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[CA/Week 6] 4. Integrals with log-type function, Part I.
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Week 6 of the course "Complex Analysis" is dedicated to integrals with multivalued functions.
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 6] 4. Integrals with log-type function, Part I.
[CA/Week 6] 6. The second type of integrals with the log-function, Part I
[CA/Week 6] 8. Integrals with asymmetric integrand and log function, Part I.
[CA/Week 6] 7. The second type of integrals with the log-function, Part II.
[CA/Week 6] 9. Integrals with asymmetric integrand and log function, Part II.
[CA/Week 4] 9. Practice with regular branches V.
[CA/Week 4] 8. Practice with regular branches IV.
[CA/Week 6] 1. Integrals with power-type integrand and two branch points, Part I.
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[CA/Week 4] 13. Practice with regular branches VII.
[CA/Week 6] 5. Integrals with log-type function, Part II.
[CA/Week 6] 3. Integrals with power-type integrand and two branch points, Part III.
[CA/Week 6] 2. Integrals with power-type integrand and two branch points, Part II.
[CA/Week 4] 7. Practice with regular branches III.
[CA/Week 3] 8. Quick example of residue theorem.
[CA/Week 3] 9. Jordan's lemma and Fourier-type integrals
[CA/Week 3] 6. Integration with residues. Practice with residues
[CA/Week 3] 7. First practice with the computation of integrals with the help of residues.
[CA/Week 4] 3. Extraction of the regular branch of the power type function [example]
[CA/Week 3] 11. More advanced Fourier-type integrals
[CA/Week 3] 12. Principal value integration
CalcBC | Unit 6 Q01 | Reimann Sums, Intro to Integration
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Contour Integral, Generating Function Method, ln(x)^n/(1+x^2+x^4)
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