Course Catalog 2011-2012
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Basic Pori International Postgraduate Open University

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Course Catalog 2011-2012

MAT-31086 Complex Analysis, 5 cr

Additional information

The course homepage is: http://matpc41.ee.tut.fi/kmf02/
Suitable for postgraduate studies

Person responsible

Seppo Pohjolainen

Lessons

Study type P1 P2 P3 P4 Summer Implementations Lecture times and places
Excercises
 2 h/week
+2 h/week

 

 

 
MAT-31086 2011-01  

Requirements

Two partial examinations or final examination.

Principles and baselines related to teaching and learning

-

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, formulas and residy. - 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 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     Applications: 
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 Edition, availability, ... Examination material Language
Book   Complex Analysis for Mathematics and Engineering   Mathews& Howell            Suomi  
Book   Complex Variables and Applications   Brown&Churchill   0-07-114065-4          Suomi  
Summary of lectures   Complex functions   Seppo Pohjolainen            English  

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

Prerequisite relations (Requires logging in to POP)



Correspondence of content

Course Corresponds course  Description 
MAT-31086 Complex Analysis, 5 cr MAT-31080 Complex Analysis, 5 cr  

More precise information per implementation

Implementation Description Methods of instruction Implementation
MAT-31086 2011-01       Contact teaching: 0 %
Distance learning: 0 %
Self-directed learning: 0 %  

Last modified14.02.2011