Learning outcomes of the course unit
Give the bases of calculus for functions of one real variable, in such a way that the students are able to solve simple problems in the field. Students should be able to draw and read graphs of functions of one variable, to study functions of one real variable and to compute elementary integrals.
Mathematics taught in high schools
Course contents summary
Real numbers, elementary algebra, equations and inequalities. Functions and their graphs, elementary functions. The principle of induction. Maximum, minimum, supremum and infimum of sets of real numbers. Limits of sequences and of functions of a real variable. Continuity, derivatives, primitives and their properties. Integrals of continuous functions over intervals. Study of the graphs of functions of one real variable.
1.1. Real numbers.
1.2. Functions and their graphs.
1.3. Operations between functions.1.4. Polynomials, rational and trogonometric functions.
2.2. Continuos functions.
2.3. Theorems on continuos functions.
3.1. derivatives and tangent lines.
3.2. Rules of differentiation.
3.3. Derivatives of elementary functions
3.4. Exponential and logarithm functions.
3.5. Graph of functions.
4.1. Riemann integrals.
4.2. Fundamental Theorem od calculus. Definite integrals.
4.3. Indefinite integrals and methods of integrations.
5.1. Ordinary differential equations: generalities.
5.2. Linear first order differential equations.
5.3. Linear differential equations with constant coefficients.
P. Marcellini, C. Sbordone: Calcolo, Liguori Editore
A. Nannicini, L. Verdi, S. Vessella: Note ed esercizi svolti di Calcolo 1, Pitagora Editrice
Lectures and exercises in the classroom
Assessment methods and criteria
The examination consists of a written test followed by an oral one. Students with sufficient marks in the written test are allowed to the oral part. The final mark will be the mean value between the marks of the written and of the oral tests.