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Analisi Matematica I: Teoria, Fondamenti e Strumenti di Calcolo by Abate Vincenzo

Analisi Matematica I: Teoria, Fondamenti e Strumenti di Calcolo

by Abate Vincenzo
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Book cover type: Paperback
  • ISBN13: 9798277699416
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Independently Published
  • Publisher Imprint: Independently Published
  • Publication Date:
  • Pages: 180
  • Original Price: GBP 13.07
  • Language: Italian
  • Edition: N/A
  • Item Weight: 250 grams
  • BISAC Subject(s): Calculus

Questo manuale nasce dall'esigenza di offrire agli studenti dei corsi scientifici (Ingegneria, Matematica, Fisica e Informatica) una guida rigorosa e completa ai fondamenti dell'Analisi Matematica I. La trattazione mira a equilibrare la chiarezza concettuale con la praticit� del calcolo, fornendo la solida base teorica indispensabile per padroneggiare i concetti chiave della materia.

Il volume � strutturato per costruire una base logica e rigorosa, coprendo:

  • Fondamenti Numerici e Topologia: Dalla Logica e Insiemi, agli Insiemi Numerici, alla Topologia della Retta Reale e all'analisi del Valore Assoluto e degli Estremi di un Insieme.

  • Limiti e Continuit� Studio della Nozione di Funzione, Funzioni Elementari e Propriet�. La Definizione Rigorosa di Limite, Teoremi Fondamentali, Limiti Notevoli e analisi delle Forme Indeterminate. Trattazione degli Asintoti e della Continuit�.

IL CALCOLO: Approfondimento del Metodo

Il cuore del testo si concentra sullo sviluppo teorico delle tecniche di calcolo:

  • Calcolo Differenziale: Dalla Definizione di Derivata (Destra e Sinistra) alle Regole e Teoremi Fondamentali della Derivabilit�. Trattazione approfondita del Teorema di De L'H�pital, Formula di Taylor e Resto, e Derivate di Ordine Superiore. Ampia sezione dedicata allo Studio di Funzione (Monotonia, Convessit� e Flessi) e al Differenziale.

  • Calcolo Integrale: Teoria dell'Integrale Indefinito e Primitive, Calcolo degli Integrali Immediati e Tecniche di Integrazione Avanzate. Approfondimento della Teoria dell'Integrale Definito, Teorema Fondamentale del Calcolo e Applicazioni Geometriche.

LE STRUTTURE AVANZATE: Numeri Complessi e Serie

Il volume include sezioni dedicate a concetti che fanno da ponte con corsi successivi:

  • Numeri Complessi: Studio completo delle Forme Algebrica, Trigonometrica ed Esponenziale. Operazioni Fondamentali, Formula di De Moivre per Potenze e Radici, ed Equazioni Algebriche (Teorema Fondamentale dell'Algebra).

  • Serie Numeriche e di Funzioni: Definizione e Nozioni Fondamentali (Convergenza, Divergenza, Irregolarit�). Condizione Necessaria di Convergenza, Tipi di Serie Notevoli e Criteri di Convergenza per Serie a Termini Positivi e a Segno Variabile (Leibniz). Basi per le Serie di Funzioni, Serie di Potenze e Sviluppi in Serie (Maclaurin).

Per una preparazione ottimale: Il volume � progettato per essere utilizzato in abbinamento all'eserciziario complementare, garantendo una preparazione completa: dalla teoria rigorosa allo sviluppo pratico dei metodi risolutivi.

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