Mathematical analysis 1 - Modulo I (2007/2008)

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Course code
4S00030
Name of lecturer
Marco Squassina
Number of ECTS credits allocated
3
Academic sector
MAT/05 - MATHEMATICAL ANALYSIS
Language of instruction
Italian
Location
VERONA
Period
1° Q - solo 1° anno dal Oct 15, 2007 al Nov 30, 2007.
Course news Seminars related to the course

To show the organization of the course that includes this module, follow this link * Course organization

Lesson timetable

Learning outcomes

The aim of this course is that of understanding the basic notions of mathematical analysis for real functions of one real variable. The topics can be roughly divided into two main parts: the system of real numbers and the notion of limit and its consequences.

Syllabus

The system of real numbers. Main algebraic and ordering properties. Set and functions. Injective, surjective and bijective functions. Extensions of real numbers and related algebraic and ordering properties. Real numbers and cartesian coordinates. Maximum and minimum of a set. Infimum and supremum of a set. Natural, integer and
rational numbers. Archimede's property and density of the rational numbers into real numbers. Some basic notions on complex numbers.
Limit and continuity for real functions of one real variable.
Topology of the real line. Limits on restrictions. Classification of the points of discontinuity. Sequences and subsequences. Bolzano Weierstrass Theorem. Cauchy criterion for sequences. Some elementary functions: exponential and circular functions. Main theorems for continuous functions: existence of zeros, inverse function and Weierstrass theorems. Some extra elementary functions. Uniformly continuous functions, main properties. Series of real numbers. Series with positive terms. Main criteria: comparison, root and quotient. Absolutely convergent series. Variable sign terms series. Leibniz criterion.

Reference books
Author Title Publisher Year ISBN Note
M. Conti, D. L. Ferrario, S. Terracini, G. Verzini Analisi matematica. Dal calcolo all'analisi, Vol. 1 (Edizione 1) Apogeo 2006 88-503-221 testo adottato

Assessment methods and criteria

Final written and oral exams.

Teaching aids

Documents

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