This course aims to provide students with the basic knowledge and tools in preparation for the other courses, which require mathematical notions and methods.
By the end of this course, students will be able to study the graph of the functions of one variable, as well as know the properties of the integrals of the functions of one variable.
52 hours of distance lectures until the end of sanitary emergency
1) Real numbers and the real line. Cartesian coordinates in the plane. Functions and their graphs. Limits and continuity. Theorems about continuous functions. The
derivative. Differentiation rules: product, reciprocal, quotient and chain rule. Monotone functions: the inverse function theorem. Derivatives of some elementary functions. Theorems about differentiable functions: Rolle, Lagrange, Cauchy. L’Hopital’s rule. Higher order derivatives. Extreme values, convexity and inflection. Sketching the graph of a function.
2) Integration. Sums and sigma notation. Areas as limits of sums. The definite integral. Properties of the definite integral. The fundamental Theorem of Calculus. Changes of variable: the method of substitution. Areas of plane regions. Integration by parts. Integrals of rational functions.
R.A. Adams, Calcolo Differenziale 1 Casa
Editrice Ambrosiana.
Ricevimento: Until the end of the health emergency, a special Teams channel will be set up and students can post their requests. Periodically the teacher will post the answers on Stream
DANILO PERCIVALE (President)
VALENTINA BERTELLA
SERGIO DE MICHELI
MARIA VIRGINIA CATALISANO (President Substitute)
https://corsi.unige.it/9274/p/studenti-orario
