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B005491 - MATHEMATICAL ANALYSIS II
Main information
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Further information
Type of Assessment
Course program
Academic Year 2013-14
Coorte 2012 - 3-years First Cycle Degree (DM 270/04) in MATHEMATICS
Course year
Second year - Annualità singola
Belonging Department
Mathematics and Computer Science "Ulisse Dini" (DIMAI)
Course Type
Single education field course
Scientific Area
MAT/05 - MATHEMATICAL ANALYSIS
Credits
12
Teaching Hours
120
Teaching Term
23/09/2013 ⇒ 13/06/2014
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Course Content
Real valued functions of several variables. Optimization for functions of n variables. Sequences and series of functions. Diffential equations: equations and systems of first order and of higher order. Measure and integration theory for functions of n variables. Implicit function theorem. Curves and curvilinear integrals. Differential forms. Divergence theorem. Surfaces and surface integrals.
Suggested readings (Search our library's catalogue)
N. Fusco - P. Marcellini - C. Sbordone, Analisi Matematica Due, Liguori Editore.
E. Giusti, Analisi matematica 2, Boringhieri.
P. Marcellini - C. Sbordone, Esercitazioni di Matematica, Liguori Editore, Secondo Volume (parte prima e parte seconda).
E. Giusti, Analisi matematica 2, Boringhieri.
P. Marcellini - C. Sbordone, Esercitazioni di Matematica, Liguori Editore, Secondo Volume (parte prima e parte seconda).
Learning Objectives
Knowledge acquired:
The course aims to provide basic knowledge of differential and integral calculation for real functions of n real variables.
Competence acquired:
Students are able to correctly execute exercises concerning course topics.
Skills acquired (at the end of the course):
Students will be able to apply calculation knowledge for mathematical applications.
The course aims to provide basic knowledge of differential and integral calculation for real functions of n real variables.
Competence acquired:
Students are able to correctly execute exercises concerning course topics.
Skills acquired (at the end of the course):
Students will be able to apply calculation knowledge for mathematical applications.
Prerequisites
Courses required: Mathematical Analysis I
Teaching Methods
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 300
Hours reserved to private study and other indivual formative activities: 174
Contact hours for: Lectures (hours): 60
Contact hours for: Laboratory (hours): 0
Contact hours for: Laboratory-field/practice (hours): 60
Seminars (hours): 0
Stages: 0
Intermediate examinations: 6
Hours reserved to private study and other indivual formative activities: 174
Contact hours for: Lectures (hours): 60
Contact hours for: Laboratory (hours): 0
Contact hours for: Laboratory-field/practice (hours): 60
Seminars (hours): 0
Stages: 0
Intermediate examinations: 6
Further information
Frequency of lectures, practice and lab: Recommended
Teaching Tools UniFi E-Learning: http://e-l.unifi.it
Office hours:
By appointment.
Dipartimento di Matematica "Ulisse Dini"
Viale Morgagni, 67/a
50134 - Firenze (FI)
Tel: 055 4237488
E-Mail: ""colesant@math.unifi.it"
Teaching Tools UniFi E-Learning: http://e-l.unifi.it
Office hours:
By appointment.
Dipartimento di Matematica "Ulisse Dini"
Viale Morgagni, 67/a
50134 - Firenze (FI)
Tel: 055 4237488
E-Mail: ""colesant@math.unifi.it"
Type of Assessment
Written and Oral.
Course program
Sequence and function series. Passage of the limit under the integral and derivate sign. Taylor series. Metric space and Banach space. Banach fixed-point theorem. Real function of more than one variable. Differentiability. Geometrical interpretation of gradient. Maxima and minima for function of n variables. Differential equation. Cauchy local existence and gobal theorem. Implicit function. Dini’s theorem for equation and system. Curves and line integral. Length of a curve. Linear differential form. Vectorial field. Double and triple integral. Multiple integral. Reduction formulas. Gauss-Green formula. Divergence theorem. Stokes formula. Surfaces and surface integral. Area of a regular surface.