
Course unit
MATHEMATICS 2
SC14105622, 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/02 
Algebra 
1.0 
Basic courses 
MAT/03 
Geometry 
1.0 
Basic courses 
MAT/05 
Mathematical Analysis 
6.0 
Course unit organization
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Practice 
2.0 
20 
30.0 
No turn 
Lecture 
6.0 
48 
102.0 
No turn 
Prerequisites:

All the prerequisites and contents of ` Istituzioni di Matematica 1'. In particular,
operations of sets, definition of function, graph, image and preimage of a function. 
Target skills and knowledge:

Computation of limits of sequences, Capability of establishing the character of convergence of a series of numbers and functions. Some elements of linear algebra. Capability of computing partial derivatives and differentials. Resolution of some ordinary differential equation. 
Examination methods:

The written test consists of a certain number of queries, always the same number for each written test. Each query concerns a specific part of the program. The test dates will be posted
Each query normally consists in the resolution of an exercise
The written test is sufficient provided that the students shows to be able to pass each query of the test,
If a students turns in a test which is not sufficient but which contains a certain minimum number of queries which have been granted a passing, the teacher may allow the student to access make up tests which would take place in the following written exam sessions. Such a minimum number will be indicated by the teacher.
The oral test can be accessed in any of the oral exam sessions after the written test has been evaluated as sufficient. The grade of the oral test may be either higher, or equal or lower to the grade of the written test.
In case of failure of the oral test, the teacher may ask the student to repeat the written test either completely or in part in the remaining written exam sessions. 
Assessment criteria:

The knowledge of the candidate on the topics of the program will be evaluated 
Course unit contents:

Infimum and supremum of a set of real numbers. Complex numbers and solution of equations in the complex plane. Sequences of numbers and their limit. Series and convergence criteria for series. Brief outline of the Maximum limit. Power series. The Taylor series.
Vector spaces and linear operators. Some elements of linear algebra. Normed spaces and distance. A brief outline of the punctual and uniform convergence.
Continuity and limits of functions of several variables. Directional and partial derivatives. The differential. Brief outline of the Taylor formula.
Resolution of some ordinary differential equation. 
Planned learning activities and teaching methods:

Theoretic explanations with examples and exercises 
Additional notes about suggested reading:

The student will receive precise indications on material of the following two textbooks
M. Lanza de Cristoforis, Traccia delle lezioni del corso di
Analisi Matematica 1, A.A. 2019/20, Edizioni Libreria Progetto, Padova.
M. Lanza de Cristoforis, Appunti senza pretese di
Analisi Matematica 2, A.A. 2019/20, Libreria Progetto.
and of some handouts
Should the exercises of the above texts be insufficient, we also mention the following books
G. De Marco e C. Mariconda, Esercizi di analisi uno,
DecibelZanichelli, 2008.
G. De Marco, C. Mariconda, Esercizi di Analisi Due, Libreria Progetto, 2013. 
Textbooks (and optional supplementary readings) 

, . : , . Vedi riquadro `Eventuali indicazioni sui materiali di studio


