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[CA/Week 3] 6. Integration with residues. Practice with residues
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Week 3 of the course "Complex Analysis" is dedicated to the residue theory and computation of integrals in a complex plane.
Topics of the course:
1. Algebra of complex numbers. Differentiation and integration in a complex plane.
2. Singularities of functions of complex variables.
3. Contour integration. Residue theory. Jordan's lemma.
4. Multivalued functions and regular branches
5. Analytical continuation and Riemann surfaces.
6. Integrals with multivalued functions.
7. Gamma function and its applications.
Topics of the course:
1. Algebra of complex numbers. Differentiation and integration in a complex plane.
2. Singularities of functions of complex variables.
3. Contour integration. Residue theory. Jordan's lemma.
4. Multivalued functions and regular branches
5. Analytical continuation and Riemann surfaces.
6. Integrals with multivalued functions.
7. Gamma function and its applications.
[CA/Week 3] 6. Integration with residues. Practice with residues
[CA/Week 3] 5. Practice with residues
[CA/Week 6] 3. Integrals with power-type integrand and two branch points, Part III.
[CA/Week 3] 1. Integration with residues. Introduction.
[CA/Week 3] 12. Principal value integration
[CA/Week 3] 8. Quick example of residue theorem.
[CA/Week 3] 7. First practice with the computation of integrals with the help of residues.
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[CA/Week 4] 6. Practice with regular branches II.
[CA/Week 3] 11. More advanced Fourier-type integrals
[CA/Week 3] 9. Jordan's lemma and Fourier-type integrals
[CA/Week 5] 6. Riemann surfaces, More rigorous approach
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[CA/Week 6] 6. The second type of integrals with the log-function, Part I
[CA/Week 3] 4. Riemann sphere.
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[CA/Week 6] 8. Integrals with asymmetric integrand and log function, Part I.
[CA/Week 4] 8. Practice with regular branches IV.
[CA/Week 6] 7. The second type of integrals with the log-function, Part II.
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[CA/Week 4] 7. Practice with regular branches III.
[CA/Week 4] 9. Practice with regular branches V.
[CA/Week 4] 13. Practice with regular branches VII.
[CA/Week 6] 4. Integrals with log-type function, Part I.
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