Mathematical analysis 3 (2019/2020)

Course code
4S02756
Name of lecturers
Giandomenico Orlandi, Giacomo Canevari
Coordinator
Giandomenico Orlandi
Number of ECTS credits allocated
6
Academic sector
MAT/05 - MATHEMATICAL ANALYSIS
Language of instruction
Italian
Period
II semestre dal Mar 2, 2020 al Jun 12, 2020.

Lesson timetable

Go to lesson schedule

Learning outcomes

Theory of function of one complex variable, and applications to calculus. Fourier transform and Laplace transform. Introduction to Partial Differential Equations. The aim is to provide the students with basic tools for addressing scientific issues which can be formalized in the language and methods of complex analysis and functional transforms.

Syllabus

Functions of one complex variable. Holomorphic functions. Cauchy-Riemann equations. Cauchy's integral formula. Analiticity of holomorphic functions and applications. Laurent series. Calculus of residues. Fourier transform. Laplace transform. Applications to ordinary differential equations and to to partial differential equations.

Reference books
Author Title Publisher Year ISBN Note
H. F. Weinberger A first course in partial differential equations: with Complex Variables and Transform Methods Dover 1995 978-0486686400
John H. Mathews, Russel W. Howell Complex Analysis for Mathematics and Engineering (Edizione 6) Jones & Bartlett 2010 978-1449604455

Assessment methods and criteria

The final exam consists of a written test followed, in case of a positive result, by an oral test. The written test consists of some exercises on the program.
The oral test will concentrate mainly but not exclusively on the theory.
The written part of the exam is aimed to verify the ability to solve problems related to the course program, to possess adequate analysis, synthesis and abstraction capacity, starting from requests formulated in natural or specific language.
The oral part is aimed to verify the ability to produce rigorous proofs as well as analysis, synthesis and abstraction abilities. The mark gained in the oral exam (in the interval -5, +5) will be added to the written test mark to obtain the final grading.