PRINCIPLES OF MATHEMATICS
Learning outcomes of the course unit
The goal of this course is to providestudents with a solid background in the basic tools of differential and integral calculus and to illustrate some application in the pharmaceutical field
Representation of data in a reference system,scales and units of measure, conversion factors.
Orthogonal cartesian system and its rules.
Powers and scientific notations, order of magnitude.
Logarithms and their rules.
Equations and inequalities with oe variable and how to graph them
Course contents summary
Real function with one real variable: concept of function, basic function and how to graph them
Rules of composition. composed and inverse functions.
Function limits: definition, theorems and properties. Notable limits.
Continuity: theorems and properties of continuous functions.
Differential calculus: definition of derivativeand its geometrical interpretation. Derivability of a function. Rules of derivation and calculus. n-th order derivatives.
Basic theorems:Rolle, Lagrange, Cauchy and their consequences. De L'Hospital rules and Taylor's approximation.
Graphing a function: existence field,asymptotes, increase and decrease, absolute and relative maximums and minimums, singular points,concavity and inflexion points.
Integral calculus: integrability of a function. Definite and indefinite integral. Torricelli-Barrow theorem
Properties of integrales and rules of integration. Generalized integrals.
Calculating the meam value of a function.
Differential equations and the Cauchy conditions. First order equations: parting variables or linear.
Information regarding texts will be provided at the beginning of the course
Lectures with exercises.
Written exam followed by an oral exam.