Lecture 1 [May 6; Notes by Banothu Raghu]:
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Lecture 2 [May 7; Notes by Kshitiz Khatri]:
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Lecture 3 [May 8; Notes by Banothu Raghu]:
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Lecture 4 [May 11; Notes by Kshitiz Khatri]:
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Lecture 5 [May 12; Notes by Pushpendra Ahirwar]:
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Lecture 6 [May 13; Notes by Pushpendra Ahirwar]:
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Lecture 7 [May 14; Notes by Pushpendra Ahirwar]:
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Lecture 8 [May 15; Notes by Pushpendra Ahirwar]:
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Tutorial [May 18]
Lecture 9 [May 20; Notes by Pushpendra Ahirwar]:
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Lecture 10 [May 21; Notes by Pushpendra Ahirwar]:
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Lecture 11 [May 21; Notes by Pushpendra Ahirwar]:
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Lecture 12 [May 25; Notes by Pushpendra Ahirwar]:
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Lecture 13 [May 25; Notes by Pushpendra Ahirwar]:
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Lecture 14 [May 26; Notes by Pushpendra Ahirwar]:
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Lecture 15 [May 26; Notes by Pushpendra Ahirwar]:
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Lecture 16 [May 27; Notes by Pushpendra Ahirwar]:
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Tutorial [May 27, evening]
Lecture 17 [May 28; Notes by Pushpendra Ahirwar]:
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Lecture 18 [May 29; Notes by Pushpendra Ahirwar]:
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Tutorial [May 29, evening]
Syllabus :
Definition and properties of analytic functions.
Cauchy-Riemann equations, harmonic functions.
Power series and their properties. Elementary functions.
Cauchy's theorem and its applications.
Taylor series ans Laurent expansions.
Residues and the Cauchy residue formula. Evaluation of improper integrals.
Conformal mappings.
Inversion of Laplace transforms.
Text/References:
1. R. V. Churchill and J. W. Brown, Complex variables and applications
(7th Edition), McGraw-Hill (2003).
2. J. M. Howie, Complex analysis, Springer-Verlag (2004).
3. M. J. Ablowitz and A. S. Fokas, Complex Variables- Introduction and
Applications, Cambridge University Press, 1998 (Indian Edition).
4. E. Kreyszig, Advanced engineering mathematics (8th Edition), John
Wiley (1999).
Additional References:
1. T. W. Gamelin, Complex Analysis, Springer-Verlag (2001).
2. J. B. Conway, Functions of one complex variable, 2nd Ed., Springer-Verlag (1978).
3. L. V. Ahlfors, Complex Analysis, 3rd Ed., McGraw-Hill (1978).
1The instructor welcomes this initiative on the part of students, but is not
responsible for the accuracy of these notes. So, please use at your own risk!