### Course Catalog 2010-2011 International

Basic Pori International Postgraduate Open University Search

|Degrees|     |Study blocks|     |Courses|

# MAT-31086 Complex Analysis, 5 cr

#### 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 2010-01 Thursday 12 - 14, S2

#### Requirements

Two partial examinations or final examination.

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#### 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

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