|SCIENTIFIC DISCIPLINARY SECTOR||MAT/05|
|MODULES||This unit is a module of:|
The course is directed to first year students which are familiar with basic notions in elementary Mathematics
The course aims to provide the basic knowledge preparatory to other courses that require mathematical methods and tools.
The course provides basic notions about Functions of one variable, integration of continuous functions and first order ODE’s in view of applications in Physics and Nautic Engineering.
Basic notions in elementary mathematics.
90 hours of lectures . Distance lectures until the end of sanitary emergency an subsequently frontal lectures.
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. 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.
3) L’Hopital’s rule. Taylor’ formula and its applications.
3) Ordinary differential equations. First order equations: separable equations, linear equations. Cauchy problems: existence and uniqueness theorem. Linear ODE’s with constant coefficients.
R.A. Adams, Calcolo Differenziale 1 Casa
Notes & Exercises in aulaweb ( a.a. 10/11 and the following)
Office hours: 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
All class schedules are posted on the EasyAcademy portal.
A written test is required which could be followed by another confirmation test
Outcome of written test and its confirmation.
Professor will receive students by appointment.