To allow the acquisition of the deductive logical method and to provide the basic mathematical tools of differential and integral calculus, including integrals of functions of several variables and equations and systems of differential equations. Each topic will be rigorously introduced and treated, sometimes carrying out detailed demonstrations, and also making extensive reference to physical meaning, geometric interpretation and numerical application. A correct methodology and a fair ability in the use of the concepts of integral-differential calculus and their results should enable students, in principle, to easily deal with the more applicative topics that will be dealt with in the subsequent courses.
Curriculum
teacher profile teaching materials
Palumbo-Signorino: Argomenti di Analisi Matematica
"Esercitazioni di Matematica: vol. 1.1 e 1.2", P. Marcellini, C. Sbordone, editore Liguori
Programme
Real numbers. The principle of induction. The logical-deductive method and construction of proofs. Basic definitions of functions. Elementary functions. Limits. Theory of continuous and differentiable functions. Taylor formulas, notable limits, and orders of magnitude. L'Hôpital's rule. Integration: methods for finding antiderivatives of rational and trigonometric functions. Notable substitutions. Euler's method. Sequences and series. Improper integrals. Ordinary differential equations. Linear systems with constant coefficients. The method of separation of variables. Functions of several variables. Limits, continuity, differentiability, and Taylor's formula. Maxima and minima on open and closed sets.Core Documentation
Marcellini- Sbordone Elementi di Analisi MatematicaPalumbo-Signorino: Argomenti di Analisi Matematica
"Esercitazioni di Matematica: vol. 1.1 e 1.2", P. Marcellini, C. Sbordone, editore Liguori
Reference Bibliography
Marcellini- Sbordone Elementi di Analisi Matematica Palumbo-Signorino: Argomenti di Analisi Matematica "Esercitazioni di Matematica: vol. 1.1 e 1.2", P. Marcellini, C. Sbordone, editore LiguoriAttendance
following the class is highly reccommendedType of evaluation
The exam consists of a written test (which can be replaced by passing two mid-term tests) and an oral confirmation test teacher profile teaching materials
Palumbo-Signorino: Argomenti di Analisi Matematica
"Esercitazioni di Matematica: vol. 1.1 e 1.2", P. Marcellini, C. Sbordone, editore Liguori
Programme
Real numbers. The principle of induction. The logical-deductive method and construction of proofs. Basic definitions of functions. Elementary functions. Limits. Theory of continuous and differentiable functions. Taylor formulas, notable limits, and orders of magnitude. L'Hôpital's rule. Integration: methods for finding antiderivatives of rational and trigonometric functions. Notable substitutions. Euler's method. Sequences and series. Improper integrals. Ordinary differential equations. Linear systems with constant coefficients. The method of separation of variables. Functions of several variables. Limits, continuity, differentiability, and Taylor's formula. Maxima and minima on open and closed sets.Core Documentation
Marcellini- Sbordone Elementi di Analisi MatematicaPalumbo-Signorino: Argomenti di Analisi Matematica
"Esercitazioni di Matematica: vol. 1.1 e 1.2", P. Marcellini, C. Sbordone, editore Liguori
Reference Bibliography
Marcellini- Sbordone Elementi di Analisi Matematica Palumbo-Signorino: Argomenti di Analisi Matematica "Esercitazioni di Matematica: vol. 1.1 e 1.2", P. Marcellini, C. Sbordone, editore LiguoriAttendance
following the class is highly reccommendedType of evaluation
The exam consists of a written test (which can be replaced by passing two mid-term tests) and an oral confirmation test