MAT-60106 Complex Analysis, 5 cr
Lisätiedot
The course homepage is in Moodle:
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 represent the original function. - can find zeros and poles of a function from its Laurent's series - can compute complex integrals using residy. - can make a Laplace-transform for a given function and apply complex analysis in dealing with transformed functions. - 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 |
Tietoa esitietovaatimuksista
Recommended prerequisite information consists of Engineering Mathematics (19 cr) or Mathematics (19 cr)
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 |