
Course unit
CALCULUS (Ult. numero di matricola pari)
SCP4063454, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Basic courses 
MAT/05 
Mathematical Analysis 
12.0 
Course unit organization
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Practice 
3.0 
36 
39.0 
No turn 
Lecture 
9.0 
72 
153.0 
No turn 
Prerequisites:

The language of mathematics, basics of logics and set theory. The natural, integer, rational and real numbers sets: order relations, operations and their properties. Polinomials, quotients and factorization of polinomilas. Elementary functions (polinomial, power,exponential, logaritmic and trigonometric functions), their properties and graphs.
 rational and non rational equations, inequalities and systems. 
Target skills and knowledge:

The fundamental notions of mathematical analysis related with the properties of real numbers and to the definition of limit.The evaluation of limits of one variable functions using both notable basic limits and Taylor's formula.†?The definition and the properties of the derivative of one variable functions. The ability of calculate derivatives and to use them to solve problems depending on parameters and to draw the graph of a function.
The course will provide tools, like integral calculus, number series and
functions of two variables, that are used for courses on Probability
and Statistics. 
Examination methods:

The examination is written;
The text contains three or four exercises and some theoretical questions where one has to write the statement and/or the proof of a theorem presented in class.The
commission may require an oral examination in case the written one has
not been sufficient for a clear grading. 
Assessment criteria:

Each exercise contributes for a certain specified amount to the highest grade of 33/30 (corresponding to 30 cum laude).The correctness, clarity of exposition and completeness of the answers given to the different exercises are the criteria for the evaluation. 
Course unit contents:

 Sets of numbers. Real functions. Limits of functions, properties and theorems; limits of sequences; continuous functions, theorems on continuous functions. derivatives: definition, rules, properties and theorems. Taylor's and di MacLaurin's formulas Applications of the derivatives and the graph of a function.
Contents: Definite and indefinite integrals; primitive functions; Fundamental
Theorem of Calculus; integration by parts and by substitution;
integration techniques. Generalized integrals and convergence
criteria. Numeric series: definition and properties. Geometric, harmonic and generalized harmonic series. Convergence criteria. Absolute convergence. Alternate series and Leibnitz criterion.
 Functions of two variables: basic notions on topology, limits andcontinuity. Partial derivatives, Schwarz theorem. Local and global minima/maxima, with or without constraints. Lagrange multipliers.The detailed contents with the list of theorems and proofs, up to dated for each weak, can be found in the web course page. 
Planned learning activities and teaching methods:

The course consists in 108 hours of lectures, about one half of them is devoted to numerical and theoretical exercises.The teacher will use, as far as possible, various technological tools to improve the learning and to let the students to have as much as possible education material to their disposal. The students are required to attend the lectures and to devote a right amount of time to autonomous study. The last one is of fundamental importance to develop the logic and practical abilities related with the topics covered in the course. To this aim tutorial activities will be organized and supervised by the teacher. 
Textbooks (and optional supplementary readings) 

M. Bertsch, R. Dal Passo e L. Giacomelli, Analisi Matematica. : McGrawHill, .

Marco Bramanti, Esercitazioni di Analisi Matematica 1. : Esculapio, .

Marco Bramanti, Carlo D. Pagani e Sandro Salsa, Analisi Matematica 1,. : Zanichelli, 2008.


