MATHEMATICAL ANALYSIS I - canale 4

Main objective: providing basic knowledge and tools regarding differential and integral calculus and number series.

1. Real numbers: Definition, algebraic and topological properties.

2. Sequences: Limits and relative algebra, comparison criteria and monotone sequences

3. Functions: Limits, relationship with sequences, continuity, uniform continuity and Weierstrass Theorem

4. Functions: Derivatives, tangent lines, Lagrange Theorem and its consequences

5. Functions: Higer derivatives, convexity, Taylor's formula and drawing a graph

6. Series: Basic properties and criteria for convergence of series with non-negative terms

7. Series: Oscillating series and Liebnitz criterion, power series

8. Integrals: Riemann integrability, Riemann criterion and classes of integrable functions

9. Integrals: Antiderivatives, Fundamental theorem of Calculus and Calculus rules

10. Integral: Generalized and improper integrals and criterions for convergence

1. Di Fazio G., Zamboni P., Analisi Matematica 1, Monduzzi Editoriale.

2. Di Fazio G., Zamboni P., Eserciziari per l'Ingegneria, Analisi Matematica 1, EdiSES.

3. D'Apice C., Manzo R. Verso l'esame di Matematica, vol. 1 e 2, Maggioli editore