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HU Credits:
4
Degree/Cycle:
1st degree (Bachelor)
Responsible Department:
Mathematics
Semester:
1st Semester
Teaching Languages:
Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Evgeny Strahov
Coordinator Office Hours:
Wednesdays, 16:00-17:00
Teaching Staff:
Prof Evgeny Strahov,
Mr. Shaul Ragimov
Course/Module description:
Complex functions of a complex variable: continuity, differentiability, analyticity, harmoniticity. Cauchy-Riemann equations. Rational functions, Mobius transformations, contour integration, Cauchy's theorem and consequences, maximum modulus theorem. The fundamental theorem of algebra.
Residue theorem and its uses. Analytic functions, conformal mappings, Riemann mapping theorem.
Course/Module aims:
Complex functions of a complex variable: continuity, differentiability, analyticity, harmoniticity. Cauchy-Riemann equations. Rational functions, Mobius transformations, contour integration, Cauchy's theorem and consequences, maximum modulus theorem. The fundamental theorem of algebra.
Residue theorem and its uses. Analytic functions, conformal mappings, Riemann mapping theorem.
Learning outcomes - On successful completion of this module, students should be able to:
Understanding of the basic concepts of complex analysis.
Knowledge of basic theorems in complex analysis, including proofs, and be able to apply them effectively.
Familiarity with computational methods in complex analysis, in particular for contour integration.
Familiarity with some applications of complex analysis to other areas of
mathematics.
Attendance requirements(%):
Attendence is expected. Please see notes.
Teaching arrangement and method of instruction:
Lecture + exercise (using Zoom)
Course/Module Content:
Complex functions of a complex variable: continuity, differentiability, analyticity, harmoniticity. Cauchy-Riemann equations. Rational functions, Mobius transformations, contour integration, Cauchy's theorem and consequences, maximum modulus theorem. The fundamental theorem of algebra.
Residue theorem and its uses. Analytic functions, conformal mappings, Riemann mapping theorem.
Required Reading:
None
Additional Reading Material:
Ash and Novinger - Complex Variables (2nd edition)
L. Ahlfors, Complex Analysis.
E. M. Stein, R. Shakarchi. Complex Analysis
M. A. Evgrafov, Analytic Functions.
B. V. Shabat, Introduction to Complex Analysis. Part I.
Course/Module evaluation:
End of year written/oral examination 90 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 0 %
Assignments 10 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %
Additional information:
While there will be no formal check of attendance, attendance in both lecture and practice session is expected.
Other or additional topics may be studied.
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