Mathematics II

Presentation

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

It is intended to introduce fundamental concepts and practices of mathematical analysis that enable the student to:

- Perform the integration of real functions of a real variable using direct integration and substitution or by parts techniques.

- Calculating a definite integral and geometrically interpret the result.

- Evaluate the convergence of improper integrals.

- Calculate multiple integrals.

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

Programme

IT Engineering

Level of Qualification|Semesters|ECTS

| Semestral | 4

Year | Type of course unit | Language

1 |Mandatory |Português

Code

ULP452-505

Recommended complementary curricular units

Mathematics I

Professional Internship

Não

Syllabus

Part I - Theory of Errors

- Absolute error and relative error. Uncertainty. Error propagation.

Part II - Integral calculus

Indefinite integral:

- Definition and Properties

- Direct Primitives

- Integration methodologies (immediate primitivation, by substitution and by parts) and its application

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

Defined Integral

- Definition and properties. Geometric meaning

- Calculation and applications

Improper integrals

Integration of functions with more than one variable: fundamental concepts, calculation and applications.

Part III - Ordinary Differential Equations (ODE)

- Definitions

- Border conditions

- Integration of the main 1st and 2nd order ODE.

Objectives

At the end of the course the student should be able to:

- 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 face-to-face 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.

Revisions of core subjects will be made to ensure continuous and sustained learning.

MODALITY OF CONTINUOUS EVALUATION WITH FINAL TEST

It is composed of two written tests, carried out in the classroom, with similar weights. The minimum grade is 7.

MODALITY OF FINAL EVALUATION

Follows the general rules of the ULP. 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.

Office Hours