Differential calculation

Comparative relations


Definition of O,o ~ relations for functions and for sequences,


properties and operations for the o relation, comparative growths,


properties and operations for equivalents (transitivity, product, quotient, right composition and power, absolute value)


Links between equivalents and limits




Differential calculus


Derivability at a point: definitions, link with continuity, operations (+,.x,/) and formulas, derivative of a compound and a reciprocal application,


Derivability on an interval,


Successive derivatives, Leibniz formula, Cn class functions and operations,


Rolle's theorem, Finite Increase Theorem,


Applications : link derivative / direction of variation of a function,


AF inequalities,


Taylor Young formula, Taylor-Lagrange formula




DL


Limited developments in 0, in any real a and in infinity,


Generalized development, (according to the (x^k) scale with k in Z) in 0, in any real a and in infinity,


Forms, Calculation of limits,


Tangents and asymptotic branches, relative positions