First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
PHYSICS
Course unit
MATHEMATICAL ANALYSIS 1 (Iniziali cognome A-L)
SC05100190, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course First cycle degree in
PHYSICS
SC1158, Degree course structure A.Y. 2014/15, A.Y. 2018/19
A1301
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Number of ECTS credits allocated 8.0
Type of assessment Mark
Course unit English denomination MATHEMATICAL ANALYSIS 1
Website of the academic structure http://fisica.scienze.unipd.it/2018/laurea
Department of reference Department of Physics and Astronomy
E-Learning website https://elearning.unipd.it/dfa/course/view.php?idnumber=2018-SC1158-000ZZ-2018-SC05100190-A1301
Mandatory attendance No
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 DAVIDE VITTONE MAT/05
Other lecturers FRANCESCOPAOLO MONTEFALCONE MAT/05

Mutuated
Course unit code Course unit name Teacher in charge Degree course code
SC05100190 MATHEMATICAL ANALYSIS 1 (Iniziali cognome A-L) DAVIDE VITTONE SC1160

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Basic courses MAT/05 Mathematical Analysis 8.0

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 24 51.0 No turn
Lecture 5.0 40 85.0 No turn

Calendar
Start of activities 01/10/2018
End of activities 18/01/2019
Show course schedule 2019/20 Reg.2014 course timetable

Examination board
Board From To Members of the board
9 Analisi Matematica 1 01/10/2018 30/11/2019 TREU GIULIA (Presidente)
VITTONE DAVIDE (Membro Effettivo)
MONTEFALCONE FRANCESCOPAOLO (Supplente)
MONTI ROBERTO (Supplente)
8 Analisi Matematica 1 01/10/2018 30/11/2019 VITTONE DAVIDE (Presidente)
TREU GIULIA (Membro Effettivo)
MARASTONI CORRADO (Supplente)
MONTEFALCONE FRANCESCOPAOLO (Supplente)
MONTI ROBERTO (Supplente)
7 Analisi Matematica 1 01/10/2017 30/11/2018 VITTONE DAVIDE (Presidente)
MARASTONI CORRADO (Membro Effettivo)
MONTI ROBERTO (Supplente)

Syllabus
Prerequisites: Elementary functions of one variable: exponential, absolute value, logarithms, trigonometric functions. Cartesian geometry of the plane: lines, conic sections, geometric loci.

Whoever feels he has gaps in his Mathematical formation can consult the Precalculus Course on the EduOpen platform: https://learn.eduopen.org/eduopen/course_details.php?courseid=109
Target skills and knowledge: Ability of developing basic arguments about the topological properties of the real line and the completeness axiom.

Computations with complex numbers: trigonometric forms, n-th roots.

Limits and continuity: computation of limits and study of the continuity of a function. Knowledge of the fundamental results' proofs (Bolzano's and intermediate value theorems).

Differential calculus: study of the derivative of a function and mastery of the basic results of differential calculus (monotonicity vs. sign of the derivative, convexity study). Ability to perform a function study. Applications to the calculus of limits (Taylor formula, de l'Hôpital rule).

Integration: ability to integrate basic functions and to utilize the formulas for integration by substitution and by parts. ability of integrating rational functions. Knowledge of the meaning of the integral of a function (Riemann sums, areas). Mastery of the Fundamental Theorem of Calculus.

Differential equations. Mastery of the tecniques for solving differential equations with separation of variables, 1st order linear equations, 2nd order linear equations with constant coefficients. Knowledge of the meaning of a Cauchy problem.
Examination methods: Written exam mainly made by exercises; an oral exam, mainly dealing with the theoretical part of the course, is optional. The written exam can be replaced by two intermediate partial examinations.
Assessment criteria: Mastery of the acquired knowledge and ability in utilizing it for the solution of simple problems. Completeness and clarity of the solutions to the exercises (also of theoretical type) proposed in the written examination. In case of oral examination, mastery of the proofs exposed in the course.
Course unit contents: NUMBER SETS
Elements of number theory. Induction. Natural, integer, and rational numbers. The real line, completeness, max, min, inf, sup. Complex numbers and complex roots. Topology of the real line.

REAL FUNCTIONS OF ONE VARIABLE AND LIMITS
Real functions, notion of limit and properties of limits.

SEQUENCES OF REAL NUMBERS
Sequences and countable sets. Limit of a sequence. Topology vs. sequences. Monotone and recursive sequences.

CONTINUITY
Definition of continuity for real functions. Bolzano and Weierstrass theorems. Uniform continuity.

DIFFERENTIATION
Differentiation. Monotonicity and classical theorems. L'Hôpital's rule. Higher derivatives and convexity. Taylor formula. Function study.

INTEGRATION
Riemann integral. Primitives and integration techniques. Area of planar regions.

BASIC ORDINARY DIFFERENTIAL EQUATIONS
Generalites. Cauchy problems and qualitative studies. First order differential equations, separation of variables. Linear differential equations: generalities, the second order case with constant coefficients.
Planned learning activities and teaching methods: Blackboard lectures.
Additional notes about suggested reading: Possible references not included among the reference texts will be directly recommended in the classroom.
Textbooks (and optional supplementary readings)
  • Giusti, Enrico, Analisi matematica 1. Torino: Bollati-Boringhieri, 2002. Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)