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B006808 - REAL ANALYSIS II
Main information
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Further information
Type of Assessment
Course program
Academic Year 2012-13
Course year
Second year - First Semester
Belonging Department
Statistics, IT and its applications "G. Parenti" (DISIA)
Course Type
Single education field course
Scientific Area
MAT/05 - MATHEMATICAL ANALYSIS
Credits
6
Teaching Hours
48
Teaching Term
24/09/2012 ⇒ 21/12/2012
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Course Content
Sequences of functions. Series of functions, powers series, Taylor and Fourier series. Functions of several variables. Maxima and minima in several variables. maxima and minima for functions with constraints Ordinary differential equations. Cauchy theorem. Equations with separable variables. Multiple integrals. Curves. Differential forms, closed and exact forms. Dini's theorem.
Suggested readings (Search our library's catalogue)
Fusco - Marcellini - Sbordone, Elementi di Analisi Matematica 2 ed. Liguori
Marcellini - Sbordone,
Esercitazioni di Matematica - 2 volume - parte prima e seconda ed. Liguori
Marcellini - Sbordone,
Esercitazioni di Matematica - 2 volume - parte prima e seconda ed. Liguori
Learning Objectives
Knowledge: Calculus in several variables. Acquired skills: Calculus in several variables. Ordinary differential equations. Function Spaces
Acquired ability (at the end of the course): Ability to face multi-dimensional problems and ability to deal with first order differential equations
Acquired ability (at the end of the course): Ability to face multi-dimensional problems and ability to deal with first order differential equations
Prerequisites
Prerequisites : Analysis I: Integral and Differential Calculus
Teaching Methods
Number of total hours of the course: 150
Numero of hours of personal study and other individual learning: 94
Numero of hours for classroom activities: 48
Numero of hours relative to laboratory (laboratory classes): 0
Number of hours on activities of exercises (laboratory and field): 0
Number of hours relating to seminars: 0
Number of hours related to work experience: 0
Number of hours per course tests: 8
Numero of hours of personal study and other individual learning: 94
Numero of hours for classroom activities: 48
Numero of hours relative to laboratory (laboratory classes): 0
Number of hours on activities of exercises (laboratory and field): 0
Number of hours relating to seminars: 0
Number of hours related to work experience: 0
Number of hours per course tests: 8
Further information
Frequency of lessons and exercises: strongly suggested
Tools used to support the teaching activity: UniFi E-Learning: http://el.unifi.it
Office hours: Monday 'and Tuesday' from 13.30 to 15.30 in his office (Department of Mathematics "Ulisse Dini").
Tools used to support the teaching activity: UniFi E-Learning: http://el.unifi.it
Office hours: Monday 'and Tuesday' from 13.30 to 15.30 in his office (Department of Mathematics "Ulisse Dini").
Type of Assessment
Written and Oral
Course program
Sequences and series of functions, power series, Fourier series. Functions in several variables, limits of functions of several variables, partial derivatives and differentiability , Theorems concerning the differential, Schwartz theorem, maxima and minima of functions of several variables, maxima and minima for functions with constraints. First order differential equations, Cauchy Theorem., linear differential equations of the second order, the Wronskian theorem, resolution of certain types of equations (separation of variables, linear equations with constant coefficients, method of the variation of the constants) Curves. Curvilnear integral. Exact and closed differential forms, Integral in several variables. Implicit functions and Dini's theorem