# MAT-60106 Complex Analysis, 5 cr

#### Lisätiedot

The course homepage is:

https://moodle2.tut.fi/

#### Vastuuhenkilö

Petteri Laakkonen

#### Osaamistavoitteet

After passing the course the student: - recognizes elementary functions and their properties and is able to solve equations consisting of elementary functions. - can decide when a function is analytic and knows the main features of such functions - is able to calculate complex integrals using the fundamental theorem of analysis, integral theorems, and formulas. - can find the Laurent's series for a given function,and knows when the series represents the original function. - can find zeros and poles of a function from its Laurent's series - can compute complex integrals using residues. - can make logical conclusions, ie. is able to make mathematical proofs.

#### Sisältö

 Sisältö Ydinsisältö Täydentävä tietämys Erityistietämys 1. Complex numbers and elementary functions. Complex plane and its topology. Complex function. Applications 2. Continuous and differentiable functions. Analytical Fuctions. Cauchy-Riemann and Laplace equations. Applications: - Elliptic partial differential equations 3. Complex Integral. The fundamental theorem of analysis. Cauchy's integral theorem, Cauchy's integral formula 4. Taylor's and Laurent's series. Residue. Zeros of Riemann's function

#### Oppimateriaali

 Tyyppi Nimi Tekijä ISBN URL Lisätiedot Tenttimateriaali Book Complex Analysis for Mathematics and Engineering Mathews& Howell No Book Complex Variables and Applications Brown&Churchill 0-07-114065-4 No

#### Esitietovaatimukset

 Opintojakso P/S Selite MAT-01400 Insinöörimatematiikka X 4 Advisable 1 MAT-01410 Insinöörimatematiikka A 4 Advisable 1 MAT-01430 Insinöörimatematiikka C 4 Advisable 1 MAT-01460 Matematiikka 4 Advisable 1 MAT-01466 Mathematics 4 Advisable 1

1 . Engineering Mathematics or Mathematics (19 cr)

Tietoa esitietovaatimuksista
Recommended prerequisite information consists of Engineering Mathematics (19 cr), Mathematics (19 cr), or any combination of courses with corresponding contents. In particular basic knowledge of (multivariate) differentiation and integration of real functions is required.

#### Vastaavuudet

 Opintojakso Vastaa opintojaksoa Selite MAT-60106 Complex Analysis, 5 cr MAT-60100 Complex Analysis, 5 cr MAT-60106 Complex Analysis, 5 cr MAT-31086 Complex Analysis, 5 cr

 Päivittäjä: Laakkonen Petteri, 10.12.2018