ITA | ENG
B012823 - MATHEMATICAL AND STATISTICAL METHODS
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Further information
Type of Assessment
Course program
Academic Year 2020-21
Coorte 2020 - Second Cycle Degree in CHEMICAL SCIENCES
Course year
First year - First Semester
Belonging Department
Chemistry "Ugo Schiff"
Course Type
Single education field course
Scientific Area
MAT/07 - MATHEMATICAL PHYSICS
Credits
6
Teaching Hours
48
Teaching Term
14/09/2020 ⇒ 23/12/2020
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Teaching Language
Italian
Course Content
Complex analysis, Hilbert spaces, Fourier series, Fourier transform, examples and applications
Suggested readings (Search our library's catalogue)
Matematica per l'Ingegneria dell'Informazione
Giulio Cesare Barozzi
Zanichelli
Giulio Cesare Barozzi
Zanichelli
Learning Objectives
The understanding and ability to use some important mathematical techniques of great usefulness in the fields of physics, chemistry and, more in general, of applied mathematics
Prerequisites
Integration theory, calculus, both numerical and functions sequences and series (or at least power series). O.D.E. Algebraic properties of complex number, knowledge of the most important complex functions
Teaching Methods
Classroom lessons during which exercises will be solved
Further information
None
Type of Assessment
Oral exam with exercises
Course program
The most important complex functions, holomorphic functions, complex derivative and its representation, Cauchy-Riemann conditions. Power series and holomorphic functions. Representation formula for holomorphic functions, residue theorem.
Hilbert spaces, Fourier series and its properties, pointwise convergence, arithmetic average convergence and L_2 convergence of a Fourier series. Fourier transform and its properties, inverse Fourier transform, Fourier transform in L_2 space. Exercises and applications
Hilbert spaces, Fourier series and its properties, pointwise convergence, arithmetic average convergence and L_2 convergence of a Fourier series. Fourier transform and its properties, inverse Fourier transform, Fourier transform in L_2 space. Exercises and applications