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(objectives)
Allow the acquisition of the method deductive logic and provide the basic mathematical tools of the calculation of differential and integral. Each topic will be introduced and strictly the treaty, carrying, sometimes, detailed demonstrations, and also doing large reference to physical meaning, geometric interpretation and application number. Proper methodology and a reasonable skill in the use of the concepts of calculation and its entirety and differential results will put in grade students in principle to face so easy application more topics that will take place in the following courses.
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Code
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20810293 |
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Language
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ITA |
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Type of certificate
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Profit certificate
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Credits
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12
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Scientific Disciplinary Sector Code
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MAT/05
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Contact Hours
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108
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Type of Activity
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Basic compulsory activities
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Teacher
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PROCESI MICHELA
(syllabus)
Numerical sets (N, Z, Q and R), axiomatic construction of R, construction of N and principle of induction, complex numbers; elements of topology in R and Bolzano-Weierstrass theorem; real functions of real variable, limits of functions and their properties, limits of sequences, notable limits, the Napier number; continuous functions and their properties; derivative of functions and their properties, the fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l'Hopital, Taylor's formula), convex / concave functions; function graph; Riemann integration and properties, integrability of continuous functions, fundamental theorem of integral calculus, integration by substitution and by parts, integration rules; numerical series, simple and absolute convergence, convergence criteria for series with positive terms and for series with any terms; Taylor series; improper integrals.
(reference books)
Analisi matematica I Marcellini-Sbordone
Analisi matematica I Pagani-Salsa
Esercitazioni di Matematica Marcellini-Sbordone
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Dates of beginning and end of teaching activities
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From to |
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Delivery mode
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Traditional
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Attendance
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not mandatory
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Evaluation methods
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Written test
Oral exam
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Teacher
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FRANCIA DARIO
(syllabus)
Numerical sets (N, Z, Q and R), axiomatic construction of R, construction of N and principle of induction, complex numbers; elements of topology in R and Bolzano-Weierstrass theorem; real functions of real variable, limits of functions and their properties, limits of sequences, notable limits, the Napier number; continuous functions and their properties; derivative of functions and their properties, the fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l'Hopital, Taylor's formula), convex / concave functions; function graph; Riemann integration and properties, integrability of continuous functions, fundamental theorem of integral calculus, integration by substitution and by parts, integration rules; numerical series, simple and absolute convergence, convergence criteria for series with positive terms and for series with any terms; Taylor series; improper integrals.
(reference books)
Analisi matematica I Marcellini-Sbordone
Analisi matematica I Pagani-Salsa
Esercitazioni di Matematica Marcellini-Sbordone
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|
Dates of beginning and end of teaching activities
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From to |
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Delivery mode
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Traditional
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Attendance
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not mandatory
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Evaluation methods
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Written test
Oral exam
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Università Roma Tre