To complete the basic preparation of Mathematical Analysis with particular regard to derivation and integration theory, and to series expansions.
teacher profile teaching materials
Differentiability of functions. Rules for computing derivatives. Derivatives and monotonicity. Fundamental theorems on derivatives (Fermat, Rolle, Cauchy, Lagrange). Theorem of Bernoulli-Hopital. Critical points. Second derivative. Convex functions. Qualitative study of functions. Successive derivatives and Taylor's formula. Use of Taylor's formula in computing limits.
Riemann's integral: partial sums, integrability. Integrability of monotone and piecewise continuous functions. Computation of primitives. Fundamental theorem of calculus. Integral remainder in Taylor's formula. Improper integrals; comparison with series.
Complex numbers, exponential series in the complex plane and fundamental theorem of algebra.
Fruizione: 20410388 AM120-ANALISI MATEMATICA 2 in Matematica L-35 HAUS EMANUELE, MATALONI SILVIA
Programme
Open, closed and compact sets. Weierstrass Theorem. Uniformly continuous functions.Differentiability of functions. Rules for computing derivatives. Derivatives and monotonicity. Fundamental theorems on derivatives (Fermat, Rolle, Cauchy, Lagrange). Theorem of Bernoulli-Hopital. Critical points. Second derivative. Convex functions. Qualitative study of functions. Successive derivatives and Taylor's formula. Use of Taylor's formula in computing limits.
Riemann's integral: partial sums, integrability. Integrability of monotone and piecewise continuous functions. Computation of primitives. Fundamental theorem of calculus. Integral remainder in Taylor's formula. Improper integrals; comparison with series.
Complex numbers, exponential series in the complex plane and fundamental theorem of algebra.
Core Documentation
Luigi Chierchia, Corso di Analisi, prima parte, Una introduzione rigorosa all'analisi matematica su R.Type of evaluation
The written exam may be replaced by the two intermediate tests. teacher profile teaching materials
Differentiability of functions. Rules for computing derivatives. Derivatives and monotonicity. Fundamental theorems on derivatives (Fermat, Rolle, Cauchy, Lagrange). Theorem of Bernoulli-Hopital. Critical points. Second derivative. Convex functions. Qualitative study of functions. Successive derivatives and Taylor's formula. Use of Taylor's formula in computing limits.
Riemann's integral: partial sums, integrability. Integrability of monotone and piecewise continuous functions. Computation of primitives. Fundamental theorem of calculus. Integral remainder in Taylor's formula. Improper integrals; comparison with series. Taylor series.
Complex numbers, exponential series in the complex plane and fundamental theorem of algebra.
Fruizione: 20410388 AM120-ANALISI MATEMATICA 2 in Matematica L-35 HAUS EMANUELE, MATALONI SILVIA
Programme
Standard topology of R, subsequences, limit inferior and limit superior, Theorems of Bolzano-Weierstrass and Weierstrass. Open, closed and compact sets. Uniformly continuous functions.Differentiability of functions. Rules for computing derivatives. Derivatives and monotonicity. Fundamental theorems on derivatives (Fermat, Rolle, Cauchy, Lagrange). Theorem of Bernoulli-Hopital. Critical points. Second derivative. Convex functions. Qualitative study of functions. Successive derivatives and Taylor's formula. Use of Taylor's formula in computing limits.
Riemann's integral: partial sums, integrability. Integrability of monotone and piecewise continuous functions. Computation of primitives. Fundamental theorem of calculus. Integral remainder in Taylor's formula. Improper integrals; comparison with series. Taylor series.
Complex numbers, exponential series in the complex plane and fundamental theorem of algebra.
Core Documentation
Luigi Chierchia, Corso di Analisi, prima parte, Una introduzione rigorosa all'analisi matematica su R.Type of evaluation
The written exam may be replaced by the two intermediate tests.