Study Guide 2015-2016

MAT-60106 Complex Analysis, 5 cr

Additional information

The course homepage is: https://moodle2.tut.fi/

Person responsible

Seppo Pohjolainen

Lessons

Implementation 1: MAT-60106 2015-01

Study type P1 P2 P3 P4 Summer
Excercises
 2 h/week
+2 h/week

 

 

 

Lecture times and places: Tuesday 13 - 14 S2 , Thursday 12 - 14 S2

Requirements

Two partial examinations or final examination.

Learning Outcomes

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.

Content

Content Core content Complementary knowledge Specialist knowledge
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   
5. Laplace-transform. Applications to engineering problems.    Applications: - differential equations - transfer fuction  

Study material

Type Name Author ISBN URL Additional information Examination material
Book   Complex Analysis for Mathematics and Engineering   Mathews& Howell         No   
Book   Complex Variables and Applications   Brown&Churchill   0-07-114065-4       No   
Summary of lectures   Complex functions   Seppo Pohjolainen         No   

Additional information about prerequisites
Recommended prerequisite information consists of Engineering Mathematics (19 cr) or Mathematics (19 cr)



Correspondence of content

Course Corresponds course  Description 
MAT-60106 Complex Analysis, 5 cr MAT-60100 Complex Analysis, 5 cr  
MAT-60106 Complex Analysis, 5 cr MAT-31086 Complex Analysis, 5 cr  

Last modified 12.01.2015