Real numbers.
Functions of one real variable.
Limits and derivatives for functions of one real variable.
Taylor expansions.
The theory of integration for function of one real variable.
Optimization problems in dimension one.
Functions of several variable.
Differential calculus for functions of several variables.
Optimization problems for functions of several variables.
Theory
P. Marcellini, C. Sbordone: Calcolo, edizioni Liguori
Exercises
P. Marcellini, C. Sbordone, Esercitazioni di Matematica, Prima e seconda parte, edizioni Liguori
Learning Objectives
KNOWLEDGE ACQUIRED
Limits and derivatives
The graph of a function
Taylor expansion of a function
Integrals of functions of one variable
Optimization techniques for functions of one and several real variables.
Competence acquired
Compute limits and derivatives
Study of the graph of a given function
Determine the Taylor expansion of a given function
Compute an integral. Solve an optimization problem for a function of either one or more variables.
Prerequisites
Basic notions of mathematics taught in high school. In particular: formal
calculus; polynomials; algebraic, exponential and logarithmic equations.
Basic notions in analytic geometry (the Cartesian plane, lines circles,
parabolas, etc.). Trigonometric functions.
Teaching Methods
Frontal and exercise classes
Type of Assessment
The exam is made of two parts. In the first part, written, the student is asked to solve some exercises, such as, for instance. the study of the graph of a function; the computation of an integral; the study of an infinite series; the solution of an ordinary differential equation. In the second part, which can be either written or oral, the student is asked to expose the theoretical results presented in the course.
Course program
Real numbers.
Functions of one real variable.
Limits and derivatives for functions of one real variable.
Taylor expansions.
The theory of integration for function of one real variable.
Optimization problems in dimension one.
Functions of several variable.
Differential calculus for functions of several variables.
Optimization problems for functions of several variables.