Mathematical Analysis I

Code:

EC0001

Acronym:

AMAT1

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2007/2008 - 1S

Active?	Yes
Responsible unit:	Mathematics Division
Course/CS Responsible:	Master in Civil Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
LEC	0	Plano de estudos de transição para 2006/07	1	7	7	75	187
MIEC	334	Syllabus since 2006/2007	1	-	7	75	187
		Plano de estudos de transição para 2006/07	1	-	7	75	187

Teaching language

Portuguese

Objectives

Consolidation and spread, in some extent, the knowledge in Mathematics the students have gathered in secondary school. Development of scientific and mathematical way of thinking. Understanding, manipulation and application of the concepts of one variable integration and series. Indication of a basic set of mathematical knowledge required by other subjects for civil engineering. Development of the ability to apply new mathematical concepts.

Program

Mathematical methodology, foundations of logic, real numbers axiomatic, some topologic concepts. Bolzano-Weierstrass theorem. Real functions of real variables: continuity and limit. Intermediate values and Weierstrass theorems. Differential calculus for one variable functions: definitions and geometric interpretation. Rolle, Lagrange and Cauchy theorems. Derivatives of inverse and composed functions. Practical rules and applications of derivation. Integral calculus of real functions of real variables: Riemann integral, integral operations, undefined integrals. Fundamental theorem of calculus, Barrow´s formula and mean-value theorem. Integration of rational functions. Integration by parts and integration by substitution. Improper integrals. Calculation of areas in the plan. Numerical sequences and series: Cauchy sequence, convergence and sum of a serie, absolute and conditional convergence. Series of nonnegative terms: comparison, d'Alembert, Cauchy, integral criteria. Alternating series: Leibniz test. Sequences and series of functions: pointwise and uniform convergences. Power series. Polynomial approximation, Taylor polynomials and formula.

Mandatory literature

Stewart, James; Cálculo. ISBN: 85-221-0235-X (vol. 1)
Stewart, James; Cálculo. ISBN: 85-221-0236-8 (vol. 2)

Complementary Bibliography

M. Spivac; Calculus, Volumes 1 e 2, Addison Wesley
Apostol, Tom M.; Calculus. ISBN: 84-291-5001-3
Apontamentos e colectânea de exercícios de apoio às aulas, disponível na opção Conteúdos da página SIFEUP da disciplina
Larson, Hostetler & Edwards; Cálculo, Volumes 1 e 2 (Oitava Edição), McGraw-Hill, 2006. ISBN: 85-86804-56-8
Wrede, Robert; Schaum.s outline of theory and problems of advanced calculus. ISBN: 0-07-137567-8

Teaching methods and learning activities

Concepts and important results are presented in theoretical classes, with geometric interpretation, when possible, and enlightening examples. Some constructive demonstrations are presented. There will be a strong call for concepts understanding and calculation ability. The students will be alerted to the available computational tools, their performance and limitations. In practical classes, the students are guided to the resolution of selected problems.

Software

Maxima

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Subject Classes	Participação presencial	75,00
	Exame	2,50		2007-12-05
	Exame	2,50		2008-01-28
	Total:	-	0,00

Eligibility for exams

Limits for absences to classes are determined by Art. 4.1 ( 25 % of the expected practical classes).

Calculation formula of final grade

Two write tests, M1 and M2.
The Final Classification (CF) is
CF=0.4M1+0.6M2.
(M1 and M2 -20 values)

Examinations or Special Assignments

"Mini-test", only for the students with a final mark of 9. This test will be an additional chance for the students that are close to reach the minimum needed on this subject.

Special assessment (TE, DA, ...)

Final exam.

Classification improvement

According art. 10.2. from General Rules for Evaluation, improvement of classification will be submitted to the previous formula

Observations

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Working time estimated out of classes: 4 hours