Infinitesimal Calculus I

Code:

M111

Acronym:

M111

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2014/2015 - 1S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=2384
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Physics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:AST	5	Plano de Estudos a partir de 2008	1	-	7,5	-
L:F	62	Plano de estudos a partir de 2008	1	-	7,5	-
L:M	110	Plano de estudos a partir de 2009	1	-	7,5	-
MI:EF	56	Plano de Estudos a partir de 2007	1	-	7,5	-

Teaching language

Portuguese

Objectives

To learn the basic concepts of the Differential and Integral Calculus about functions of one real variable.

Learning outcomes and competences

The student should master the basic concepts of analysis of real functions in one real variable, namely: sequence, series, derivative, primitive, integral, and Taylor series. It is also intended that this unit allows students to work rigorously with concepts that, thus far, have been introduced only in an intuitive way.

Working method

Presencial

Program

Sequences. Continuity of real functions of a real variable. Bolzano and Weierstrass theorems. Inverse trigonometrical functions. Derivatives. Local extrema. The Taylor polynomial. Anti-derivatives. The Riemann integral and its basics properties. The fundamental theorem of Calculus. Improper integrals (possibily only the case that is necessary for integral criterion for the convergence of series). Numerical series and power series: convergence criteria. Sequences and series of real functions of a real variable: pointwise and uniform convergence; convergence criteria; series of continuous functions.

Mandatory literature

Adams Robert A.; Calculus. ISBN: 0-321-27000-2
Stewart James; Calculus. ISBN: 978-0-495-38273-7

Complementary Bibliography

Lima Elon Lages; Curso de análise
Spivak Michael; Calculus. ISBN: 0-914098-89-6

Teaching methods and learning activities

The contents of the syllabus are presented in the lectures, where examples are given to illustrate the concepts. There are also practical lessons, where exercises and related problems are solved. All resources are available for students at the unit’s web page.

Software

sage (software matemático gratuito) - http://www.sagemath.org/pt/

keywords

Physical sciences > Mathematics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Exame	50,00
Teste	50,00
Total:	100,00

Eligibility for exams

No conditions, that is, all registered students are admitted to exam.

Calculation formula of final grade

The regular evaluation will be based on two tests (24/10 and 28/11) and a final examination, the classification distributed over five points ​​in each test 10 and in the final exam. The final grade is the sum of the grades of the tests and exam, with successive roudning to centesimals, decimals, and units.

All registered students are admitted to the tests and exam.

There will be an extra exam available to any student who does not obtain approval according to the above scheme.

Classification improvement

The general evaluation rules apply.