Mathematical analysis 1 - mod.2 (2008/2009)

Learning outcomes

In the second unit of the course, we present the basic results of differential
and integral calculus in one variable. We conclude with the theory of series of real numbers.

Mean value theorem. Sign of the first derivative and monotonicity. De L'Hopital Theorem. Taylor's theorem (with error term in Peano and Lagrange form). Taylor
polynomials of some elementary functions, Taylor series.

The problem of computing areas: integration in the sense of Riemann. Integrability of monotonic and continuous functions. The fundamental theorem of calculus.
Integration rules. Generalized integrals.

Solution of some first order O.D.E.: linear equations, separation of variables.

Infinite series of real numbers: some convergence criteria. Basic properties
of power series.

Written test and oral exam.