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Università degli Studi di Parma Università degli Studi di Parma
University of Parma
Course catalogue
Università degli Studi di Parma
course catalogue

MATHEMATICAL ANALYSIS 1
cod. 1003712

Academic year 2010/11
1° year of course - Annual
Professor
Academic discipline
Analisi matematica (MAT/05)
Field
"discipline matematiche per l'architettura"
Type of training activity
Basic
100 hours
of face-to-face activities
8 credits
hub: PARMA
course unit
in - - -
lectures timetable unavailable
exam calls

Integrated course unit module: MATHEMATICS LABORATORY

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Learning objectives

The course presents the functional notions of Mathematical Analysis highlighting the typical deductive reasoning techniques and provides basic math instruments for many teachings in the Architecture degree course.

Prerequisites

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Course unit content

Set, subsets, set of parts. Principle of induction and applications. Equivalence and order relations: majorants, minorants, limitation. Functions: Injectivity, surjectivity and Images. Sequences. Monotone functions. Composition of functions and invertibility. Digression on numbers: rational numbers and real numbers and their properties. Ordered fields and absolute value. Powers with real exponent. Graphs of f(x), kf(x), f(x+h), f(x)+h, |f(x)|. Graphs of elementary functions: power, root, exponential, logarithmic function. Revision of trigonometry. Functions of a real variable. Limits, continuity (and related theorems), derivatives, differentials. Theorems of Fermat, Rolle, Cauchy, Lagrange (with demonstrations). De l’Hospital’s rule. Function graphs. Infinitesimals and infinites. Taylor-Maclaurin polynomials with Peano remainder. Definite and indefinite integrals. Integration methods. Fundamental theorem of integral calculus. Integral function. Geometric applications. Improper integrals. Convergence criteria. Definition and solving of first order linear equations.

Full programme

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Bibliography

Acerbi-Buttazzo, "Matematica preuniversitaria di base", Casa Editrice Pitagora, Bologna.
Acerbi-Buttazzo, "Analisi matematica ABC 1. Funzioni di una variabile", Casa Editrice Pitagora, Bologna.
Mucci Domenico, "Analisi matematica: esercizi", Casa Editrice Pitagora, Bologna.

Teaching methods

Oral lesson and laboratory

Assessment methods and criteria

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Other information

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