The aim of this course is to provide a practical working tool for students where rigorous Calculus is needed. The main focus is on the study of functions of one real variable (continuity, derivative, maxima/minima, integration) and a brief introduction to multivariable calculus (oriented towards finding maxima/minima). The last part of the course is oriented towards basic ordinary differential equations (for example separation of variables, linear first-order, and constant coefficients ODE).
The aim of this course is to provide a practical working tool for students where rigorous Calculus is needed. The main focus is on the study of functions of one real variable (continuity, derivative, maxima/minima, integration) and a brief introduction to multivariable calculus (oriented towards understanding the objects and finding maxima/minima). The last part of the course is oriented towards basic ordinary differential equations.
During the course theory and example classes will be given. During theory classes, definitions, theorems and main proofs will be given, with lots of examples and exercises. In the example classes, exercises will be discussed and solved with the class, aiming to a ameliorate the calculus skills of the students.
Numbers: natural, integer, rational, real numbers. Definitions and first examples of functions; continuity, derivability and theorems about them, study of maxima/minima, integration. Definitions and examples of functions of two variables: various representations. Continuity and differentiability for multivariable functions. Maxima/minima. Ordinary differential equations: separation of variables, constant and nonconstant linear differential equations
Paolo MARCELLINI, Carlo SBORDONE: Elementi di analisi matematica 1, editore Liguori, Napoli.
Marco BARONTI, Filippo DE MARI, Robertus VAN DER PUTTEN, Irene VENTURI: Calculus problems. editore Springer.
MAURIZIO CHICCO (President)
EDOARDO MAININI
VALENTINA BERTELLA (President Substitute)
https://corsi.unige.it/10948/p/studenti-orario
The exam will consist of a written part and an oral part. The oral part is accessible only if the score in the written test is higher or equal to 14.
During the written test, the student will solve exercises mainly concerning limits, integrals, study of functions (possibly of more than one variable) and ordinary differential equations. During the oral examination student must highlight critical analysis, skills and ability to apply the concepts learnt to solve easy exercises, possibly some (guided) applications to the real world.
