First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
OPTICS AND OPTOMETRY
Course unit
MATHEMATICS 2
SC14105622, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course First cycle degree in
OPTICS AND OPTOMETRY
SC1168, Degree course structure A.Y. 2016/17, A.Y. 2019/20
N0
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Number of ECTS credits allocated 8.0
Type of assessment Mark
Course unit English denomination MATHEMATICS 2
Website of the academic structure http://otticaeoptometria.scienze.unipd.it/2019/laurea
Department of reference Department of Physics and Astronomy
Mandatory attendance
Language of instruction Italian
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge MASSIMO LANZA DE CRISTOFORIS MAT/05

ECTS: details
Type Scientific-Disciplinary 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

Calendar
Start of activities 02/03/2020
End of activities 12/06/2020
Show course schedule 2019/20 Reg.2016 course timetable

Syllabus
Prerequisites: All the prerequisites and contents of ` Istituzioni di Matematica 1'. In particular,
operations of sets, definition of function, graph, image and pre-image 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 hand-outs

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,
Decibel-Zanichelli, 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