Academic Year 2019/2020 - 1° Year

MAT/05 - 9 CFU - Annual Tuition

__Main objective__: providing basic knowledge and tools regarding differential and integral calculus and number series.

The course will be divide into two parts. The first one involves the construction and properties of the field of real numbers, basic topology notions, sequences and functions, ending with derivatives and applications. The second involves series and integrals. Both parts will be followed by a written partial exam.

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.