SF1628 Complex Analysis 6.0 credits
This course has been discontinued.
Last planned examination: Spring 2020
Decision to discontinue this course:
No information inserted
Content and learning outcomes
Course contents
- Meromorphic and analytic functions of one complex variable. Basic transcendental functions, harmonic functions.
- Integration in the complex plane, Cauchy’s theorem, Cauchy’s integral formula and consequences thereof. Residues.
- Taylor and Laurent series, zeros and poles, the principle of the argument.
- Conformal mapping and applications.
Intended learning outcomes
After the course the student should be able to
- Understand, interpret and use the basic concepts: complex number, analytic function, harmonic function, Taylor and Laurent series, singularity, residue, conformal mapping, meromorphic function.
- Prove certain fundamental theorems about analytic functions, e.g. Cauchy’s integral formula
- Determine the stability of certain dynamical systems using the Nyqvist criterion
- Use conformal mapping to solve certain applied problems regarding heat conduction, electrical engineering and fluid mechanics.
- Use Taylor and Laurent expansions to derive properties of analytic and meromorphic functions.
- Compute integrals by means of residues.
- Analyze zeros and poles of meromorphic functions, classify singularities.
In order to get a higher the student should also be able to
- Explain the theory of analytic functions and prove the most important theorems.
Literature and preparations
Specific prerequisites
Calculus, introductory courses, SF1602 + SF1603 and SF1604 Linear Algebra.
Recommended prerequisites
Equipment
Literature
Saff&Snider:
Fundamentals of Complex Variables with Applications to Engineerin and Science, 3:rd ed.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
Examination
- TEN1 - Examination, 6.0 credits, grading scale: A, B, C, D, E, FX, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Other requirements for final grade
Written and/or oral examination, possibly in conjunction with certain other assignments.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.