MAT-60106 Complex Analysis, 5 cr


The course homepage is:


Petteri Laakkonen


Toteutuskerta Periodi Vastuuhenkilö Suoritusvaatimukset
MAT-60106 2019-01 2 Petteri Laakkonen
Final examination and exercise activity.


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 definition, the fundamental theorem of analysis, and Cauchy's integral theorem 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 residues - can make logical conclusions, i.e., is able to make mathematical proofs


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 formulas      
4. Taylor's and Laurent's series. Residue.  Applying residues to calculate real integrals.   


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   
Book   Introduction to Complex Analysis   R. P. Agarwal, K. Perera, and S. Pinelas   978-1-4614-0195-7       No   


Opintojakso P/S Selite
MAT-01300 Insinöörimatematiikka X 3 Mandatory   1
MAT-01310 Insinöörimatematiikka A 3 Mandatory   1
MAT-01330 Insinöörimatematiikka C 3 Mandatory   1
MAT-01360 Matematiikka 3 Mandatory   1
MAT-01366 Mathematics 3 Mandatory   1
MAT-02100 Usean muuttujan funktiot Advisable   2
MAT-02106 Multivariable Calculus Advisable   2

1 . Required prerequisite knowledge.

2 . Recommended prerequisite knowledge.

Tietoa esitietovaatimuksista
Prerequisite information consists of Engineering Mathematics 1-3 (15 cr), Mathematics 1-3 (15 cr), or any combination of courses with corresponding contents. In particular, basic knowledge of differentiation and integration of real functions is required. Knowledge on the basic contents of Multivariate calculus (formerly Mathematics 4), e.g., on partial differentiation, is recommended.


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, 03.10.2019