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 |
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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 |