Learning outcome addressed: be aware of need of real numbers

Learning outcome addressed: learning best lower/upper bound of a set (Infimum and Supremum)

Learning outcome addressed: fine properties of Real Numbers, determining inf and sup of a set

Learning outcome addressed: properties of roots, exp and log, solving equations and inequalities.

Learning outcome addressed: properties of the modulus of a number, solving equations and inequalities with moduluses

Learning outcome addressed: writing a simple mathematical model involving sequences of numbers

Learning outcome addressed: definition of limit of a sequence and how to check existence of finite and infinite limits or non existence of a limit

Learning outcome addressed: basic level skills for computing limits

Learning outcome addressed: comparison techniques to discuss non trivial limits

Learning outcome addressed: exponential limit (one of the most important limits at all)

Learning outcome addressed: definition and calculation of an infinite sum

Learning outcome addressed: checking convergence/divergence of constant sign series by comparison

Learning outcome addressed: checking convergence/divergence of constant sign series by asymptotic tests

Learning outcome addressed: checking convergence for alternating sign sums

Learning outcome addressed: proving convergence/non convergence for general variable sign series

Learning outcome addressed: definition of limit of a function and how to check its existence and value

Learning outcome addressed: what is a continuous function and how to check it

Learning outcome addressed: basic level skills for computing limits of functions

Learning outcome addressed: intermediate level skills for computing limits of functions

Learning outcome addressed: intermediate level skills for computing limits of functions

Learning outcome addressed: continuity of the elementary functions

Learning outcome addressed: discussing continuity for functions built on elementary functions through algebraic or composition operations

Learning outcome addressed: discussing existence and search of solutions of equations

Learning outcome addressed: existence and continuity of inverse functions and inverses of elementary functions

Learning outcome addressed: discussing existence of min/max points for continuous functions on intervals

Learning outcome addressed: what is a differentiable function, how do we compute derivative and tangent line, comparison with continuous functions

Learning outcome addressed: computing derivatives

Learning outcome addressed: calculus of the derivative of an inverse function, derivatives of inverses of elementary function

Learning outcome addressed: knowing the Fermat, Rolle and Lagrange theorems

Learning outcome addressed: applying Lagrange's test to check differentiability

Learning outcome addressed: how to determine if a function is increasing/decreasing

Learning outcome addressed: setting up, solving and interpreting solutions for opmitization problems

Learning outcome addressed: concave and convex functions, how to check convexity, basic properties

Learning outcome addressed: how to plot a qualitative graph of a function

Learning outcome addressed: using study of functions techniques to solve for equations and inequalities.

Learning outcome addressed: applying Hopital's rule to compute limits

Learning outcome addressed: computing Taylor polynomial approximation of a regular function

Learning outcome addressed: computing Maclaurin’s asymptotic expansions for elementary functions

Learning outcome addressed: applying asymptotic expansions to the calculus of limits

Learning outcome addressed: applying asymptotic expansions to convergence of numerical series