1st and 2nd order EDO

Objectives

At the end of this course, students should have acquired knowledge about:

- Learn to integrate real functions of a real variable using direct integration and substitution or by parts techniques.

- Learn to calculate a definite integral and geometrically interpret the result, as well as to know how to realize typical applications of the same.

- Learn to evaluate the convergence of improper integrals.

- Know to calculate multiple integrals.

- Learn to solve differential equations of 1st and 2nd order, including the determination of particular solutions.

Teaching methodologies and assessment

The teaching will be supported by sessions of theoretical nature, dedicated to the presentation of subjects and their illustration through application examples, and in theoretical-practical sessions dedicated to solving exercises for students' training. Complementarily, will be distributed several statements of problems for non-presential work and will be accompanied the study of the students. Where the lack of basic knowledge of the students so warrants, revisions of core subjects will be made to ensure continuous and sustained learning.

MODALITY OF CONTINUOUS EVALUATION

It is composed of two written tests, carried out in the classroom, with similar weights.

MODALITY OF FINAL EVALUATION

It follows the general ULP rules. It consists of a written test, weighting 100%

References

- Azenha, A., Jerónimo, M. E. (1995), Elementos de Cálculo Diferencial e Integral em IR e IRn, Editora MacGraw Hill.

- E.W. Swokowski (1995), Cálculo com Geometria Analítica (Vol.1 e II), Makron Books.

- B. Demidovitch, Problemas e Exercícios de Análise Matemática, McGraw-Hill.

- Textos de apoio e coleções de exercícios fornecidos ao longo das aulas pelos docentes

Office Hours